Welcome to PINA documentation! Here you can find the modules of the package divided in different sections. The high-level structure of the package is depicted in our API.
The pipeline to solve differential equations with PINA follows just five steps:
- Define the Problems the user aim to solve
- Generate data using built in Geometrical Domains, or load high level simulation results as :doc:`LabelTensor <label_tensor>`
- Choose or build one or more Models to solve the problem
- Choose a solver across PINA available Solvers, or build one using the :doc:`SolverInterface <solver/solver_interface>`
- Train the model with the PINA :doc:`Trainer <solver/solver_interface>`, enhance the train with Callbacks
.. toctree::
:titlesonly:
Trainer <trainer.rst>
Dataset <data/dataset.rst>
DataModule <data/data_module.rst>
.. toctree::
:titlesonly:
LabelTensor <label_tensor.rst>
Graph <graph/graph.rst>
LabelBatch <graph/label_batch.rst>
.. toctree::
:titlesonly:
GraphBuilder <graph/graph_builder.rst>
RadiusGraph <graph/radius_graph.rst>
KNNGraph <graph/knn_graph.rst>
.. toctree::
:titlesonly:
Condition Interface <condition/condition_interface.rst>
Base Condition <condition/base_condition.rst>
Condition <condition/condition.rst>
Data Condition <condition/data_condition.rst>
Domain Equation Condition <condition/domain_equation_condition.rst>
Input Equation Condition <condition/input_equation_condition.rst>
Input Target Condition <condition/input_target_condition.rst>
.. toctree::
:titlesonly:
Batch Manager <data/manager/batch_manager.rst>
Data Manager Interface <data/manager/data_manager_interface.rst>
Data Manager <data/manager/data_manager.rst>
Graph Data Manager <data/manager/graph_data_manager.rst>
Tensor Data Manager <data/manager/tensor_data_manager.rst>
.. toctree::
:titlesonly:
SolverInterface <solver/solver_interface.rst>
SingleSolverInterface <solver/single_solver_interface.rst>
MultiSolverInterface <solver/multi_solver_interface.rst>
SupervisedSolverInterface <solver/supervised_solver/supervised_solver_interface.rst>
DeepEnsembleSolverInterface <solver/ensemble_solver/ensemble_solver_interface.rst>
PINNInterface <solver/physics_informed_solver/pinn_interface.rst>
PINN <solver/physics_informed_solver/pinn.rst>
GradientPINN <solver/physics_informed_solver/gradient_pinn.rst>
CausalPINN <solver/physics_informed_solver/causal_pinn.rst>
CompetitivePINN <solver/physics_informed_solver/competitive_pinn.rst>
SelfAdaptivePINN <solver/physics_informed_solver/self_adaptive_pinn.rst>
RBAPINN <solver/physics_informed_solver/rba_pinn.rst>
DeepEnsemblePINN <solver/ensemble_solver/ensemble_pinn.rst>
SupervisedSolver <solver/supervised_solver/supervised.rst>
DeepEnsembleSupervisedSolver <solver/ensemble_solver/ensemble_supervised.rst>
ReducedOrderModelSolver <solver/supervised_solver/reduced_order_model.rst>
GAROM <solver/garom.rst>
AutoregressiveSolverInterface <solver/autoregressive_solver/autoregressive_solver_interface.rst>
AutoregressiveSolver <solver/autoregressive_solver/autoregressive_solver.rst>
.. toctree::
:titlesonly:
:maxdepth: 5
FeedForward <model/feed_forward.rst>
MultiFeedForward <model/multi_feed_forward.rst>
ResidualFeedForward <model/residual_feed_forward.rst>
Spline <model/spline.rst>
SplineSurface <model/spline_surface.rst>
DeepONet <model/deeponet.rst>
MIONet <model/mionet.rst>
KernelNeuralOperator <model/kernel_neural_operator.rst>
FourierIntegralKernel <model/fourier_integral_kernel.rst>
FNO <model/fourier_neural_operator.rst>
AveragingNeuralOperator <model/average_neural_operator.rst>
LowRankNeuralOperator <model/low_rank_neural_operator.rst>
GraphNeuralOperator <model/graph_neural_operator.rst>
GraphNeuralKernel <model/graph_neural_operator_integral_kernel.rst>
PirateNet <model/pirate_network.rst>
EquivariantGraphNeuralOperator <model/equivariant_graph_neural_operator.rst>
SINDy <model/sindy.rst>
Vectorized Spline <model/vectorized_spline.rst>
Kolmogorov-Arnold Network <model/kolmogorov_arnold_network.rst>
.. toctree::
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Residual Block <model/block/residual.rst>
EnhancedLinear Block <model/block/enhanced_linear.rst>
Spectral Convolution Block <model/block/spectral.rst>
Fourier Block <model/block/fourier_block.rst>
Averaging Block <model/block/average_neural_operator_block.rst>
Low Rank Block <model/block/low_rank_block.rst>
Graph Neural Operator Block <model/block/gno_block.rst>
Continuous Convolution Interface <model/block/convolution_interface.rst>
Continuous Convolution Block <model/block/convolution.rst>
Orthogonal Block <model/block/orthogonal.rst>
PirateNet Block <model/block/pirate_network_block.rst>
KAN Block <model/block/kan_block.rst>
.. toctree::
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Deep Tensor Network Block <model/block/message_passing/deep_tensor_network_block.rst>
E(n) Equivariant Network Block <model/block/message_passing/en_equivariant_network_block.rst>
Interaction Network Block <model/block/message_passing/interaction_network_block.rst>
Radial Field Network Block <model/block/message_passing/radial_field_network_block.rst>
EquivariantGraphNeuralOperatorBlock <model/block/message_passing/equivariant_graph_neural_operator_block.rst>
.. toctree::
:titlesonly:
Proper Orthogonal Decomposition <model/block/pod_block.rst>
Periodic Boundary Condition Embedding <model/block/pbc_embedding.rst>
Fourier Feature Embedding <model/block/fourier_embedding.rst>
Radial Basis Function Interpolation <model/block/rbf_block.rst>
.. toctree::
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Optimizer <optim/optimizer_interface.rst>
Scheduler <optim/scheduler_interface.rst>
TorchOptimizer <optim/torch_optimizer.rst>
TorchScheduler <optim/torch_scheduler.rst>
.. toctree::
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Adaptive Function Interface <adaptive_function/adaptive_function_interface.rst>
Base Adaptive Function <adaptive_function/base_adaptive_function.rst>
Adaptive CELU <adaptive_function/adaptive_celu.rst>
Adaptive ELU <adaptive_function/adaptive_elu.rst>
Adaptive Exp <adaptive_function/adaptive_exp.rst>
Adaptive GELU <adaptive_function/adaptive_gelu.rst>
Adaptive Mish <adaptive_function/adaptive_mish.rst>
Adaptive ReLU <adaptive_function/adaptive_relu.rst>
Adaptive Sigmoid <adaptive_function/adaptive_sigmoid.rst>
Adaptive SiLU <adaptive_function/adaptive_silu.rst>
Adaptive SIREN <adaptive_function/adaptive_siren.rst>
Adaptive Softmax <adaptive_function/adaptive_softmax.rst>
Adaptive Softmin <adaptive_function/adaptive_softmin.rst>
Adaptive Tanh <adaptive_function/adaptive_tanh.rst>
.. toctree::
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Equation Interface <equation/equation_interface.rst>
Base Equation <equation/base_equation.rst>
Equation <equation/equation.rst>
System Equation <equation/system_equation.rst>
Differential Operators <operator.rst>
.. toctree::
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Acoustic Wave Equation <equation/zoo/acoustic_wave_equation.rst>
Advection Equation <equation/zoo/advection_equation.rst>
Allen-Cahn Equation <equation/zoo/allen_cahn_equation.rst>
Diffusion-Reaction Equation <equation/zoo/diffusion_reaction_equation.rst>
Fixed Flux <equation/zoo/fixed_flux.rst>
Fixed Gradient <equation/zoo/fixed_gradient.rst>
Fixed Laplacian <equation/zoo/fixed_laplacian.rst>
Fixed Value <equation/zoo/fixed_value.rst>
Helmholtz Equation <equation/zoo/helmholtz_equation.rst>
Poisson Equation <equation/zoo/poisson_equation.rst>
.. toctree::
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ProblemInterface <problem/problem_interface.rst>
BaseProblem <problem/base_problem.rst>
InverseProblem <problem/inverse_problem.rst>
ParametricProblem <problem/parametric_problem.rst>
SpatialProblem <problem/spatial_problem.rst>
TimeDependentProblem <problem/time_dependent_problem.rst>
.. toctree::
:titlesonly:
AcousticWaveProblem <problem/zoo/acoustic_wave_problem.rst>
AdvectionProblem <problem/zoo/advection_problem.rst>
AllenCahnProblem <problem/zoo/allen_cahn_problem.rst>
DiffusionReactionProblem <problem/zoo/diffusion_reaction_problem.rst>
HelmholtzProblem <problem/zoo/helmholtz_problem.rst>
InversePoisson2DSquareProblem <problem/zoo/inverse_poisson_problem.rst>
Poisson2DSquareProblem <problem/zoo/poisson_problem.rst>
SupervisedProblem <problem/zoo/supervised_problem.rst>
.. toctree::
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DomainInterface <domain/domain_interface.rst>
BaseDomain <domain/base_domain.rst>
CartesianDomain <domain/cartesian_domain.rst>
EllipsoidDomain <domain/ellipsoid_domain.rst>
SimplexDomain <domain/simplex_domain.rst>
.. toctree::
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OperationInterface <domain/operation_interface.rst>
BaseOperation <domain/base_operation.rst>
Union <domain/union.rst>
Intersection <domain/intersection.rst>
Difference <domain/difference.rst>
Exclusion <domain/exclusion.rst>
.. toctree::
:titlesonly:
Switch Optimizer <callback/optim/switch_optimizer.rst>
Switch Scheduler <callback/optim/switch_scheduler.rst>
Normalizer Data <callback/processing/normalizer_data_callback.rst>
PINA Progress Bar <callback/processing/pina_progress_bar.rst>
Metric Tracker <callback/processing/metric_tracker.rst>
Refinement Interface <callback/refinement/refinement_interface.rst>
R3 Refinement <callback/refinement/r3_refinement.rst>
.. toctree::
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LossInterface <loss/loss_interface.rst>
LpLoss <loss/lploss.rst>
PowerLoss <loss/powerloss.rst>
WeightingInterface <loss/weighting_interface.rst>
ScalarWeighting <loss/scalar_weighting.rst>
NeuralTangentKernelWeighting <loss/ntk_weighting.rst>
SelfAdaptiveWeighting <loss/self_adaptive_weighting.rst>
LinearWeighting <loss/linear_weighting.rst>