Index

_

__init__() (hpfracc.algorithms.advanced_methods.AdomianDecomposition method), [1] (hpfracc.algorithms.advanced_methods.HadamardDerivative method), [1] (hpfracc.algorithms.advanced_methods.MarchaudDerivative method), [1] (hpfracc.algorithms.advanced_methods.OptimizedAdomianDecomposition method), [1] (hpfracc.algorithms.advanced_methods.OptimizedHadamardDerivative method), [1] (hpfracc.algorithms.advanced_methods.OptimizedMarchaudDerivative method), [1] (hpfracc.algorithms.advanced_methods.OptimizedReizFellerDerivative method), [1] (hpfracc.algorithms.advanced_methods.OptimizedWeylDerivative method), [1] (hpfracc.algorithms.advanced_methods.ReizFellerDerivative method), [1] (hpfracc.algorithms.advanced_methods.WeylDerivative method), [1] (hpfracc.algorithms.optimized_methods.AdvancedFFTMethods method), [1] (hpfracc.algorithms.optimized_methods.FractionalOperator method), [1] (hpfracc.algorithms.optimized_methods.OptimizedCaputo method), [1] (hpfracc.algorithms.optimized_methods.OptimizedRiemannLiouville method), [1] (hpfracc.algorithms.optimized_methods.ParallelConfig method), [1] (hpfracc.algorithms.special_methods.FractionalFourierTransform method), [1], [2] (hpfracc.algorithms.special_methods.FractionalLaplacian method), [1], [2] (hpfracc.algorithms.special_methods.FractionalMellinTransform method), [1], [2] (hpfracc.algorithms.special_methods.FractionalZTransform method), [1], [2] (hpfracc.algorithms.special_methods.SpecialMethodsConfig method), [1], [2] (hpfracc.algorithms.special_methods.SpecialOptimizedMarchaudDerivative method), [1], [2] (hpfracc.algorithms.special_methods.SpecialOptimizedReizFellerDerivative method), [1], [2] (hpfracc.algorithms.special_methods.SpecialOptimizedWeylDerivative method), [1], [2] (hpfracc.algorithms.special_methods.UnifiedSpecialMethods method), [1], [2] (hpfracc.AtanganaBaleanuDerivative method), [1] (hpfracc.CaputoDerivative method), [1] (hpfracc.CaputoFabrizioDerivative method), [1] (hpfracc.CaputoIntegral method), [1] (hpfracc.core.definitions.CaputoDefinition method) (hpfracc.core.definitions.FractionalDefinition method) (hpfracc.core.definitions.FractionalIntegral method) (hpfracc.core.definitions.FractionalOrder method) (hpfracc.core.definitions.GrunwaldLetnikovDefinition method) (hpfracc.core.definitions.RiemannLiouvilleDefinition method) (hpfracc.core.derivatives.BaseFractionalDerivative method), [1] (hpfracc.core.derivatives.CaputoDerivative method), [1] (hpfracc.core.derivatives.FractionalDerivativeChain method), [1] (hpfracc.core.derivatives.FractionalDerivativeFactory method), [1] (hpfracc.core.derivatives.FractionalDerivativeOperator method), [1] (hpfracc.core.derivatives.GrunwaldLetnikovDerivative method), [1] (hpfracc.core.derivatives.RiemannLiouvilleDerivative method), [1] (hpfracc.core.fractional_implementations._AlphaCompatibilityWrapper method), [1] (hpfracc.core.fractional_implementations.AdomianDecompositionMethod method), [1] (hpfracc.core.fractional_implementations.AtanganaBaleanuDerivative method), [1] (hpfracc.core.fractional_implementations.CaputoDerivative method), [1] (hpfracc.core.fractional_implementations.CaputoFabrizioDerivative method), [1] (hpfracc.core.fractional_implementations.FractionalFourierTransform method), [1] (hpfracc.core.fractional_implementations.FractionalLaplacian method), [1] (hpfracc.core.fractional_implementations.GrunwaldLetnikovDerivative method), [1] (hpfracc.core.fractional_implementations.HadamardDerivative method), [1] (hpfracc.core.fractional_implementations.MarchaudDerivative method), [1] (hpfracc.core.fractional_implementations.MillerRossDerivative method), [1] (hpfracc.core.fractional_implementations.ParallelOptimizedCaputo method), [1] (hpfracc.core.fractional_implementations.ParallelOptimizedRiemannLiouville method), [1] (hpfracc.core.fractional_implementations.ReizFellerDerivative method), [1] (hpfracc.core.fractional_implementations.RiemannLiouvilleDerivative method), [1] (hpfracc.core.fractional_implementations.RieszFisherOperator method), [1] (hpfracc.core.fractional_implementations.WeylDerivative method), [1] (hpfracc.core.integrals.CaputoIntegral method), [1] (hpfracc.core.integrals.FractionalIntegral method), [1] (hpfracc.core.integrals.FractionalIntegralFactory method), [1] (hpfracc.core.integrals.HadamardIntegral method), [1] (hpfracc.core.integrals.MarchaudIntegral method), [1] (hpfracc.core.integrals.MillerRossIntegral method), [1] (hpfracc.core.integrals.RiemannLiouvilleIntegral method), [1] (hpfracc.core.integrals.WeylIntegral method), [1] (hpfracc.core.utilities.MemoryTrackerContext method) (hpfracc.core.utilities.PerformanceMonitor method) (hpfracc.core.utilities.TimerContext method) (hpfracc.FractionalFourierTransform method), [1] (hpfracc.FractionalLaplacian method), [1] (hpfracc.FractionalMellinTransform method), [1] (hpfracc.FractionalOrder method), [1], [2], [3] (hpfracc.FractionalZTransform method), [1] (hpfracc.HadamardDerivative method), [1] (hpfracc.MarchaudDerivative method), [1] (hpfracc.ml.backends.BackendManager method), [1], [2] (hpfracc.ml.core.FractionalAttention method) (hpfracc.ml.core.FractionalAutoML method) (hpfracc.ml.core.FractionalLossFunction method) (hpfracc.ml.core.FractionalNeuralNetwork method) (hpfracc.ml.core.MLConfig method) (hpfracc.ml.gnn_layers.BaseFractionalGNNLayer method), [1] (hpfracc.ml.gnn_layers.FractionalGraphAttention method), [1] (hpfracc.ml.gnn_layers.FractionalGraphPooling method), [1] (hpfracc.ml.gnn_models.BaseFractionalGNN method), [1] (hpfracc.ml.gnn_models.FractionalGAT method), [1], [2], [3] (hpfracc.ml.gnn_models.FractionalGCN method) (hpfracc.ml.gnn_models.FractionalGraphSAGE method), [1], [2], [3] (hpfracc.ml.gnn_models.FractionalGraphUNet method), [1], [2], [3] (hpfracc.ml.gpu_optimization.AMPFractionalEngine method), [1], [2], [3] (hpfracc.ml.gpu_optimization.ChunkedFFT method), [1], [2], [3] (hpfracc.ml.gpu_optimization.GPUOptimizedSpectralEngine method), [1] (hpfracc.ml.gpu_optimization.GPUOptimizedStochasticSampler method), [1] (hpfracc.ml.gpu_optimization.GPUProfiler method), [1], [2], [3] (hpfracc.ml.gpu_optimization.PerformanceMetrics method), [1] (hpfracc.ml.graph_sde_coupling.GraphFractionalSDELayer method) (hpfracc.ml.graph_sde_coupling.MultiScaleGraphSDE method) (hpfracc.ml.graph_sde_coupling.SpatialTemporalCoupling method) (hpfracc.ml.layers.BackendManager method), [1] (hpfracc.ml.layers.FractionalBatchNorm1d method), [1] (hpfracc.ml.layers.FractionalConv1D method), [1] (hpfracc.ml.layers.FractionalConv2D method), [1] (hpfracc.ml.layers.FractionalDropout method), [1] (hpfracc.ml.layers.FractionalLayerBase method), [1] (hpfracc.ml.layers.FractionalLayerNorm method), [1] (hpfracc.ml.layers.FractionalLinear method), [1] (hpfracc.ml.layers.FractionalLSTM method), [1] (hpfracc.ml.layers.FractionalMaxUnpool1d method), [1] (hpfracc.ml.layers.FractionalMaxUnpool2d method), [1] (hpfracc.ml.layers.FractionalMaxUnpool3d method), [1] (hpfracc.ml.layers.FractionalOps method), [1] (hpfracc.ml.layers.FractionalPooling method), [1] (hpfracc.ml.layers.FractionalSelfAttention method), [1] (hpfracc.ml.layers.FractionalTransformer method), [1] (hpfracc.ml.layers.LayerConfig method), [1] (hpfracc.ml.losses.FractionalBCELoss method) (hpfracc.ml.losses.FractionalCombinedLoss method) (hpfracc.ml.losses.FractionalCosineEmbeddingLoss method) (hpfracc.ml.losses.FractionalCrossEntropyLoss method) (hpfracc.ml.losses.FractionalCTCLoss method) (hpfracc.ml.losses.FractionalCustomLoss method) (hpfracc.ml.losses.FractionalHuberLoss method) (hpfracc.ml.losses.FractionalKLDivergenceLoss method) (hpfracc.ml.losses.FractionalKLDivLoss method) (hpfracc.ml.losses.FractionalLossFunction method) (hpfracc.ml.losses.FractionalMarginRankingLoss method) (hpfracc.ml.losses.FractionalMomentMatchingLoss method) (hpfracc.ml.losses.FractionalMSELoss method) (hpfracc.ml.losses.FractionalMultiMarginLoss method) (hpfracc.ml.losses.FractionalNLLLoss method) (hpfracc.ml.losses.FractionalPathwiseLoss method) (hpfracc.ml.losses.FractionalPoissonNLLLoss method) (hpfracc.ml.losses.FractionalSDEMSELoss method) (hpfracc.ml.losses.FractionalSmoothL1Loss method) (hpfracc.ml.losses.FractionalTripletMarginLoss method) (hpfracc.ml.neural_fsde.NeuralFractionalSDE method), [1] (hpfracc.ml.neural_fsde.NeuralFSDEConfig method), [1] (hpfracc.ml.neural_ode.BaseNeuralODE method), [1] (hpfracc.ml.neural_ode.NeuralFODE method), [1] (hpfracc.ml.neural_ode.NeuralODE method), [1] (hpfracc.ml.neural_ode.NeuralODEConfig method), [1] (hpfracc.ml.neural_ode.NeuralODETrainer method), [1] (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalLayer method), [1], [2], [3] (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalOrder method), [1] (hpfracc.ml.probabilistic_sde.BayesianNeuralFractionalSDE method) (hpfracc.ml.sde_adjoint_utils.CheckpointConfig method) (hpfracc.ml.sde_adjoint_utils.MixedPrecisionConfig method) (hpfracc.ml.sde_adjoint_utils.MixedPrecisionManager method) (hpfracc.ml.sde_adjoint_utils.SDEAdjointOptimizer method) (hpfracc.ml.sde_adjoint_utils.SDEStateCheckpoint method) (hpfracc.ml.sde_adjoint_utils.SparseGradientAccumulator method) (hpfracc.ml.spectral_autograd.BoundedAlphaParameter method), [1], [2] (hpfracc.ml.spectral_autograd.SpectralFractionalLayer method), [1] (hpfracc.ml.spectral_autograd.SpectralFractionalNetwork method), [1] (hpfracc.ml.stochastic_memory_sampling.ControlVariateSampler method), [1] (hpfracc.ml.stochastic_memory_sampling.ImportanceSampler method), [1] (hpfracc.ml.stochastic_memory_sampling.StochasticFractionalLayer method), [1] (hpfracc.ml.stochastic_memory_sampling.StochasticMemorySampler method), [1], [2], [3] (hpfracc.ml.stochastic_memory_sampling.StratifiedSampler method), [1] (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3] (hpfracc.ml.variance_aware_training.AdaptiveSamplingManager method), [1] (hpfracc.ml.variance_aware_training.StochasticSeedManager method), [1] (hpfracc.ml.variance_aware_training.VarianceAwareCallback method), [1] (hpfracc.ml.variance_aware_training.VarianceAwareTrainer method), [1], [2], [3] (hpfracc.ml.variance_aware_training.VarianceMetrics method), [1] (hpfracc.ml.variance_aware_training.VarianceMonitor method), [1] (hpfracc.OptimizedCaputo method), [1], [2], [3] (hpfracc.OptimizedGrunwaldLetnikov method) (hpfracc.OptimizedRiemannLiouville method), [1], [2], [3] (hpfracc.ReizFellerDerivative method), [1] (hpfracc.RiemannLiouvilleIntegral method), [1] (hpfracc.solvers.coupled_solvers.CoupledSolution method) (hpfracc.solvers.coupled_solvers.CoupledSystemSolver method) (hpfracc.solvers.coupled_solvers.OperatorSplittingSolver method) (hpfracc.solvers.noise_models.BrownianMotion method), [1], [2] (hpfracc.solvers.noise_models.ColouredNoise method), [1], [2] (hpfracc.solvers.noise_models.FractionalBrownianMotion method), [1], [2] (hpfracc.solvers.noise_models.LevyNoise method), [1], [2] (hpfracc.solvers.noise_models.NoiseConfig method), [1], [2] (hpfracc.solvers.ode_solvers.FixedStepODESolver method) (hpfracc.solvers.pde_solvers.FractionalAdvectionSolver method) (hpfracc.solvers.pde_solvers.FractionalDiffusionSolver method) (hpfracc.solvers.pde_solvers.FractionalPDESolver method) (hpfracc.solvers.pde_solvers.FractionalReactionDiffusionSolver method) (hpfracc.solvers.sde_solvers.FastHistoryConvolution method), [1], [2] (hpfracc.solvers.sde_solvers.FractionalEulerMaruyama method), [1], [2] (hpfracc.solvers.sde_solvers.FractionalMilstein method), [1], [2] (hpfracc.solvers.sde_solvers.FractionalSDESolver method), [1], [2] (hpfracc.solvers.sde_solvers.SDESolution method), [1], [2] (hpfracc.WeylDerivative method), [1] __repr__() (hpfracc.FractionalOrder method) __str__() (hpfracc.FractionalOrder method) _aggregate_attention() (hpfracc.ml.gnn_layers.FractionalGraphAttention method), [1] _AlphaCompatibilityWrapper (class in hpfracc.core.fractional_implementations), [1] _analytical_method() (hpfracc.algorithms.special_methods.FractionalMellinTransform method), [1], [2] (hpfracc.FractionalMellinTransform method), [1] _apply_activation() (hpfracc.ml.core.FractionalNeuralNetwork method) (hpfracc.ml.gnn_layers.FractionalGraphAttention method), [1] _apply_dropout() (hpfracc.ml.gnn_layers.FractionalGraphAttention method), [1]

_auto_select_method() (hpfracc.algorithms.special_methods.UnifiedSpecialMethods method), [1], [2] _build_diffusion_network() (hpfracc.ml.neural_fsde.NeuralFractionalSDE method), [1] _build_drift_network() (hpfracc.ml.neural_fsde.NeuralFractionalSDE method), [1] _build_network() (hpfracc.ml.core.FractionalNeuralNetwork method) (hpfracc.ml.gnn_models.BaseFractionalGNN method), [1] (hpfracc.ml.gnn_models.FractionalGAT method), [1], [2] (hpfracc.ml.gnn_models.FractionalGCN method), [1], [2] (hpfracc.ml.gnn_models.FractionalGraphSAGE method), [1], [2] (hpfracc.ml.gnn_models.FractionalGraphUNet method), [1], [2] (hpfracc.ml.neural_ode.BaseNeuralODE method), [1] _build_spatial_matrix() (hpfracc.solvers.pde_solvers.FractionalAdvectionSolver method) (hpfracc.solvers.pde_solvers.FractionalDiffusionSolver method) _caputo_numpy() (in module hpfracc.algorithms.optimized_methods), [1] _check_torchdiffeq() (hpfracc.ml.neural_ode.NeuralFODE method), [1] (hpfracc.ml.neural_ode.NeuralODE method), [1] _check_variance() (hpfracc.ml.variance_aware_training.VarianceAwareCallback method), [1] _chirp_based_method() (hpfracc.algorithms.special_methods.FractionalFourierTransform method), [1], [2] (hpfracc.FractionalFourierTransform method), [1] _coerce_function() (hpfracc.CaputoIntegral method), [1] (hpfracc.core.integrals.CaputoIntegral method), [1] (hpfracc.core.integrals.RiemannLiouvilleIntegral method), [1] (hpfracc.RiemannLiouvilleIntegral method), [1] _compute_adomian_polynomial() (hpfracc.algorithms.advanced_methods.AdomianDecomposition method), [1] _compute_array_numpy() (hpfracc.core.integrals.HadamardIntegral method), [1] (hpfracc.core.integrals.MarchaudIntegral method), [1] (hpfracc.core.integrals.MillerRossIntegral method), [1] (hpfracc.core.integrals.RiemannLiouvilleIntegral method), [1] (hpfracc.core.integrals.WeylIntegral method), [1] (hpfracc.RiemannLiouvilleIntegral method), [1] _compute_array_torch() (hpfracc.core.integrals.HadamardIntegral method), [1] (hpfracc.core.integrals.MarchaudIntegral method), [1] (hpfracc.core.integrals.MillerRossIntegral method), [1] (hpfracc.core.integrals.RiemannLiouvilleIntegral method), [1] (hpfracc.core.integrals.WeylIntegral method), [1] (hpfracc.RiemannLiouvilleIntegral method), [1] _compute_fractional_coefficients() (hpfracc.solvers.ode_solvers.FixedStepODESolver method) _compute_frft() (hpfracc.algorithms.special_methods.SpecialOptimizedWeylDerivative method), [1], [2] _compute_hadamard() (hpfracc.algorithms.advanced_methods.HadamardDerivative method), [1] (hpfracc.HadamardDerivative method), [1] _compute_hybrid() (hpfracc.algorithms.special_methods.SpecialOptimizedWeylDerivative method), [1], [2] _compute_integral_term() (hpfracc.algorithms.advanced_methods.AdomianDecomposition method), [1] _compute_laplacian() (hpfracc.algorithms.special_methods.SpecialOptimizedReizFellerDerivative method), [1], [2] _compute_marchaud_segment() (hpfracc.algorithms.advanced_methods.MarchaudDerivative method), [1] (hpfracc.MarchaudDerivative method), [1] _compute_memory_optimized() (hpfracc.algorithms.advanced_methods.MarchaudDerivative method), [1] (hpfracc.MarchaudDerivative method), [1] _compute_moment() (hpfracc.ml.losses.FractionalMomentMatchingLoss method) _compute_parallel() (hpfracc.algorithms.advanced_methods.WeylDerivative method), [1] (hpfracc.WeylDerivative method), [1] _compute_scalar() (hpfracc.core.integrals.HadamardIntegral method), [1] (hpfracc.core.integrals.MarchaudIntegral method), [1] (hpfracc.core.integrals.MillerRossIntegral method), [1] (hpfracc.core.integrals.RiemannLiouvilleIntegral method), [1] (hpfracc.core.integrals.WeylIntegral method), [1] (hpfracc.RiemannLiouvilleIntegral method), [1] _compute_serial() (hpfracc.algorithms.advanced_methods.WeylDerivative method), [1] (hpfracc.WeylDerivative method), [1] _compute_single_term() (hpfracc.algorithms.advanced_methods.AdomianDecomposition method), [1] _compute_spatial_derivative() (hpfracc.solvers.pde_solvers.FractionalDiffusionSolver method) _compute_spectral() (hpfracc.algorithms.advanced_methods.ReizFellerDerivative method), [1] (hpfracc.algorithms.special_methods.SpecialOptimizedReizFellerDerivative method), [1], [2] (hpfracc.ReizFellerDerivative method), [1] _compute_spectral_transform() (hpfracc.ml.gpu_optimization.GPUOptimizedSpectralEngine method), [1] _compute_standard() (hpfracc.algorithms.advanced_methods.MarchaudDerivative method), [1] (hpfracc.algorithms.special_methods.SpecialOptimizedMarchaudDerivative method), [1], [2] (hpfracc.MarchaudDerivative method), [1] _compute_standard_fft() (hpfracc.algorithms.special_methods.SpecialOptimizedWeylDerivative method), [1], [2] _compute_temporal_derivative() (hpfracc.solvers.pde_solvers.FractionalDiffusionSolver method) _compute_terms_parallel() (hpfracc.algorithms.advanced_methods.AdomianDecomposition method), [1] _compute_terms_serial() (hpfracc.algorithms.advanced_methods.AdomianDecomposition method), [1] _compute_transform_matrix() (hpfracc.algorithms.special_methods.FractionalFourierTransform method), [1], [2] (hpfracc.FractionalFourierTransform method), [1] _compute_weyl_kernel() (hpfracc.algorithms.special_methods.SpecialOptimizedWeylDerivative method), [1], [2] _compute_z_transform() (hpfracc.algorithms.special_methods.SpecialOptimizedMarchaudDerivative method), [1], [2] _contour_integration() (hpfracc.algorithms.special_methods.FractionalZTransform method), [1], [2] (hpfracc.FractionalZTransform method), [1] _detect_available_backends() (hpfracc.ml.backends.BackendManager method), [1], [2] (hpfracc.ml.layers.BackendManager method), [1] _determine_optimal_method() (hpfracc.algorithms.special_methods.SpecialOptimizedWeylDerivative method), [1], [2] _direct_method() (hpfracc.algorithms.special_methods.FractionalZTransform method), [1], [2] (hpfracc.FractionalZTransform method), [1] _discrete_method() (hpfracc.algorithms.special_methods.FractionalFourierTransform method), [1], [2] (hpfracc.FractionalFourierTransform method), [1] _euler_step() (hpfracc.solvers.ode_solvers.FixedStepODESolver method) _factorial() (in module hpfracc.algorithms.special_methods), [1], [2] _fallback_compute() (hpfracc.ml.gpu_optimization.GPUOptimizedSpectralEngine method), [1] _fast_approximation() (hpfracc.algorithms.special_methods.FractionalFourierTransform method), [1], [2] (hpfracc.FractionalFourierTransform method), [1] _fast_binomial_coefficients_numpy() (in module hpfracc.algorithms.optimized_methods), [1] _fast_history_sum() (in module hpfracc.solvers.ode_solvers) _fft_based_method() (hpfracc.algorithms.special_methods.FractionalFourierTransform method), [1], [2] (hpfracc.FractionalFourierTransform method), [1] _fft_convolution() (in module hpfracc.solvers.ode_solvers) (in module hpfracc.solvers.sde_solvers), [1], [2] _fft_method() (hpfracc.algorithms.special_methods.FractionalMellinTransform method), [1], [2] (hpfracc.algorithms.special_methods.FractionalZTransform method), [1], [2] (hpfracc.FractionalMellinTransform method), [1] (hpfracc.FractionalZTransform method), [1] _finite_difference_method() (hpfracc.algorithms.special_methods.FractionalLaplacian method), [1], [2] (hpfracc.FractionalLaplacian method), [1] _finite_difference_step() (hpfracc.solvers.pde_solvers.FractionalDiffusionSolver method) _fractional_hermite() (hpfracc.algorithms.special_methods.FractionalFourierTransform method), [1], [2] (hpfracc.FractionalFourierTransform method), [1] _get_activation() (hpfracc.ml.neural_ode.BaseNeuralODE method), [1] _get_gamma_function() (in module hpfracc.solvers.ode_solvers) (in module hpfracc.solvers.sde_solvers), [1], [2] _get_intelligent_selector() (in module hpfracc.solvers.ode_solvers) (in module hpfracc.solvers.pde_solvers) (in module hpfracc.solvers.sde_solvers), [1], [2] _get_spatial_operator() (hpfracc.solvers.pde_solvers.FractionalAdvectionSolver method) (hpfracc.solvers.pde_solvers.FractionalDiffusionSolver method) _get_tensor_lib_for_backend() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] _get_torch() (in module hpfracc.core.utilities) _gpu_sample_indices() (hpfracc.ml.gpu_optimization.GPUOptimizedStochasticSampler method), [1] _grunwald_coefficients() (hpfracc.algorithms.special_methods.FractionalLaplacian method), [1], [2] (hpfracc.FractionalLaplacian method), [1] _grunwald_letnikov_coeffs() (hpfracc.solvers.pde_solvers.FractionalDiffusionSolver method) _grunwald_letnikov_numpy() (in module hpfracc.algorithms.optimized_methods), [1] _hermite_decomposition() (hpfracc.algorithms.special_methods.FractionalFourierTransform method), [1], [2] (hpfracc.FractionalFourierTransform method), [1] _hermite_function() (hpfracc.algorithms.special_methods.FractionalFourierTransform method), [1], [2] (hpfracc.FractionalFourierTransform method), [1] _hypergeometric_series_impl() (in module hpfracc.core.utilities) _initialize_backend_configs() (hpfracc.ml.backends.BackendManager method), [1], [2] _initialize_layer() (hpfracc.ml.gnn_layers.BaseFractionalGNNLayer method), [1] (hpfracc.ml.gnn_layers.FractionalGraphAttention method), [1] (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] (hpfracc.ml.gnn_layers.FractionalGraphPooling method), [1] _initialize_weights() (hpfracc.ml.core.FractionalAttention method) (hpfracc.ml.core.FractionalNeuralNetwork method) (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] (hpfracc.ml.layers.FractionalConv1D method), [1] (hpfracc.ml.layers.FractionalConv2D method), [1] (hpfracc.ml.layers.FractionalLinear method), [1] (hpfracc.ml.neural_ode.BaseNeuralODE method), [1] _integral_method() (hpfracc.algorithms.special_methods.FractionalLaplacian method), [1], [2] (hpfracc.FractionalLaplacian method), [1] _inverse_fft() (hpfracc.algorithms.special_methods.FractionalMellinTransform method), [1], [2] (hpfracc.FractionalMellinTransform method), [1] _inverse_numerical() (hpfracc.algorithms.special_methods.FractionalMellinTransform method), [1], [2] (hpfracc.FractionalMellinTransform method), [1] _jax_activation() (hpfracc.ml.gnn_layers.FractionalGraphAttention method), [1] (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] _jax_forward() (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] _jax_fractional_derivative() (hpfracc.ml.gnn_layers.BaseFractionalGNNLayer method), [1] _jax_scatter_add() (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] _jnp_gradient_edge_order_2() (in module hpfracc.algorithms.optimized_methods), [1] _log_variance_summary() (hpfracc.ml.variance_aware_training.VarianceAwareCallback method), [1] _numba_activation() (hpfracc.ml.gnn_layers.FractionalGraphAttention method), [1] (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] _numba_forward() (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] _numba_fractional_derivative() (hpfracc.ml.gnn_layers.BaseFractionalGNNLayer method), [1] _numba_scatter_add() (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] _numerical_method() (hpfracc.algorithms.special_methods.FractionalMellinTransform method), [1], [2] (hpfracc.FractionalMellinTransform method), [1] _numpy_fft() (in module hpfracc.ml.spectral_autograd), [1] _process_chunk() (hpfracc.algorithms.advanced_methods.WeylDerivative method), [1] (hpfracc.WeylDerivative method), [1] _process_chunks() (hpfracc.ml.gpu_optimization.ChunkedFFT method), [1], [2] _process_marchaud_chunk() (hpfracc.algorithms.advanced_methods.MarchaudDerivative method), [1] (hpfracc.MarchaudDerivative method), [1] _register_hooks() (hpfracc.ml.variance_aware_training.VarianceAwareTrainer method), [1], [2] _residue_method() (hpfracc.algorithms.special_methods.FractionalZTransform method), [1], [2] (hpfracc.FractionalZTransform method), [1] _resolve_backend() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] _riemann_liouville_numpy() (in module hpfracc.algorithms.optimized_methods), [1] _select_array_backend() (in module hpfracc.solvers.pde_solvers) _select_fft_backend() (in module hpfracc.solvers.ode_solvers) _select_optimal_backend() (hpfracc.ml.backends.BackendManager method), [1], [2] _setup_layer() (hpfracc.ml.layers.FractionalLayerBase method), [1] (hpfracc.ml.neural_ode.BaseNeuralODE method), [1] _setup_loss_function() (hpfracc.ml.neural_ode.NeuralODETrainer method), [1] _setup_optimizer() (hpfracc.ml.neural_ode.NeuralODETrainer method), [1] _solve_adams_bashforth() (hpfracc.solvers.ode_solvers.FixedStepODESolver method) _solve_euler() (hpfracc.solvers.ode_solvers.FixedStepODESolver method) _solve_fractional_ode_optimized() (hpfracc.ml.neural_ode.NeuralFODE method), [1] _solve_fractional_sde_torch() (hpfracc.ml.neural_fsde.NeuralFractionalSDE method), [1] _solve_optimized_euler() (hpfracc.ml.neural_ode.NeuralODE method), [1] _solve_predictor_corrector() (hpfracc.solvers.ode_solvers.FixedStepODESolver method) _solve_runge_kutta() (hpfracc.solvers.ode_solvers.FixedStepODESolver method) _solve_spatial_step() (hpfracc.solvers.pde_solvers.FractionalDiffusionSolver method) _solve_torchdiffeq() (hpfracc.ml.neural_ode.NeuralODE method), [1] _spatial_step() (hpfracc.solvers.coupled_solvers.OperatorSplittingSolver method) _spectral_method() (hpfracc.algorithms.special_methods.FractionalFourierTransform method), [1], [2] (hpfracc.algorithms.special_methods.FractionalLaplacian method), [1], [2] (hpfracc.FractionalFourierTransform method), [1] (hpfracc.FractionalLaplacian method), [1] _spectral_step() (hpfracc.solvers.pde_solvers.FractionalDiffusionSolver method) _temporal_step() (hpfracc.solvers.coupled_solvers.OperatorSplittingSolver method) _torch_forward() (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] _torch_fractional_derivative() (hpfracc.ml.gnn_layers.BaseFractionalGNNLayer method), [1] _validate() (hpfracc.core.definitions.FractionalOrder method) (hpfracc.FractionalOrder method), [1], [2] (hpfracc.ml.neural_ode.NeuralODETrainer method), [1] _validate_alpha() (hpfracc.solvers.ode_solvers.FixedStepODESolver method) _validate_chain() (hpfracc.core.derivatives.FractionalDerivativeChain method), [1] _validate_orders() (hpfracc.solvers.pde_solvers.FractionalDiffusionSolver method) (hpfracc.solvers.pde_solvers.FractionalPDESolver method) _validate_parameters() (hpfracc.core.derivatives.BaseFractionalDerivative method), [1] (hpfracc.core.integrals.FractionalIntegral method), [1]

A

abs() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] accumulate() (hpfracc.ml.sde_adjoint_utils.SparseGradientAccumulator method) activation (hpfracc.ml.layers.LayerConfig attribute), [1] (hpfracc.ml.neural_ode.NeuralODEConfig attribute), [1] AdaptiveSamplingManager (class in hpfracc.ml.variance_aware_training), [1] add() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] adjoint_forward() (hpfracc.ml.neural_fsde.NeuralFractionalSDE method), [1] AdomianDecomposition (class in hpfracc.algorithms.advanced_methods), [1] AdomianDecompositionMethod (class in hpfracc.core.fractional_implementations), [1] AdvancedFFTMethods (class in hpfracc.algorithms.optimized_methods), [1] alpha (hpfracc.ml.spectral_autograd.SpectralFractionalLayer property), [1] (hpfracc.solvers.noise_models.NoiseConfig attribute), [1], [2] AMPFractionalEngine (class in hpfracc.ml.gpu_optimization), [1], [2]

amplitude (hpfracc.solvers.noise_models.NoiseConfig attribute), [1], [2] analytical_fractional_integral() (in module hpfracc.core.integrals), [1] apply() (hpfracc.ml.spectral_autograd.SpectralFractionalDerivative static method), [1], [2] apply_activation() (hpfracc.ml.layers.FractionalLayerBase method), [1] apply_dropout() (hpfracc.ml.layers.FractionalLayerBase method), [1] apply_fractional_derivative() (hpfracc.ml.gnn_layers.BaseFractionalGNNLayer method), [1] (hpfracc.ml.layers.FractionalLayerBase method), [1] (hpfracc.ml.layers.FractionalOps method), [1] arange() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] AtanganaBaleanuDerivative (class in hpfracc), [1] (class in hpfracc.core.fractional_implementations), [1] atol (hpfracc.ml.neural_ode.NeuralODEConfig attribute), [1] AUTO (hpfracc.ml.backends.BackendType attribute), [1], [2] autocast() (hpfracc.ml.sde_adjoint_utils.MixedPrecisionManager method)

B

backend (hpfracc.ml.core.MLConfig attribute) (hpfracc.ml.layers.LayerConfig attribute), [1] BackendManager (class in hpfracc.ml.backends), [1], [2] (class in hpfracc.ml.layers), [1] BackendType (class in hpfracc.ml.backends), [1], [2] backward() (hpfracc.ml.gpu_optimization.AMPFractionalEngine method), [1], [2], [3] (hpfracc.ml.spectral_autograd.SpectralFractionalFunction static method), [1] (hpfracc.ml.stochastic_memory_sampling.StochasticFractionalDerivative static method), [1] BaseFractionalDerivative (class in hpfracc.core.derivatives), [1] BaseFractionalGNN (class in hpfracc.ml.gnn_models), [1] BaseFractionalGNNLayer (class in hpfracc.ml.gnn_layers), [1] BaseNeuralODE (class in hpfracc.ml.neural_ode), [1]

batch_size (hpfracc.ml.core.MLConfig attribute) BayesianNeuralFractionalSDE (class in hpfracc.ml.probabilistic_sde) benchmark_backends() (in module hpfracc.ml.spectral_autograd), [1] benchmark_gpu_optimization() (in module hpfracc.ml.gpu_optimization), [1] bessel_function_first_kind() (in module hpfracc.core.utilities) beta (hpfracc.solvers.noise_models.NoiseConfig attribute), [1], [2] beta() (in module hpfracc.special) beta_function() (in module hpfracc.special) BIDIRECTIONAL (hpfracc.ml.graph_sde_coupling.CouplingType attribute) binomial_coefficient() (in module hpfracc.core.utilities) (in module hpfracc.special) BoundedAlphaParameter (class in hpfracc.ml.spectral_autograd), [1], [2] BrownianMotion (class in hpfracc.solvers.noise_models), [1], [2]

C

CAPUTO (hpfracc.core.definitions.DefinitionType attribute) Caputo (in module hpfracc), [1] caputo() (in module hpfracc.core.derivatives), [1], [2] CaputoDefinition (class in hpfracc.core.definitions) CaputoDerivative (class in hpfracc), [1] (class in hpfracc.core.derivatives) (class in hpfracc.core.fractional_implementations), [1] CaputoFabrizioDerivative (class in hpfracc), [1] (class in hpfracc.core.fractional_implementations), [1] CaputoIntegral (class in hpfracc), [1] (class in hpfracc.core.integrals), [1] cat() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] chain_rule() (hpfracc.core.definitions.FractionalCalculusProperties static method) check_linearity() (hpfracc.core.derivatives.FractionalDerivativeProperties static method), [1] check_numerical_stability() (in module hpfracc.core.utilities) check_semigroup_property() (hpfracc.core.derivatives.FractionalDerivativeProperties static method), [1] checkpoint_frequency (hpfracc.ml.sde_adjoint_utils.CheckpointConfig attribute) checkpoint_strategy (hpfracc.ml.sde_adjoint_utils.CheckpointConfig attribute) checkpoint_trajectory() (in module hpfracc.ml.sde_adjoint_utils) CheckpointConfig (class in hpfracc.ml.sde_adjoint_utils) ChunkedFFT (class in hpfracc.ml.gpu_optimization), [1], [2] clear() (hpfracc.ml.sde_adjoint_utils.SDEStateCheckpoint method) (hpfracc.ml.sde_adjoint_utils.SparseGradientAccumulator method) clear_checkpoints() (hpfracc.ml.sde_adjoint_utils.SDEAdjointOptimizer method) clear_history() (hpfracc.ml.gpu_optimization.GPUProfiler method), [1], [2] clip() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] clone() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] coefficient_of_variation (hpfracc.ml.variance_aware_training.VarianceMetrics attribute), [1] ColouredNoise (class in hpfracc.solvers.noise_models), [1], [2] compile_function() (hpfracc.ml.backends.BackendManager method), [1], [2] compute() (hpfracc.algorithms.advanced_methods.HadamardDerivative method), [1] (hpfracc.algorithms.advanced_methods.MarchaudDerivative method), [1] (hpfracc.algorithms.advanced_methods.ReizFellerDerivative method), [1] (hpfracc.algorithms.advanced_methods.WeylDerivative method), [1] (hpfracc.algorithms.optimized_methods.FractionalOperator method), [1] (hpfracc.algorithms.optimized_methods.OptimizedCaputo method), [1] (hpfracc.algorithms.optimized_methods.OptimizedGrunwaldLetnikov method), [1] (hpfracc.algorithms.optimized_methods.OptimizedRiemannLiouville method), [1] (hpfracc.algorithms.special_methods.FractionalFourierTransform method), [1], [2] (hpfracc.algorithms.special_methods.FractionalLaplacian method), [1], [2] (hpfracc.algorithms.special_methods.SpecialOptimizedMarchaudDerivative method), [1], [2] (hpfracc.algorithms.special_methods.SpecialOptimizedReizFellerDerivative method), [1], [2] (hpfracc.algorithms.special_methods.SpecialOptimizedWeylDerivative method), [1], [2] (hpfracc.AtanganaBaleanuDerivative method), [1] (hpfracc.CaputoDerivative method), [1] (hpfracc.CaputoFabrizioDerivative method), [1] (hpfracc.CaputoIntegral method), [1] (hpfracc.core.derivatives.BaseFractionalDerivative method), [1] (hpfracc.core.derivatives.CaputoDerivative method), [1] (hpfracc.core.derivatives.FractionalDerivativeChain method), [1] (hpfracc.core.derivatives.GrunwaldLetnikovDerivative method), [1] (hpfracc.core.derivatives.RiemannLiouvilleDerivative method), [1] (hpfracc.core.fractional_implementations.AtanganaBaleanuDerivative method), [1] (hpfracc.core.fractional_implementations.CaputoDerivative method), [1] (hpfracc.core.fractional_implementations.CaputoFabrizioDerivative method), [1] (hpfracc.core.fractional_implementations.FractionalFourierTransform method), [1] (hpfracc.core.fractional_implementations.FractionalLaplacian method), [1] (hpfracc.core.fractional_implementations.GrunwaldLetnikovDerivative method), [1] (hpfracc.core.fractional_implementations.HadamardDerivative method), [1] (hpfracc.core.fractional_implementations.MarchaudDerivative method), [1] (hpfracc.core.fractional_implementations.MillerRossDerivative method), [1] (hpfracc.core.fractional_implementations.ParallelOptimizedCaputo method), [1] (hpfracc.core.fractional_implementations.ParallelOptimizedRiemannLiouville method), [1] (hpfracc.core.fractional_implementations.ReizFellerDerivative method), [1] (hpfracc.core.fractional_implementations.RiemannLiouvilleDerivative method), [1] (hpfracc.core.fractional_implementations.RieszFisherOperator method), [1] (hpfracc.core.fractional_implementations.WeylDerivative method), [1] (hpfracc.core.integrals.CaputoIntegral method), [1] (hpfracc.core.integrals.FractionalIntegral method), [1] (hpfracc.core.integrals.RiemannLiouvilleIntegral method), [1] (hpfracc.core.integrals.WeylIntegral method), [1] (hpfracc.FractionalFourierTransform method), [1] (hpfracc.FractionalLaplacian method), [1] (hpfracc.HadamardDerivative method), [1] (hpfracc.MarchaudDerivative method), [1] (hpfracc.OptimizedCaputo method), [1], [2] (hpfracc.OptimizedGrunwaldLetnikov method), [1], [2], [3] (hpfracc.OptimizedRiemannLiouville method), [1], [2] (hpfracc.ReizFellerDerivative method), [1] (hpfracc.RiemannLiouvilleIntegral method), [1] (hpfracc.WeylDerivative method), [1] compute_adomian_polynomials() (hpfracc.core.fractional_implementations.AdomianDecompositionMethod method), [1] compute_baseline() (hpfracc.ml.stochastic_memory_sampling.ControlVariateSampler method), [1] compute_derivative() (hpfracc.algorithms.optimized_methods.AdvancedFFTMethods method), [1] (hpfracc.algorithms.special_methods.UnifiedSpecialMethods method), [1], [2] compute_loss() (hpfracc.ml.core.FractionalCrossEntropyLoss method) (hpfracc.ml.core.FractionalLossFunction method) (hpfracc.ml.core.FractionalMSELoss method) (hpfracc.ml.losses.FractionalBCELoss method) (hpfracc.ml.losses.FractionalCombinedLoss method) (hpfracc.ml.losses.FractionalCosineEmbeddingLoss method) (hpfracc.ml.losses.FractionalCrossEntropyLoss method) (hpfracc.ml.losses.FractionalCTCLoss method) (hpfracc.ml.losses.FractionalCustomLoss method) (hpfracc.ml.losses.FractionalHuberLoss method) (hpfracc.ml.losses.FractionalKLDivergenceLoss method) (hpfracc.ml.losses.FractionalKLDivLoss method) (hpfracc.ml.losses.FractionalLossFunction method) (hpfracc.ml.losses.FractionalMarginRankingLoss method) (hpfracc.ml.losses.FractionalMomentMatchingLoss method) (hpfracc.ml.losses.FractionalMSELoss method) (hpfracc.ml.losses.FractionalMultiMarginLoss method) (hpfracc.ml.losses.FractionalNLLLoss method) (hpfracc.ml.losses.FractionalPathwiseLoss method) (hpfracc.ml.losses.FractionalPoissonNLLLoss method) (hpfracc.ml.losses.FractionalSDEMSELoss method) (hpfracc.ml.losses.FractionalSmoothL1Loss method) (hpfracc.ml.losses.FractionalTripletMarginLoss method)

compute_numerical() (hpfracc.algorithms.special_methods.FractionalFourierTransform method), [1], [2] (hpfracc.algorithms.special_methods.FractionalLaplacian method), [1], [2] (hpfracc.AtanganaBaleanuDerivative method), [1] (hpfracc.CaputoDerivative method), [1] (hpfracc.CaputoFabrizioDerivative method), [1] (hpfracc.core.derivatives.BaseFractionalDerivative method), [1] (hpfracc.core.derivatives.CaputoDerivative method) (hpfracc.core.derivatives.FractionalDerivativeOperator method), [1] (hpfracc.core.derivatives.GrunwaldLetnikovDerivative method) (hpfracc.core.derivatives.RiemannLiouvilleDerivative method) (hpfracc.core.fractional_implementations.AtanganaBaleanuDerivative method), [1] (hpfracc.core.fractional_implementations.CaputoDerivative method), [1] (hpfracc.core.fractional_implementations.CaputoFabrizioDerivative method), [1] (hpfracc.core.fractional_implementations.FractionalFourierTransform method), [1] (hpfracc.core.fractional_implementations.FractionalLaplacian method), [1] (hpfracc.core.fractional_implementations.GrunwaldLetnikovDerivative method), [1] (hpfracc.core.fractional_implementations.HadamardDerivative method), [1] (hpfracc.core.fractional_implementations.MarchaudDerivative method), [1] (hpfracc.core.fractional_implementations.MillerRossDerivative method), [1] (hpfracc.core.fractional_implementations.ParallelOptimizedCaputo method), [1] (hpfracc.core.fractional_implementations.ParallelOptimizedRiemannLiouville method), [1] (hpfracc.core.fractional_implementations.ReizFellerDerivative method), [1] (hpfracc.core.fractional_implementations.RiemannLiouvilleDerivative method), [1] (hpfracc.core.fractional_implementations.RieszFisherOperator method), [1] (hpfracc.core.fractional_implementations.WeylDerivative method), [1] (hpfracc.FractionalFourierTransform method), [1] (hpfracc.FractionalLaplacian method), [1] compute_weights() (hpfracc.ml.stochastic_memory_sampling.ControlVariateSampler method), [1] (hpfracc.ml.stochastic_memory_sampling.ImportanceSampler method), [1] (hpfracc.ml.stochastic_memory_sampling.StochasticMemorySampler method), [1], [2] (hpfracc.ml.stochastic_memory_sampling.StratifiedSampler method), [1] concatenate() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] ControlVariateSampler (class in hpfracc.ml.stochastic_memory_sampling), [1] ConvergenceError convolve() (hpfracc.solvers.sde_solvers.FastHistoryConvolution method), [1], [2] correlation_time (hpfracc.solvers.noise_models.NoiseConfig attribute), [1], [2] cos() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3] CoupledSolution (class in hpfracc.solvers.coupled_solvers) CoupledSystemSolver (class in hpfracc.solvers.coupled_solvers) coupling (hpfracc.solvers.coupled_solvers.CoupledSolution attribute) CouplingType (class in hpfracc.ml.graph_sde_coupling) create() (hpfracc.core.derivatives.FractionalDerivativeFactory method), [1] (hpfracc.core.integrals.FractionalIntegralFactory method), [1] create_bayesian_fsde() (in module hpfracc.ml.probabilistic_sde) create_beta_alpha_layer() (in module hpfracc.ml.probabilistic_fractional_orders), [1] create_definition() (in module hpfracc.core.definitions) create_derivative_operator() (in module hpfracc.core.derivatives), [1] create_fractional_derivative() (in module hpfracc.core.derivatives), [1], [2] create_fractional_integral() (in module hpfracc.core.fractional_implementations), [1] (in module hpfracc.core.integrals), [1] create_fractional_integral_factory() (in module hpfracc.core.integrals), [1] create_fractional_layer() (in module hpfracc.ml.spectral_autograd), [1] create_gpu_optimized_components() (in module hpfracc.ml.gpu_optimization), [1] create_model() (hpfracc.ml.gnn_models.FractionalGNNFactory static method), [1], [2], [3] create_neural_fsde() (in module hpfracc.ml.neural_fsde), [1] create_neural_ode() (in module hpfracc.ml.neural_ode), [1] create_neural_ode_trainer() (in module hpfracc.ml.neural_ode), [1] create_noise_model() (in module hpfracc.solvers.noise_models), [1], [2] create_normal_alpha_layer() (in module hpfracc.ml.probabilistic_fractional_orders), [1] create_probabilistic_fractional_layer() (in module hpfracc.ml.probabilistic_fractional_orders), [1] create_riesz_fisher_operator() (in module hpfracc.core.fractional_implementations), [1] create_stochastic_fractional_layer() (in module hpfracc.ml.stochastic_memory_sampling), [1] create_tensor() (hpfracc.ml.backends.BackendManager method), [1], [2] (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] (in module hpfracc.ml.tensor_ops), [1] create_uniform_alpha_layer() (in module hpfracc.ml.probabilistic_fractional_orders), [1] create_variance_aware_trainer() (in module hpfracc.ml.variance_aware_training), [1] current_metrics (hpfracc.ml.variance_aware_training.VarianceMonitor property), [1]

D

decompose_function() (hpfracc.core.fractional_implementations.AdomianDecompositionMethod method), [1] DefinitionType (class in hpfracc.core.definitions) device (hpfracc.ml.core.MLConfig attribute) (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute), [1] (hpfracc.ml.layers.LayerConfig attribute), [1] (hpfracc.ml.neural_ode.NeuralODEConfig attribute), [1] diffusion() (hpfracc.ml.graph_sde_coupling.GraphFractionalSDELayer method) (hpfracc.ml.neural_fsde.NeuralFractionalSDE method), [1] diffusion_dim (hpfracc.ml.neural_fsde.NeuralFSDEConfig attribute), [1] diffusion_func (hpfracc.solvers.sde_solvers.SDESolution attribute), [1], [2] diffusion_function() (hpfracc.ml.neural_fsde.NeuralFractionalSDE method), [1]

diffusion_net (hpfracc.ml.neural_fsde.NeuralFSDEConfig attribute), [1] divide() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] drift() (hpfracc.ml.graph_sde_coupling.GraphFractionalSDELayer method) (hpfracc.ml.neural_fsde.NeuralFractionalSDE method), [1] drift_func (hpfracc.solvers.sde_solvers.SDESolution attribute), [1], [2] drift_function() (hpfracc.ml.neural_fsde.NeuralFractionalSDE method), [1] drift_net (hpfracc.ml.neural_fsde.NeuralFSDEConfig attribute), [1] dropout (hpfracc.ml.layers.LayerConfig attribute), [1] dropout() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3] dtype (hpfracc.ml.core.MLConfig attribute) (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute), [1]

E

early_stopping_patience (hpfracc.ml.core.MLConfig attribute) einsum() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] enable_amp (hpfracc.ml.sde_adjoint_utils.MixedPrecisionConfig attribute) enable_benchmarking (hpfracc.ml.layers.LayerConfig attribute), [1] enable_caching (hpfracc.ml.layers.LayerConfig attribute), [1] enable_checkpointing (hpfracc.ml.sde_adjoint_utils.CheckpointConfig attribute) enable_deterministic_mode() (hpfracc.ml.variance_aware_training.VarianceAwareTrainer method), [1], [2] enable_performance_monitoring (hpfracc.ml.neural_ode.NeuralODEConfig attribute), [1] end_timer() (hpfracc.core.utilities.PerformanceMonitor method) (hpfracc.ml.gpu_optimization.GPUProfiler method), [1], [2] estimate_derivative() (hpfracc.ml.stochastic_memory_sampling.ControlVariateSampler method), [1] (hpfracc.ml.stochastic_memory_sampling.ImportanceSampler method), [1] (hpfracc.ml.stochastic_memory_sampling.StochasticMemorySampler method), [1], [2] (hpfracc.ml.stochastic_memory_sampling.StratifiedSampler method), [1]

eval() (hpfracc.ml.gnn_layers.FractionalGraphAttention method), [1] (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] (hpfracc.ml.gnn_layers.FractionalGraphPooling method), [1] execution_time (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute), [1] exp() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3] expand() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] extra_repr() (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalLayer method), [1], [2] (hpfracc.ml.spectral_autograd.BoundedAlphaParameter method), [1], [2] (hpfracc.ml.stochastic_memory_sampling.StochasticFractionalLayer method), [1] eye() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2]

F

factorial_fractional() (in module hpfracc.core.utilities) FastHistoryConvolution (class in hpfracc.solvers.sde_solvers), [1], [2] fft() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] fft_chunked() (hpfracc.ml.gpu_optimization.ChunkedFFT method), [1], [2] fit() (hpfracc.ml.probabilistic_sde.BayesianNeuralFractionalSDE method) FixedStepODESolver (class in hpfracc.solvers.ode_solvers) forward() (hpfracc.ml.core.FractionalAttention method) (hpfracc.ml.core.FractionalLossFunction method) (hpfracc.ml.core.FractionalNeuralNetwork method) (hpfracc.ml.gnn_layers.BaseFractionalGNNLayer method), [1] (hpfracc.ml.gnn_layers.FractionalGraphAttention method), [1] (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] (hpfracc.ml.gnn_layers.FractionalGraphPooling method), [1] (hpfracc.ml.gnn_models.BaseFractionalGNN method), [1] (hpfracc.ml.gnn_models.FractionalGAT method), [1], [2], [3] (hpfracc.ml.gnn_models.FractionalGCN method), [1], [2], [3] (hpfracc.ml.gnn_models.FractionalGraphSAGE method), [1], [2], [3] (hpfracc.ml.gnn_models.FractionalGraphUNet method), [1], [2], [3] (hpfracc.ml.gpu_optimization.AMPFractionalEngine method), [1], [2], [3] (hpfracc.ml.gpu_optimization.GPUOptimizedSpectralEngine method), [1] (hpfracc.ml.graph_sde_coupling.GraphFractionalSDELayer method) (hpfracc.ml.graph_sde_coupling.MultiScaleGraphSDE method) (hpfracc.ml.graph_sde_coupling.SpatialTemporalCoupling method) (hpfracc.ml.layers.FractionalBatchNorm1d method), [1] (hpfracc.ml.layers.FractionalConv1D method), [1] (hpfracc.ml.layers.FractionalConv2D method), [1] (hpfracc.ml.layers.FractionalDropout method), [1] (hpfracc.ml.layers.FractionalLayerBase method), [1] (hpfracc.ml.layers.FractionalLayerNorm method), [1] (hpfracc.ml.layers.FractionalLinear method), [1] (hpfracc.ml.layers.FractionalLSTM method), [1] (hpfracc.ml.layers.FractionalMaxUnpool1d method), [1] (hpfracc.ml.layers.FractionalMaxUnpool2d method), [1] (hpfracc.ml.layers.FractionalMaxUnpool3d method), [1] (hpfracc.ml.layers.FractionalPooling method), [1] (hpfracc.ml.layers.FractionalSelfAttention method), [1] (hpfracc.ml.layers.FractionalTransformer method), [1] (hpfracc.ml.losses.FractionalLossFunction method) (hpfracc.ml.neural_fsde.NeuralFractionalSDE method), [1] (hpfracc.ml.neural_ode.BaseNeuralODE method), [1] (hpfracc.ml.neural_ode.NeuralFODE method), [1] (hpfracc.ml.neural_ode.NeuralODE method), [1] (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalLayer method), [1], [2], [3] (hpfracc.ml.spectral_autograd.BoundedAlphaParameter method), [1], [2] (hpfracc.ml.spectral_autograd.SpectralFractionalFunction static method), [1] (hpfracc.ml.spectral_autograd.SpectralFractionalLayer method), [1] (hpfracc.ml.spectral_autograd.SpectralFractionalNetwork method), [1] (hpfracc.ml.stochastic_memory_sampling.StochasticFractionalDerivative static method), [1] (hpfracc.ml.stochastic_memory_sampling.StochasticFractionalLayer method), [1] forward_with_state() (hpfracc.ml.layers.FractionalLSTM method), [1] fractional_attention() (hpfracc.ml.core.FractionalAttention method) fractional_derivative() (in module hpfracc.ml.spectral_autograd), [1] fractional_exponential() (in module hpfracc.core.utilities) fractional_forward() (hpfracc.ml.core.FractionalNeuralNetwork method) (hpfracc.ml.losses.FractionalLossFunction method) fractional_fourier_transform() (in module hpfracc.algorithms.special_methods), [1], [2] fractional_integral_properties() (in module hpfracc.core.integrals), [1] fractional_laplacian() (in module hpfracc.algorithms.special_methods), [1], [2] fractional_loss() (hpfracc.ml.core.FractionalLossFunction method) fractional_mellin_transform() (in module hpfracc.algorithms.special_methods), [1], [2] fractional_order (hpfracc.ml.core.MLConfig attribute) (hpfracc.ml.layers.LayerConfig attribute), [1] (hpfracc.ml.neural_ode.NeuralODEConfig attribute), [1] (hpfracc.solvers.sde_solvers.SDESolution attribute), [1], [2] fractional_order() (hpfracc.ml.neural_fsde.NeuralFractionalSDE method), [1] fractional_part (hpfracc.core.definitions.FractionalOrder property) (hpfracc.FractionalOrder property), [1], [2] fractional_power() (in module hpfracc.core.utilities) fractional_z_transform() (in module hpfracc.algorithms.special_methods), [1], [2] FractionalAdvectionSolver (class in hpfracc.solvers.pde_solvers) FractionalAttention (class in hpfracc.ml.core) FractionalAutoML (class in hpfracc.ml.core) FractionalBatchNorm1d (class in hpfracc.ml.layers), [1] FractionalBCELoss (class in hpfracc.ml.losses) FractionalBrownianMotion (class in hpfracc.solvers.noise_models), [1], [2]

FractionalCalculusError FractionalCalculusProperties (class in hpfracc.core.definitions) FractionalCombinedLoss (class in hpfracc.ml.losses) FractionalConv1D (class in hpfracc.ml.layers), [1] FractionalConv2D (class in hpfracc.ml.layers), [1] FractionalCosineEmbeddingLoss (class in hpfracc.ml.losses) FractionalCrossEntropyLoss (class in hpfracc.ml.core) (class in hpfracc.ml.losses) FractionalCTCLoss (class in hpfracc.ml.losses) FractionalCustomLoss (class in hpfracc.ml.losses) FractionalDefinition (class in hpfracc.core.definitions) FractionalDerivativeChain (class in hpfracc.core.derivatives), [1] FractionalDerivativeFactory (class in hpfracc.core.derivatives), [1] FractionalDerivativeOperator (class in hpfracc.core.derivatives), [1] FractionalDerivativeProperties (class in hpfracc.core.derivatives), [1] FractionalDiffusionSolver (class in hpfracc.solvers.pde_solvers) FractionalDropout (class in hpfracc.ml.layers), [1] FractionalEulerMaruyama (class in hpfracc.solvers.sde_solvers), [1], [2] FractionalFourierTransform (class in hpfracc), [1] (class in hpfracc.algorithms.special_methods), [1], [2] (class in hpfracc.core.fractional_implementations), [1] FractionalGAT (class in hpfracc.ml.gnn_models), [1], [2] FractionalGCN (class in hpfracc.ml.gnn_models), [1], [2] FractionalGNNFactory (class in hpfracc.ml.gnn_models), [1], [2] FractionalGraphAttention (class in hpfracc.ml.gnn_layers), [1] FractionalGraphConv (class in hpfracc.ml.gnn_layers), [1] FractionalGraphPooling (class in hpfracc.ml.gnn_layers), [1] FractionalGraphSAGE (class in hpfracc.ml.gnn_models), [1], [2] FractionalGraphUNet (class in hpfracc.ml.gnn_models), [1], [2] FractionalHuberLoss (class in hpfracc.ml.losses) FractionalIntegral (class in hpfracc.core.definitions) (class in hpfracc.core.integrals), [1] FractionalIntegralFactory (class in hpfracc.core.integrals), [1] FractionalKLDivergenceLoss (class in hpfracc.ml.losses) FractionalKLDivLoss (class in hpfracc.ml.losses) FractionalLaplacian (class in hpfracc), [1] (class in hpfracc.algorithms.special_methods), [1], [2] (class in hpfracc.core.fractional_implementations), [1] FractionalLayerBase (class in hpfracc.ml.layers), [1] FractionalLayerNorm (class in hpfracc.ml.layers), [1] FractionalLinear (class in hpfracc.ml.layers), [1] FractionalLossFunction (class in hpfracc.ml.core) (class in hpfracc.ml.losses) FractionalLSTM (class in hpfracc.ml.layers), [1] FractionalMarginRankingLoss (class in hpfracc.ml.losses) FractionalMaxUnpool1d (class in hpfracc.ml.layers), [1] FractionalMaxUnpool2d (class in hpfracc.ml.layers), [1] FractionalMaxUnpool3d (class in hpfracc.ml.layers), [1] FractionalMellinTransform (class in hpfracc), [1] (class in hpfracc.algorithms.special_methods), [1], [2] FractionalMilstein (class in hpfracc.solvers.sde_solvers), [1], [2] FractionalMomentMatchingLoss (class in hpfracc.ml.losses) FractionalMSELoss (class in hpfracc.ml.core) (class in hpfracc.ml.losses) FractionalMultiMarginLoss (class in hpfracc.ml.losses) FractionalNeuralNetwork (class in hpfracc.ml.core) FractionalNLLLoss (class in hpfracc.ml.losses) FractionalOperator (class in hpfracc.algorithms.optimized_methods), [1] FractionalOps (class in hpfracc.ml.layers), [1] FractionalOrder (class in hpfracc), [1], [2] (class in hpfracc.core.definitions) FractionalPathwiseLoss (class in hpfracc.ml.losses) FractionalPDESolver (class in hpfracc.solvers.pde_solvers) FractionalPoissonNLLLoss (class in hpfracc.ml.losses) FractionalPooling (class in hpfracc.ml.layers), [1] FractionalReactionDiffusionSolver (class in hpfracc.solvers.pde_solvers) FractionalSDEMSELoss (class in hpfracc.ml.losses) FractionalSDESolver (class in hpfracc.solvers.sde_solvers), [1], [2] FractionalSelfAttention (class in hpfracc.ml.layers), [1] FractionalSmoothL1Loss (class in hpfracc.ml.losses) FractionalTransformer (class in hpfracc.ml.layers), [1] FractionalTripletMarginLoss (class in hpfracc.ml.losses) FractionalZTransform (class in hpfracc), [1] (class in hpfracc.algorithms.special_methods), [1], [2] from_numpy() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2]

G

gamma() (in module hpfracc.special) gamma_function() (in module hpfracc.special) GATED (hpfracc.ml.graph_sde_coupling.CouplingType attribute) gather() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] generalized_binomial() (in module hpfracc.special) generate_increment() (hpfracc.solvers.noise_models.BrownianMotion method), [1], [2] (hpfracc.solvers.noise_models.ColouredNoise method), [1], [2] (hpfracc.solvers.noise_models.FractionalBrownianMotion method), [1], [2] (hpfracc.solvers.noise_models.LevyNoise method), [1], [2] (hpfracc.solvers.noise_models.NoiseModel method), [1], [2] generate_noise_trajectory() (in module hpfracc.solvers.noise_models), [1], [2] get_active_backend() (in module hpfracc.ml.backends), [1] get_advantages() (hpfracc.core.definitions.CaputoDefinition method) (hpfracc.core.definitions.GrunwaldLetnikovDefinition method) (hpfracc.core.definitions.RiemannLiouvilleDefinition method) get_alpha() (hpfracc.ml.spectral_autograd.SpectralFractionalLayer method), [1] get_alpha_statistics() (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalLayer method), [1], [2] get_analytical_solutions() (hpfracc.core.definitions.FractionalCalculusProperties static method) (hpfracc.core.derivatives.FractionalDerivativeProperties static method), [1] get_available_definitions() (in module hpfracc.core.definitions) get_available_implementations() (hpfracc.core.derivatives.FractionalDerivativeFactory method), [1] get_available_methods() (hpfracc.core.integrals.FractionalIntegralFactory method), [1] (in module hpfracc.core.utilities) get_available_models() (hpfracc.ml.gnn_models.FractionalGNNFactory static method), [1], [2] get_backend_config() (hpfracc.ml.backends.BackendManager method), [1], [2] get_backend_info() (hpfracc.ml.gnn_models.BaseFractionalGNN method), [1] get_backend_manager() (in module hpfracc.ml.backends), [1] get_best_model() (hpfracc.ml.core.FractionalAutoML method) get_chain_info() (hpfracc.core.derivatives.FractionalDerivativeChain method), [1] get_current_k() (hpfracc.ml.variance_aware_training.AdaptiveSamplingManager method), [1] get_default_precision() (in module hpfracc.core.utilities) get_definition_formula() (hpfracc.core.definitions.FractionalDefinition method) get_definition_info() (hpfracc.core.derivatives.BaseFractionalDerivative method), [1] get_definition_properties() (hpfracc.core.definitions.FractionalCalculusProperties method) get_dense_gradient() (hpfracc.ml.sde_adjoint_utils.SparseGradientAccumulator method) get_fft_backend() (in module hpfracc.ml.spectral_autograd), [1], [2] get_formula() (hpfracc.core.definitions.FractionalIntegral method)

get_fractional_order() (hpfracc.ml.neural_fsde.NeuralFractionalSDE method), [1] (hpfracc.ml.neural_ode.NeuralFODE method), [1] get_history() (hpfracc.ml.variance_aware_training.VarianceMonitor method), [1] get_info() (hpfracc.core.derivatives.FractionalDerivativeOperator method), [1] get_integral_properties() (hpfracc.core.definitions.FractionalCalculusProperties method) get_limitations() (hpfracc.core.definitions.CaputoDefinition method) (hpfracc.core.definitions.GrunwaldLetnikovDefinition method) (hpfracc.core.definitions.RiemannLiouvilleDefinition method) get_logger() (in module hpfracc.core.utilities) get_method_properties() (in module hpfracc.core.utilities) get_metrics() (hpfracc.ml.variance_aware_training.VarianceMonitor method), [1] get_model_info() (hpfracc.ml.gnn_models.FractionalGNNFactory static method), [1], [2] get_next_seed() (hpfracc.ml.variance_aware_training.StochasticSeedManager method), [1] get_parameter_posterior() (hpfracc.ml.probabilistic_sde.BayesianNeuralFractionalSDE method) get_performance_summary() (hpfracc.ml.gpu_optimization.GPUOptimizedSpectralEngine method), [1] (hpfracc.ml.gpu_optimization.GPUOptimizedStochasticSampler method), [1] get_properties() (hpfracc.core.definitions.FractionalCalculusProperties method) (hpfracc.core.definitions.FractionalDefinition method) (hpfracc.core.definitions.FractionalIntegral method) get_sparsity_ratio() (hpfracc.ml.sde_adjoint_utils.SparseGradientAccumulator method) get_statistics() (hpfracc.core.utilities.PerformanceMonitor method) get_summary() (hpfracc.ml.gpu_optimization.GPUProfiler method), [1], [2] (hpfracc.ml.variance_aware_training.VarianceMonitor method), [1] get_tensor_lib() (hpfracc.ml.backends.BackendManager method), [1], [2] get_tensor_ops() (in module hpfracc.ml.tensor_ops), [1] get_total_order() (hpfracc.core.derivatives.FractionalDerivativeChain method), [1] get_variance_summary() (hpfracc.ml.variance_aware_training.VarianceAwareTrainer method), [1], [2] gpu_optimization_context() (in module hpfracc.ml.gpu_optimization), [1] GPUOptimizedSpectralEngine (class in hpfracc.ml.gpu_optimization), [1] GPUOptimizedStochasticSampler (class in hpfracc.ml.gpu_optimization), [1] GPUProfiler (class in hpfracc.ml.gpu_optimization), [1], [2] GraphFractionalSDELayer (class in hpfracc.ml.graph_sde_coupling) GRUNWALD_LETNIKOV (hpfracc.core.definitions.DefinitionType attribute) grunwald_letnikov() (in module hpfracc.core.derivatives), [1], [2] GrunwaldLetnikovDefinition (class in hpfracc.core.definitions) GrunwaldLetnikovDerivative (class in hpfracc.core.derivatives) (class in hpfracc.core.fractional_implementations), [1] guide() (in module hpfracc.ml.probabilistic_fractional_orders), [1]

H

hadamard_derivative() (in module hpfracc.algorithms.advanced_methods), [1] HadamardDerivative (class in hpfracc), [1] (class in hpfracc.algorithms.advanced_methods), [1] (class in hpfracc.core.fractional_implementations), [1] HadamardIntegral (class in hpfracc.core.integrals), [1] half_precision (hpfracc.ml.sde_adjoint_utils.MixedPrecisionConfig attribute) hidden_dim (hpfracc.ml.neural_ode.NeuralODEConfig attribute), [1] hpfracc module, [1] hpfracc.algorithms.advanced_methods module, [1] hpfracc.algorithms.optimized_methods module, [1] hpfracc.algorithms.special_methods module, [1], [2] hpfracc.core.definitions module hpfracc.core.definitions.DEFAULT_FRACTIONAL_ORDER (in module hpfracc.ml.losses) hpfracc.core.derivatives module, [1] hpfracc.core.derivatives.SUPPORTED_METHODS (in module hpfracc.ml.losses) hpfracc.core.fractional_implementations module, [1] hpfracc.core.integrals module, [1] hpfracc.core.utilities module hpfracc.ml.backends module, [1] hpfracc.ml.backends.DEFAULT_BACKEND (in module hpfracc.ml.losses) hpfracc.ml.backends.SUPPORTED_BACKENDS (in module hpfracc.ml.losses) hpfracc.ml.core module hpfracc.ml.gnn_layers module, [1] hpfracc.ml.gnn_models module, [1] hpfracc.ml.gnn_models.SUPPORTED_GNN_TYPES (in module hpfracc.ml.losses) hpfracc.ml.gpu_optimization module, [1]

hpfracc.ml.graph_sde_coupling module hpfracc.ml.layers module, [1] hpfracc.ml.losses module hpfracc.ml.neural_fsde module, [1] hpfracc.ml.neural_ode module, [1] hpfracc.ml.probabilistic_fractional_orders module, [1] hpfracc.ml.probabilistic_sde module hpfracc.ml.sde_adjoint_utils module hpfracc.ml.spectral_autograd module, [1] hpfracc.ml.stochastic_memory_sampling module, [1] hpfracc.ml.tensor_ops module, [1] hpfracc.ml.tensor_ops.DEFAULT_DTYPE (in module hpfracc.ml.losses) hpfracc.ml.variance_aware_training module, [1] hpfracc.solvers.coupled_solvers module hpfracc.solvers.noise_models module, [1], [2] hpfracc.solvers.ode_solvers module hpfracc.solvers.pde_solvers module hpfracc.solvers.sde_solvers module, [1], [2] hpfracc.special module hurst (hpfracc.solvers.noise_models.NoiseConfig attribute), [1], [2] hypergeometric_series() (in module hpfracc.core.utilities)

I

ifft() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] ifft_chunked() (hpfracc.ml.gpu_optimization.ChunkedFFT method), [1], [2] ImportanceSampler (class in hpfracc.ml.stochastic_memory_sampling), [1] init() (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalOrder method), [1] input_dim (hpfracc.ml.neural_ode.NeuralODEConfig attribute), [1] input_shape (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute), [1] integer_part (hpfracc.core.definitions.FractionalOrder property) (hpfracc.FractionalOrder property), [1], [2]

inverse_transform() (hpfracc.algorithms.special_methods.FractionalMellinTransform method), [1], [2] (hpfracc.algorithms.special_methods.FractionalZTransform method), [1], [2] (hpfracc.FractionalMellinTransform method), [1] (hpfracc.FractionalZTransform method), [1] is_fractional (hpfracc.core.definitions.FractionalOrder property) (hpfracc.FractionalOrder property), [1], [2] is_integer (hpfracc.core.definitions.FractionalOrder property) (hpfracc.FractionalOrder property), [1], [2] is_standard_bm (hpfracc.solvers.noise_models.FractionalBrownianMotion property), [1], [2]

J

JAX (hpfracc.ml.backends.BackendType attribute), [1], [2]

L

L1L2Schemes (class in hpfracc.algorithms.optimized_methods), [1] LayerConfig (class in hpfracc.ml.layers), [1] learn_alpha (hpfracc.ml.neural_fsde.NeuralFSDEConfig attribute), [1] learnable (hpfracc.ml.spectral_autograd.SpectralFractionalLayer property), [1] learning_rate (hpfracc.ml.core.MLConfig attribute) leibniz_rule() (hpfracc.core.definitions.FractionalCalculusProperties static method) LevyNoise (class in hpfracc.solvers.noise_models), [1], [2] linearity_property() (hpfracc.core.definitions.FractionalCalculusProperties static method) linspace() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] load_checkpoint() (hpfracc.ml.sde_adjoint_utils.SDEStateCheckpoint method)

load_model() (hpfracc.ml.core.FractionalNeuralNetwork class method) load_state_checkpoint() (hpfracc.ml.sde_adjoint_utils.SDEAdjointOptimizer method) load_state_dict() (hpfracc.ml.gnn_layers.FractionalGraphAttention method), [1] (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] (hpfracc.ml.gnn_layers.FractionalGraphPooling method), [1] log() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3] log_gamma() (in module hpfracc.special) log_interval (hpfracc.ml.core.MLConfig attribute) log_prob() (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalOrder method), [1] loss_scaling (hpfracc.ml.sde_adjoint_utils.MixedPrecisionConfig attribute)

M

MARCHAUD (hpfracc.core.definitions.DefinitionType attribute) marchaud_derivative() (in module hpfracc.algorithms.advanced_methods), [1] MarchaudDerivative (class in hpfracc), [1] (class in hpfracc.algorithms.advanced_methods), [1] (class in hpfracc.core.fractional_implementations), [1] MarchaudIntegral (class in hpfracc.core.integrals), [1] matmul() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3] max() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] max_checkpoints (hpfracc.ml.sde_adjoint_utils.CheckpointConfig attribute) max_epochs (hpfracc.ml.core.MLConfig attribute) mean (hpfracc.ml.variance_aware_training.VarianceMetrics attribute), [1] mean() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3] median() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] memory_optimization (hpfracc.ml.neural_ode.NeuralODEConfig attribute), [1] memory_peak (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute), [1] memory_tracker() (hpfracc.core.utilities.PerformanceMonitor method) memory_usage_decorator() (in module hpfracc.core.utilities) memory_used (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute), [1] MemoryTrackerContext (class in hpfracc.core.utilities) metadata (hpfracc.solvers.coupled_solvers.CoupledSolution attribute) (hpfracc.solvers.sde_solvers.SDESolution attribute), [1], [2] method (hpfracc.ml.layers.LayerConfig attribute), [1] (hpfracc.solvers.sde_solvers.SDESolution attribute), [1], [2] MILLER_ROSS (hpfracc.core.definitions.DefinitionType attribute) MillerRossDerivative (class in hpfracc.core.fractional_implementations), [1] MillerRossIntegral (class in hpfracc.core.integrals), [1] min() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] mittag_leffler() (in module hpfracc.special) mittag_leffler_derivative() (in module hpfracc.special) mittag_leffler_fast() (in module hpfracc.special) mittag_leffler_function() (in module hpfracc.special) MixedPrecisionConfig (class in hpfracc.ml.sde_adjoint_utils) MixedPrecisionManager (class in hpfracc.ml.sde_adjoint_utils) MLConfig (class in hpfracc.ml.core) model() (in module hpfracc.ml.probabilistic_fractional_orders), [1] model_save_path (hpfracc.ml.core.MLConfig attribute)

modified_bessel_function_first_kind() (in module hpfracc.core.utilities) module hpfracc, [1] hpfracc.algorithms.advanced_methods, [1] hpfracc.algorithms.optimized_methods, [1] hpfracc.algorithms.special_methods, [1], [2] hpfracc.core.definitions hpfracc.core.derivatives, [1] hpfracc.core.fractional_implementations, [1] hpfracc.core.integrals, [1] hpfracc.core.utilities hpfracc.ml.backends, [1] hpfracc.ml.core hpfracc.ml.gnn_layers, [1] hpfracc.ml.gnn_models, [1] hpfracc.ml.gpu_optimization, [1] hpfracc.ml.graph_sde_coupling hpfracc.ml.layers, [1] hpfracc.ml.losses hpfracc.ml.neural_fsde, [1] hpfracc.ml.neural_ode, [1] hpfracc.ml.probabilistic_fractional_orders, [1] hpfracc.ml.probabilistic_sde hpfracc.ml.sde_adjoint_utils hpfracc.ml.spectral_autograd, [1] hpfracc.ml.stochastic_memory_sampling, [1] hpfracc.ml.tensor_ops, [1] hpfracc.ml.variance_aware_training, [1] hpfracc.solvers.coupled_solvers hpfracc.solvers.noise_models, [1], [2] hpfracc.solvers.ode_solvers hpfracc.solvers.pde_solvers hpfracc.solvers.sde_solvers, [1], [2] hpfracc.special MonolithicSolver (class in hpfracc.solvers.coupled_solvers) multiply() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] MultiScaleGraphSDE (class in hpfracc.ml.graph_sde_coupling)

N

n (hpfracc.core.definitions.CaputoDefinition property) (hpfracc.core.definitions.RiemannLiouvilleDefinition property) named_parameters() (hpfracc.ml.gnn_layers.FractionalGraphAttention method), [1] (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] (hpfracc.ml.gnn_layers.FractionalGraphPooling method), [1] NeuralFODE (class in hpfracc.ml.neural_ode), [1] NeuralFractionalSDE (class in hpfracc.ml.neural_fsde), [1] NeuralFSDEConfig (class in hpfracc.ml.neural_fsde), [1] NeuralODE (class in hpfracc.ml.neural_ode), [1] NeuralODEConfig (class in hpfracc.ml.neural_ode), [1] NeuralODETrainer (class in hpfracc.ml.neural_ode), [1] no_grad() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2]

noise_type (hpfracc.ml.neural_fsde.NeuralFSDEConfig attribute), [1] (hpfracc.solvers.noise_models.NoiseConfig attribute), [1], [2] NoiseConfig (class in hpfracc.solvers.noise_models), [1], [2] NoiseModel (class in hpfracc.solvers.noise_models), [1], [2] norm() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] normalize_array() (in module hpfracc.core.utilities) num_layers (hpfracc.ml.neural_ode.NeuralODEConfig attribute), [1] NUMBA (hpfracc.ml.backends.BackendType attribute), [1], [2] NumbaFractionalKernels (class in hpfracc.algorithms.optimized_methods), [1] NumbaOptimizer (class in hpfracc.algorithms.optimized_methods), [1] numpyro_fsde_model() (in module hpfracc.ml.probabilistic_sde) numpyro_guide_fsde() (in module hpfracc.ml.probabilistic_sde)

O

ode_func() (hpfracc.ml.neural_ode.BaseNeuralODE method), [1] on_batch_begin() (hpfracc.ml.variance_aware_training.VarianceAwareCallback method), [1] on_batch_end() (hpfracc.ml.variance_aware_training.VarianceAwareCallback method), [1] on_epoch_begin() (hpfracc.ml.variance_aware_training.VarianceAwareCallback method), [1] on_epoch_end() (hpfracc.ml.variance_aware_training.VarianceAwareCallback method), [1] ones() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3] ones_like() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] operation (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute), [1] OperatorSplittingSolver (class in hpfracc.solvers.coupled_solvers) optimize_fractional_order() (hpfracc.ml.core.FractionalAutoML method) optimized_caputo() (in module hpfracc.algorithms.optimized_methods), [1] optimized_grunwald_letnikov() (in module hpfracc.algorithms.optimized_methods), [1] optimized_hadamard_derivative() (in module hpfracc.algorithms.advanced_methods), [1] optimized_marchaud_derivative() (in module hpfracc.algorithms.advanced_methods), [1] optimized_reiz_feller_derivative() (in module hpfracc.algorithms.advanced_methods), [1] optimized_riemann_liouville() (in module hpfracc), [1] (in module hpfracc.algorithms.optimized_methods), [1] optimized_weyl_derivative() (in module hpfracc.algorithms.advanced_methods), [1] OptimizedAdomianDecomposition (class in hpfracc.algorithms.advanced_methods), [1] OptimizedCaputo (class in hpfracc), [1], [2] (class in hpfracc.algorithms.optimized_methods), [1]

OptimizedFractionalMethods (class in hpfracc.algorithms.optimized_methods), [1] OptimizedGrunwaldLetnikov (class in hpfracc), [1], [2] (class in hpfracc.algorithms.optimized_methods), [1] OptimizedHadamardDerivative (class in hpfracc.algorithms.advanced_methods), [1] OptimizedMarchaudDerivative (class in hpfracc.algorithms.advanced_methods), [1] OptimizedReizFellerDerivative (class in hpfracc.algorithms.advanced_methods), [1] OptimizedRiemannLiouville (class in hpfracc), [1], [2] (class in hpfracc.algorithms.optimized_methods), [1] OptimizedWeylDerivative (class in hpfracc.algorithms.advanced_methods), [1] original_create_fractional_layer() (in module hpfracc.ml.spectral_autograd), [1] original_get_fft_backend() (in module hpfracc.ml.spectral_autograd), [1] original_get_fractional_kernel() (in module hpfracc.ml.spectral_autograd), [1] original_safe_fft() (in module hpfracc.ml.spectral_autograd), [1] original_safe_ifft() (in module hpfracc.ml.spectral_autograd), [1] original_set_fft_backend() (in module hpfracc.ml.spectral_autograd), [1] original_spectral_fractional_derivative() (in module hpfracc.ml.spectral_autograd), [1] OriginalSpectral (in module hpfracc.ml.spectral_autograd), [1] OriginalSpectralFractionalLayer (in module hpfracc.ml.spectral_autograd), [1] OriginalSpectralFractionalNetwork (in module hpfracc.ml.spectral_autograd), [1] output_dim (hpfracc.ml.neural_ode.NeuralODEConfig attribute), [1]

P

parallel_optimized_caputo() (in module hpfracc.algorithms.optimized_methods), [1] parallel_optimized_grunwald_letnikov() (in module hpfracc.algorithms.optimized_methods), [1] parallel_optimized_riemann_liouville() (in module hpfracc.algorithms.optimized_methods), [1] ParallelConfig (class in hpfracc.algorithms.optimized_methods), [1] ParallelLoadBalancer (class in hpfracc.algorithms.optimized_methods), [1] ParallelOptimizedCaputo (class in hpfracc.algorithms.optimized_methods), [1] (class in hpfracc.core.fractional_implementations), [1] ParallelOptimizedGrunwaldLetnikov (class in hpfracc.algorithms.optimized_methods), [1] ParallelOptimizedRiemannLiouville (class in hpfracc.algorithms.optimized_methods), [1] (class in hpfracc.core.fractional_implementations), [1] ParallelPerformanceMonitor (class in hpfracc.algorithms.optimized_methods), [1] parameters() (hpfracc.ml.core.FractionalNeuralNetwork method) (hpfracc.ml.gnn_layers.FractionalGraphAttention method), [1] (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] (hpfracc.ml.gnn_layers.FractionalGraphPooling method), [1] (hpfracc.ml.gnn_models.BaseFractionalGNN method), [1]

performance_mode (hpfracc.ml.layers.LayerConfig attribute), [1] PerformanceMetrics (class in hpfracc.ml.gpu_optimization), [1] PerformanceMonitor (class in hpfracc.core.utilities) pochhammer_symbol() (in module hpfracc.core.utilities) power() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] predict() (hpfracc.ml.probabilistic_sde.BayesianNeuralFractionalSDE method) ProbabilisticFractionalLayer (class in hpfracc.ml.probabilistic_fractional_orders), [1], [2] ProbabilisticFractionalOrder (class in hpfracc.ml.probabilistic_fractional_orders), [1]

Q

quantile() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2]

R

randn() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] randn_like() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] register_fractional_implementations() (in module hpfracc.core.fractional_implementations), [1] register_implementation() (hpfracc.core.derivatives.FractionalDerivativeFactory method), [1] (hpfracc.core.integrals.FractionalIntegralFactory method), [1] reiz_feller_derivative() (in module hpfracc.algorithms.advanced_methods), [1] ReizFellerDerivative (class in hpfracc), [1] (class in hpfracc.algorithms.advanced_methods), [1] (class in hpfracc.core.fractional_implementations), [1] relationship_between_definitions() (hpfracc.core.definitions.FractionalCalculusProperties static method) relu() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3] repeat() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] reset() (hpfracc.core.utilities.PerformanceMonitor method) (hpfracc.solvers.noise_models.ColouredNoise method), [1], [2] reset_parameters() (hpfracc.ml.gnn_layers.FractionalGraphAttention method), [1] (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] (hpfracc.ml.gnn_layers.FractionalGraphPooling method), [1]

reset_to_base() (hpfracc.ml.variance_aware_training.StochasticSeedManager method), [1] reshape() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] RIEMANN_LIOUVILLE (hpfracc.core.definitions.DefinitionType attribute) riemann_liouville() (in module hpfracc.core.derivatives), [1], [2] RiemannLiouvilleDefinition (class in hpfracc.core.definitions) RiemannLiouvilleDerivative (class in hpfracc.core.derivatives) (class in hpfracc.core.fractional_implementations), [1] RiemannLiouvilleIntegral (class in hpfracc), [1] (class in hpfracc.core.integrals), [1] RieszFisherOperator (class in hpfracc.core.fractional_implementations), [1] robust_fft() (in module hpfracc.ml.spectral_autograd), [1] robust_ifft() (in module hpfracc.ml.spectral_autograd), [1] rtol (hpfracc.ml.neural_ode.NeuralODEConfig attribute), [1]

S

safe_divide() (in module hpfracc.core.utilities) safe_fft() (in module hpfracc.ml.spectral_autograd), [1] safe_ifft() (in module hpfracc.ml.spectral_autograd), [1] sample() (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalOrder method), [1] sample_alpha() (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalLayer method), [1], [2], [3] sample_count (hpfracc.ml.variance_aware_training.VarianceMetrics attribute), [1] sample_indices() (hpfracc.ml.gpu_optimization.GPUOptimizedStochasticSampler method), [1] (hpfracc.ml.stochastic_memory_sampling.ControlVariateSampler method), [1] (hpfracc.ml.stochastic_memory_sampling.ImportanceSampler method), [1] (hpfracc.ml.stochastic_memory_sampling.StochasticMemorySampler method), [1], [2] (hpfracc.ml.stochastic_memory_sampling.StratifiedSampler method), [1] save_checkpoint() (hpfracc.ml.sde_adjoint_utils.SDEStateCheckpoint method) save_model() (hpfracc.ml.core.FractionalNeuralNetwork method) save_state_checkpoint() (hpfracc.ml.sde_adjoint_utils.SDEAdjointOptimizer method) scale (hpfracc.solvers.noise_models.NoiseConfig attribute), [1], [2] scale_gradients() (hpfracc.ml.sde_adjoint_utils.MixedPrecisionManager method) scale_loss() (hpfracc.ml.sde_adjoint_utils.MixedPrecisionManager method) SDEAdjointOptimizer (class in hpfracc.ml.sde_adjoint_utils) SDESolution (class in hpfracc.solvers.sde_solvers), [1], [2] SDEStateCheckpoint (class in hpfracc.ml.sde_adjoint_utils) select_optimal_backend() (hpfracc.ml.layers.BackendManager method), [1] semigroup_property() (hpfracc.core.definitions.FractionalCalculusProperties static method) set_backend_manager() (in module hpfracc.ml.backends), [1] set_default_precision() (in module hpfracc.core.utilities) set_deterministic_mode() (hpfracc.ml.variance_aware_training.StochasticSeedManager method), [1] set_fft_backend() (in module hpfracc.ml.spectral_autograd), [1], [2] set_implementation() (hpfracc.core.derivatives.FractionalDerivativeOperator method), [1] set_sampling_budget() (hpfracc.ml.variance_aware_training.VarianceAwareTrainer method), [1], [2] set_seed() (hpfracc.ml.variance_aware_training.StochasticSeedManager method), [1] setup_logging() (in module hpfracc.core.utilities) should_adapt() (hpfracc.ml.variance_aware_training.VarianceMonitor method), [1] sigmoid() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3] simpson_fractional_integral() (in module hpfracc.core.integrals), [1] sin() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3] smooth_function() (in module hpfracc.core.utilities) softmax() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3] solve() (hpfracc.algorithms.advanced_methods.AdomianDecomposition method), [1] (hpfracc.core.fractional_implementations.AdomianDecompositionMethod method), [1] (hpfracc.solvers.coupled_solvers.CoupledSystemSolver method) (hpfracc.solvers.coupled_solvers.MonolithicSolver method) (hpfracc.solvers.coupled_solvers.OperatorSplittingSolver method) (hpfracc.solvers.ode_solvers.FixedStepODESolver method) (hpfracc.solvers.pde_solvers.FractionalAdvectionSolver method) (hpfracc.solvers.pde_solvers.FractionalDiffusionSolver method) (hpfracc.solvers.pde_solvers.FractionalPDESolver method) (hpfracc.solvers.pde_solvers.FractionalReactionDiffusionSolver method) (hpfracc.solvers.sde_solvers.FractionalEulerMaruyama method), [1], [2] (hpfracc.solvers.sde_solvers.FractionalMilstein method), [1], [2] (hpfracc.solvers.sde_solvers.FractionalSDESolver method), [1], [2]

solve_coupled_graph_sde() (in module hpfracc.solvers.coupled_solvers) solve_equation() (hpfracc.core.fractional_implementations.AdomianDecompositionMethod method), [1] solve_fractional_advection() (in module hpfracc.solvers.pde_solvers) solve_fractional_diffusion() (in module hpfracc.solvers.pde_solvers) solve_fractional_ode() (in module hpfracc.solvers.ode_solvers) solve_fractional_pde() (in module hpfracc.solvers.pde_solvers) solve_fractional_reaction_diffusion() (in module hpfracc.solvers.pde_solvers) solve_fractional_sde() (in module hpfracc.solvers.sde_solvers), [1], [2] solve_fractional_sde_system() (in module hpfracc.solvers.sde_solvers), [1], [2] solve_fractional_system() (in module hpfracc.solvers.ode_solvers) solver (hpfracc.ml.neural_ode.NeuralODEConfig attribute), [1] SparseGradientAccumulator (class in hpfracc.ml.sde_adjoint_utils) spatial (hpfracc.solvers.coupled_solvers.CoupledSolution attribute) SPATIAL_TO_TEMPORAL (hpfracc.ml.graph_sde_coupling.CouplingType attribute) SpatialTemporalCoupling (class in hpfracc.ml.graph_sde_coupling) special_optimized_marchaud_derivative() (in module hpfracc.algorithms.special_methods), [1], [2] special_optimized_reiz_feller_derivative() (in module hpfracc.algorithms.special_methods), [1], [2] special_optimized_weyl_derivative() (in module hpfracc.algorithms.special_methods), [1], [2] SpecialMethodsConfig (class in hpfracc.algorithms.special_methods), [1], [2] SpecialOptimizedMarchaudDerivative (class in hpfracc.algorithms.special_methods), [1], [2] SpecialOptimizedReizFellerDerivative (class in hpfracc.algorithms.special_methods), [1], [2] SpecialOptimizedWeylDerivative (class in hpfracc.algorithms.special_methods), [1], [2] spectral_fractional_derivative() (in module hpfracc.ml.spectral_autograd), [1] SpectralFractionalDerivative (class in hpfracc.ml.spectral_autograd), [1], [2] SpectralFractionalFunction (class in hpfracc.ml.spectral_autograd), [1] SpectralFractionalLayer (class in hpfracc.ml.spectral_autograd), [1] SpectralFractionalNetwork (class in hpfracc.ml.spectral_autograd), [1] sqrt() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3] squeeze() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] stack() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] start_timer() (hpfracc.core.utilities.PerformanceMonitor method) (hpfracc.ml.gpu_optimization.GPUProfiler method), [1], [2] state_dict() (hpfracc.ml.gnn_layers.FractionalGraphAttention method), [1] (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] (hpfracc.ml.gnn_layers.FractionalGraphPooling method), [1] std (hpfracc.ml.variance_aware_training.VarianceMetrics attribute), [1] std() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] step() (hpfracc.ml.sde_adjoint_utils.SDEAdjointOptimizer method) step_optimizer() (hpfracc.ml.sde_adjoint_utils.MixedPrecisionManager method) stochastic_fractional_derivative() (in module hpfracc.ml.stochastic_memory_sampling), [1] StochasticFractionalDerivative (class in hpfracc.ml.stochastic_memory_sampling), [1] StochasticFractionalLayer (class in hpfracc.ml.stochastic_memory_sampling), [1] StochasticMemorySampler (class in hpfracc.ml.stochastic_memory_sampling), [1], [2] StochasticSeedManager (class in hpfracc.ml.variance_aware_training), [1] StratifiedSampler (class in hpfracc.ml.stochastic_memory_sampling), [1] subtract() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] sum() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3] switch_backend() (hpfracc.ml.backends.BackendManager method), [1], [2] (in module hpfracc.ml.backends), [1] (in module hpfracc.ml.tensor_ops), [1]

T

t (hpfracc.solvers.coupled_solvers.CoupledSolution attribute) (hpfracc.solvers.sde_solvers.SDESolution attribute), [1], [2] tanh() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3] temporal (hpfracc.solvers.coupled_solvers.CoupledSolution attribute) TEMPORAL_TO_SPATIAL (hpfracc.ml.graph_sde_coupling.CouplingType attribute) tensor() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] TensorOps (class in hpfracc.ml.tensor_ops), [1], [2] test_gpu_optimization() (in module hpfracc.ml.gpu_optimization), [1] test_variance_aware_training() (in module hpfracc.ml.variance_aware_training), [1] throughput (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute), [1] tile() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] timer() (hpfracc.core.utilities.PerformanceMonitor method) TimerContext (class in hpfracc.core.utilities) timestamp (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute), [1] (hpfracc.ml.variance_aware_training.VarianceMetrics attribute), [1] timing_decorator() (in module hpfracc.core.utilities) to_device() (hpfracc.ml.backends.BackendManager method), [1], [2]

to_numpy() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] TORCH (hpfracc.ml.backends.BackendType attribute), [1], [2] train() (hpfracc.ml.gnn_layers.FractionalGraphAttention method), [1] (hpfracc.ml.gnn_layers.FractionalGraphConv method), [1] (hpfracc.ml.gnn_layers.FractionalGraphPooling method), [1] (hpfracc.ml.neural_ode.NeuralODETrainer method), [1] (hpfracc.ml.variance_aware_training.VarianceAwareTrainer method), [1], [2] train_epoch() (hpfracc.ml.variance_aware_training.VarianceAwareTrainer method), [1], [2] train_step() (hpfracc.ml.neural_ode.NeuralODETrainer method), [1] transform() (hpfracc.algorithms.special_methods.FractionalFourierTransform method), [1], [2] (hpfracc.algorithms.special_methods.FractionalMellinTransform method), [1], [2] (hpfracc.algorithms.special_methods.FractionalZTransform method), [1], [2] (hpfracc.FractionalFourierTransform method), [1] (hpfracc.FractionalMellinTransform method), [1] (hpfracc.FractionalZTransform method), [1] transpose() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3] trapezoidal_fractional_integral() (in module hpfracc.core.integrals), [1]

U

unified_special_derivative() (in module hpfracc.algorithms.special_methods), [1], [2] UnifiedSpecialMethods (class in hpfracc.algorithms.special_methods), [1], [2] unscale_gradients() (hpfracc.ml.sde_adjoint_utils.MixedPrecisionManager method) unsqueeze() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2] update() (hpfracc.ml.variance_aware_training.VarianceMonitor method), [1] (hpfracc.solvers.sde_solvers.FastHistoryConvolution method), [1], [2]

update_k() (hpfracc.ml.variance_aware_training.AdaptiveSamplingManager method), [1] use_adjoint (hpfracc.ml.neural_ode.NeuralODEConfig attribute), [1] use_advanced_solvers (hpfracc.ml.neural_ode.NeuralODEConfig attribute), [1] use_fractional (hpfracc.ml.layers.LayerConfig attribute), [1] use_gpu (hpfracc.ml.core.MLConfig attribute) use_sde_adjoint (hpfracc.ml.neural_fsde.NeuralFSDEConfig attribute), [1]

V

validate_fractional_integral() (in module hpfracc.core.integrals), [1] validate_fractional_order() (in module hpfracc.core.definitions) (in module hpfracc.core.utilities) validate_function() (in module hpfracc.core.utilities) validate_tensor_input() (in module hpfracc.core.utilities) validation_split (hpfracc.ml.core.MLConfig attribute) ValidationError value (hpfracc.core.definitions.FractionalOrder property) (hpfracc.FractionalOrder property), [1], [2]

variance (hpfracc.ml.variance_aware_training.VarianceMetrics attribute), [1] variance() (hpfracc.solvers.noise_models.BrownianMotion method), [1], [2] VarianceAwareCallback (class in hpfracc.ml.variance_aware_training), [1] VarianceAwareTrainer (class in hpfracc.ml.variance_aware_training), [1], [2] VarianceMetrics (class in hpfracc.ml.variance_aware_training), [1] VarianceMonitor (class in hpfracc.ml.variance_aware_training), [1] vectorize_function() (in module hpfracc.core.utilities)

W

WEYL (hpfracc.core.definitions.DefinitionType attribute) weyl_derivative() (in module hpfracc.algorithms.advanced_methods), [1] WeylDerivative (class in hpfracc), [1] (class in hpfracc.algorithms.advanced_methods), [1] (class in hpfracc.core.fractional_implementations), [1]

WeylIntegral (class in hpfracc.core.integrals), [1]

Y

y (hpfracc.solvers.sde_solvers.SDESolution attribute), [1], [2]

Z

zeros() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2], [3]

zeros_like() (hpfracc.ml.tensor_ops.TensorOps method), [1], [2]