Add SINDy tutorial

[lorenzotomada]

Description

This PR fixes #661.

Checklist

• Code follows the project’s Code Style Guidelines
• Tests have been added or updated
• Documentation has been updated if necessary
• Pull request is linked to an open issue

[github-actions]

Code Coverage Summary

Filename                                                                  Stmts    Miss  Cover    Missing
----------------------------------------------------------------------  -------  ------  -------  -------------------------------------------------------------------------------------------------------
__init__.py                                                                   7       0  100.00%
graph.py                                                                    114      11  90.35%   99-100, 112, 124, 126, 142, 144, 166, 169, 182, 271
label_tensor.py                                                             251      28  88.84%   81, 121, 144-148, 165, 177, 182, 188-193, 273, 280, 332, 334, 348, 444-447, 490, 537, 629, 664-673, 710
operator.py                                                                  72       2  97.22%   269, 465
trainer.py                                                                   75       5  93.33%   195-204, 293, 314, 318
type_checker.py                                                              22       0  100.00%
utils.py                                                                     73      11  84.93%   59, 75, 141, 178, 181, 184, 220-223, 268
adaptive_function/__init__.py                                                 3       0  100.00%
adaptive_function/adaptive_function.py                                       55       0  100.00%
adaptive_function/adaptive_function_interface.py                             51       6  88.24%   98, 141, 148-151
callback/__init__.py                                                          5       0  100.00%
callback/normalizer_data_callback.py                                         68       1  98.53%   141
callback/optimizer_callback.py                                               23       0  100.00%
callback/processing_callback.py                                              49       5  89.80%   42-43, 73, 168, 171
callback/refinement/__init__.py                                               3       0  100.00%
callback/refinement/r3_refinement.py                                         28       1  96.43%   88
callback/refinement/refinement_interface.py                                  50       5  90.00%   32, 59, 67, 72, 78
condition/__init__.py                                                         7       0  100.00%
condition/condition.py                                                       19       1  94.74%   141
condition/condition_interface.py                                             37       4  89.19%   32, 76, 95, 125
condition/data_condition.py                                                  26       1  96.15%   78
condition/domain_equation_condition.py                                       19       0  100.00%
condition/input_equation_condition.py                                        43       1  97.67%   157
condition/input_target_condition.py                                          44       1  97.73%   172
data/__init__.py                                                              3       0  100.00%
data/data_module.py                                                         201      22  89.05%   41-52, 132, 172, 193, 232, 313-317, 323-327, 399, 466, 546, 637, 639
data/dataset.py                                                              82       7  91.46%   42, 123-126, 256, 293
domain/__init__.py                                                           10       0  100.00%
domain/cartesian.py                                                         112      10  91.07%   37, 47, 75-76, 92, 97, 103, 246, 256, 264
domain/difference_domain.py                                                  25       2  92.00%   54, 87
domain/domain_interface.py                                                   20       5  75.00%   37-41
domain/ellipsoid.py                                                         104      24  76.92%   52, 56, 127, 250-257, 269-282, 286-287, 290, 295
domain/exclusion_domain.py                                                   28       1  96.43%   86
domain/intersection_domain.py                                                28       1  96.43%   85
domain/operation_interface.py                                                26       1  96.15%   88
domain/simplex.py                                                            72      14  80.56%   62, 207-225, 246-247, 251, 256
domain/union_domain.py                                                       25       1  96.00%   43
equation/__init__.py                                                          4       0  100.00%
equation/equation.py                                                         15       1  93.33%   56
equation/equation_factory.py                                                101       1  99.01%   181
equation/equation_interface.py                                                4       0  100.00%
equation/system_equation.py                                                  20       0  100.00%
loss/__init__.py                                                              9       0  100.00%
loss/linear_weighting.py                                                     14       0  100.00%
loss/loss_interface.py                                                       17       2  88.24%   45, 51
loss/lp_loss.py                                                              15       0  100.00%
loss/ntk_weighting.py                                                        18       0  100.00%
loss/power_loss.py                                                           15       0  100.00%
loss/scalar_weighting.py                                                     16       0  100.00%
loss/self_adaptive_weighting.py                                              12       0  100.00%
loss/weighting_interface.py                                                  29       3  89.66%   35, 41-42
model/__init__.py                                                            14       0  100.00%
model/average_neural_operator.py                                             31       2  93.55%   73, 82
model/deeponet.py                                                            93      13  86.02%   187-190, 209, 240, 283, 293, 303, 313, 323, 333, 488, 498
model/equivariant_graph_neural_operator.py                                   51       1  98.04%   217
model/feed_forward.py                                                        89      11  87.64%   58, 195, 200, 278-292
model/fourier_neural_operator.py                                             78      10  87.18%   96-100, 110, 155-159, 218, 220, 242, 342
model/graph_neural_operator.py                                               40       2  95.00%   58, 60
model/kernel_neural_operator.py                                              34       6  82.35%   83-84, 103-104, 123-124
model/low_rank_neural_operator.py                                            27       2  92.59%   89, 98
model/multi_feed_forward.py                                                  12       5  58.33%   25-31
model/pirate_network.py                                                      27       1  96.30%   118
model/sindy.py                                                               21       0  100.00%
model/spline.py                                                              88       6  93.18%   133, 153, 161, 199, 341, 366
model/spline_surface.py                                                      48       7  85.42%   133, 146-151, 191
model/block/__init__.py                                                      13       0  100.00%
model/block/average_neural_operator_block.py                                 12       0  100.00%
model/block/convolution.py                                                   64      13  79.69%   77, 81, 85, 91, 97, 111, 114, 151, 161, 171, 181, 191, 201
model/block/convolution_2d.py                                               146      27  81.51%   155, 162, 282, 314, 379-433, 456
model/block/embedding.py                                                     48       7  85.42%   93, 143-146, 155, 168
model/block/fourier_block.py                                                 31       0  100.00%
model/block/gno_block.py                                                     22       4  81.82%   73-77, 87
model/block/integral.py                                                      18       4  77.78%   22-25, 71
model/block/low_rank_block.py                                                24       0  100.00%
model/block/orthogonal.py                                                    37       0  100.00%
model/block/pirate_network_block.py                                          25       1  96.00%   89
model/block/pod_block.py                                                     75      10  86.67%   56-59, 71, 84, 114, 151-156, 191, 216
model/block/rbf_block.py                                                    179      25  86.03%   18, 42, 53, 64, 75, 86, 97, 223, 280, 282, 298, 301, 329, 335, 363, 367, 511-524
model/block/residual.py                                                      46       0  100.00%
model/block/spectral.py                                                      83       4  95.18%   132, 140, 262, 270
model/block/stride.py                                                        28       7  75.00%   55, 58, 61, 67, 72-74
model/block/utils_convolution.py                                             22       3  86.36%   58-60
model/block/message_passing/__init__.py                                       6       0  100.00%
model/block/message_passing/deep_tensor_network_block.py                     21       0  100.00%
model/block/message_passing/en_equivariant_network_block.py                  47       1  97.87%   164
model/block/message_passing/equivariant_graph_neural_operator_block.py       36       0  100.00%
model/block/message_passing/interaction_network_block.py                     23       0  100.00%
model/block/message_passing/radial_field_network_block.py                    20       0  100.00%
optim/__init__.py                                                             5       0  100.00%
optim/optimizer_interface.py                                                  7       0  100.00%
optim/scheduler_interface.py                                                  7       0  100.00%
optim/torch_optimizer.py                                                     14       0  100.00%
optim/torch_scheduler.py                                                     19       2  89.47%   5-6
problem/__init__.py                                                           6       0  100.00%
problem/abstract_problem.py                                                 117      12  89.74%   39-40, 59-70, 149, 161, 179, 253, 257, 286
problem/inverse_problem.py                                                   22       0  100.00%
problem/parametric_problem.py                                                 8       1  87.50%   29
problem/spatial_problem.py                                                    8       0  100.00%
problem/time_dependent_problem.py                                             8       0  100.00%
problem/zoo/__init__.py                                                       8       0  100.00%
problem/zoo/advection.py                                                     23       4  82.61%   20, 73-75
problem/zoo/allen_cahn.py                                                    23       3  86.96%   20-22
problem/zoo/diffusion_reaction.py                                            32       5  84.38%   103-113
problem/zoo/helmholtz.py                                                     22       4  81.82%   59, 78-82
problem/zoo/inverse_poisson_2d_square.py                                     48       3  93.75%   44-50
problem/zoo/poisson_2d_square.py                                             16       3  81.25%   61-66
problem/zoo/supervised_problem.py                                            11       0  100.00%
solver/__init__.py                                                            6       0  100.00%
solver/garom.py                                                             107       2  98.13%   129-130
solver/solver.py                                                            188      10  94.68%   195, 218, 290, 293-294, 353, 435, 518, 559, 565
solver/ensemble_solver/__init__.py                                            4       0  100.00%
solver/ensemble_solver/ensemble_pinn.py                                      23       1  95.65%   104
solver/ensemble_solver/ensemble_solver_interface.py                          27       0  100.00%
solver/ensemble_solver/ensemble_supervised.py                                 9       0  100.00%
solver/physics_informed_solver/__init__.py                                    8       0  100.00%
solver/physics_informed_solver/causal_pinn.py                                47       3  93.62%   157, 166-167
solver/physics_informed_solver/competitive_pinn.py                           58       0  100.00%
solver/physics_informed_solver/gradient_pinn.py                              17       0  100.00%
solver/physics_informed_solver/pinn.py                                       18       0  100.00%
solver/physics_informed_solver/pinn_interface.py                             54       3  94.44%   75, 166, 222
solver/physics_informed_solver/rba_pinn.py                                   74       1  98.65%   324
solver/physics_informed_solver/self_adaptive_pinn.py                        104       1  99.04%   392
solver/supervised_solver/__init__.py                                          4       0  100.00%
solver/supervised_solver/reduced_order_model.py                              24       1  95.83%   137
solver/supervised_solver/supervised.py                                        7       0  100.00%
solver/supervised_solver/supervised_solver_interface.py                      25       1  96.00%   90
TOTAL                                                                      5056     410  91.89%

Results for commit: df4ea64

Minimum allowed coverage is 80.123%

♻️ This comment has been updated with latest results

[dario-coscia]

Hi Lorenzo! Very nice and informative tutorial, it's great to see sindy in the PINA ecosystem 😃

I have just some minor comments:

1. You wrote twice in the import section import matplotlib.pyplot as plt
2. Use \boldsymbol or \mathbf rather than \bm (not all browsers render it correctly)
3. Remove this (a bit too technical): Disclaimer: here we are assuming that the dynamical system is autonomous, ... be written as autonomous ones
4. In the tutorial you talk about L1 regularization but you are then using weight_decay which enforces L2 regularization, can you change the text accordingly?

Once addressed it can be merged without any problem from my side! Please squash all commits to one commit adding tutorial 23. Thanks again!

[GiovanniCanali]

Hi @lorenzotomada, thank you for your PR. The tutorial is very insightful and easy to follow, making it a valuable contribution to PINA.

In addition to what has been pointed out in the previous review, I would like to suggest some minor style improvements.

[lorenzotomada]

Hi @GiovanniCanali and @dario-coscia , thanks a lot for your feedback! I implemented all the required changes :)

[lorenzotomada]

@dario-coscia regarding L^1 vs L^2 normalization, I wrote this just before the definition of the solver:
Finally, we will use the SupervisedSolver to perform the training as we're dealing with a supervised problem. Recall that we should use $L^1$-regularization on the model's weights to ensure sparsity. For the ease of implementation, we adopt $L^2$ regularization, which is less common in SINDy literature but will suffice in our case..

Is that ok for you or should I update the code?