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:
ConditionInterface <condition/condition_interface.rst>
Condition <condition/condition.rst>
DataCondition <condition/data_condition.rst>
DomainEquationCondition <condition/domain_equation_condition.rst>
InputEquationCondition <condition/input_equation_condition.rst>
InputTargetCondition <condition/input_target_condition.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>
DeepEnsembleSolverInterface <solver/ensemble_solver/ensemble_solver_interface>
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>
SupervisedSolver <solver/supervised_solver/supervised.rst>
DeepEnsembleSupervisedSolver <solver/ensemble_solver/ensemble_supervised>
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::
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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/AdaptiveActivationFunctionInterface.rst>
Adaptive ReLU <adaptive_function/AdaptiveReLU.rst>
Adaptive Sigmoid <adaptive_function/AdaptiveSigmoid.rst>
Adaptive Tanh <adaptive_function/AdaptiveTanh.rst>
Adaptive SiLU <adaptive_function/AdaptiveSiLU.rst>
Adaptive Mish <adaptive_function/AdaptiveMish.rst>
Adaptive ELU <adaptive_function/AdaptiveELU.rst>
Adaptive CELU <adaptive_function/AdaptiveCELU.rst>
Adaptive GELU <adaptive_function/AdaptiveGELU.rst>
Adaptive Softmin <adaptive_function/AdaptiveSoftmin.rst>
Adaptive Softmax <adaptive_function/AdaptiveSoftmax.rst>
Adaptive SIREN <adaptive_function/AdaptiveSIREN.rst>
Adaptive Exp <adaptive_function/AdaptiveExp.rst>
.. toctree::
:titlesonly:
EquationInterface <equation/equation_interface.rst>
Equation <equation/equation.rst>
SystemEquation <equation/system_equation.rst>
Equation Factory <equation/equation_factory.rst>
Differential Operators <operator.rst>
.. toctree::
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AbstractProblem <problem/abstract_problem.rst>
InverseProblem <problem/inverse_problem.rst>
ParametricProblem <problem/parametric_problem.rst>
SpatialProblem <problem/spatial_problem.rst>
TimeDependentProblem <problem/time_dependent_problem.rst>
.. toctree::
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AcousticWaveProblem <problem/zoo/acoustic_wave.rst>
AdvectionProblem <problem/zoo/advection.rst>
AllenCahnProblem <problem/zoo/allen_cahn.rst>
DiffusionReactionProblem <problem/zoo/diffusion_reaction.rst>
HelmholtzProblem <problem/zoo/helmholtz.rst>
InversePoisson2DSquareProblem <problem/zoo/inverse_poisson_2d_square.rst>
Poisson2DSquareProblem <problem/zoo/poisson_2d_square.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>