PINN variants addition and Solvers Update (#263)
* gpinn/basepinn new classes, pinn restructure * codacy fix gpinn/basepinn/pinn * inverse problem fix * Causal PINN (#267) * fix GPU training in inverse problem (#283) * Create a `compute_residual` attribute for `PINNInterface` * Modify dataloading in solvers (#286) * Modify PINNInterface by removing _loss_phys, _loss_data * Adding in PINNInterface a variable to track the current condition during training * Modify GPINN,PINN,CausalPINN to match changes in PINNInterface * Competitive Pinn Addition (#288) * fixing after rebase/ fix loss * fixing final issues --------- Co-authored-by: Dario Coscia <dariocoscia@Dario-Coscia.local> * Modify min max formulation to max min for paper consistency * Adding SAPINN solver (#291) * rom solver * fix import --------- Co-authored-by: Dario Coscia <dariocoscia@Dario-Coscia.local> Co-authored-by: Anna Ivagnes <75523024+annaivagnes@users.noreply.github.com> Co-authored-by: valc89 <103250118+valc89@users.noreply.github.com> Co-authored-by: Monthly Tag bot <mtbot@noreply.github.com> Co-authored-by: Nicola Demo <demo.nicola@gmail.com>
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Dario Coscia
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pina/solvers/pinns/pinn.py
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170
pina/solvers/pinns/pinn.py
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""" Module for Physics Informed Neural Network. """
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import torch
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try:
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from torch.optim.lr_scheduler import LRScheduler # torch >= 2.0
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except ImportError:
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from torch.optim.lr_scheduler import (
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_LRScheduler as LRScheduler,
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) # torch < 2.0
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from torch.optim.lr_scheduler import ConstantLR
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from .basepinn import PINNInterface
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from pina.utils import check_consistency
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from pina.problem import InverseProblem
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class PINN(PINNInterface):
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r"""
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Physics Informed Neural Network (PINN) solver class.
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This class implements Physics Informed Neural
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Network solvers, using a user specified ``model`` to solve a specific
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``problem``. It can be used for solving both forward and inverse problems.
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The Physics Informed Network aims to find
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the solution :math:`\mathbf{u}:\Omega\rightarrow\mathbb{R}^m`
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of the differential problem:
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.. math::
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\begin{cases}
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\mathcal{A}[\mathbf{u}](\mathbf{x})=0\quad,\mathbf{x}\in\Omega\\
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\mathcal{B}[\mathbf{u}](\mathbf{x})=0\quad,
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\mathbf{x}\in\partial\Omega
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\end{cases}
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minimizing the loss function
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.. math::
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\mathcal{L}_{\rm{problem}} = \frac{1}{N}\sum_{i=1}^N
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\mathcal{L}(\mathcal{A}[\mathbf{u}](\mathbf{x}_i)) +
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\frac{1}{N}\sum_{i=1}^N
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\mathcal{L}(\mathcal{B}[\mathbf{u}](\mathbf{x}_i))
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where :math:`\mathcal{L}` is a specific loss function, default Mean Square Error:
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.. math::
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\mathcal{L}(v) = \| v \|^2_2.
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.. seealso::
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**Original reference**: Karniadakis, G. E., Kevrekidis, I. G., Lu, L.,
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Perdikaris, P., Wang, S., & Yang, L. (2021).
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Physics-informed machine learning. Nature Reviews Physics, 3, 422-440.
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DOI: `10.1038 <https://doi.org/10.1038/s42254-021-00314-5>`_.
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"""
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def __init__(
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self,
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problem,
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model,
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extra_features=None,
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loss=torch.nn.MSELoss(),
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optimizer=torch.optim.Adam,
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optimizer_kwargs={"lr": 0.001},
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scheduler=ConstantLR,
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scheduler_kwargs={"factor": 1, "total_iters": 0},
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):
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"""
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:param AbstractProblem problem: The formulation of the problem.
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:param torch.nn.Module model: The neural network model to use.
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:param torch.nn.Module loss: The loss function used as minimizer,
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default :class:`torch.nn.MSELoss`.
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:param torch.nn.Module extra_features: The additional input
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features to use as augmented input.
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:param torch.optim.Optimizer optimizer: The neural network optimizer to
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use; default is :class:`torch.optim.Adam`.
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:param dict optimizer_kwargs: Optimizer constructor keyword args.
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:param torch.optim.LRScheduler scheduler: Learning
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rate scheduler.
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:param dict scheduler_kwargs: LR scheduler constructor keyword args.
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"""
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super().__init__(
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models=[model],
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problem=problem,
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optimizers=[optimizer],
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optimizers_kwargs=[optimizer_kwargs],
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extra_features=extra_features,
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loss=loss
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)
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# check consistency
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check_consistency(scheduler, LRScheduler, subclass=True)
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check_consistency(scheduler_kwargs, dict)
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# assign variables
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self._scheduler = scheduler(self.optimizers[0], **scheduler_kwargs)
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self._neural_net = self.models[0]
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def forward(self, x):
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r"""
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Forward pass implementation for the PINN solver. It returns the function
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evaluation :math:`\mathbf{u}(\mathbf{x})` at the control points
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:math:`\mathbf{x}`.
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:param LabelTensor x: Input tensor for the PINN solver. It expects
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a tensor :math:`N \times D`, where :math:`N` the number of points
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in the mesh, :math:`D` the dimension of the problem,
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:return: PINN solution evaluated at contro points.
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:rtype: LabelTensor
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"""
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return self.neural_net(x)
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def loss_phys(self, samples, equation):
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"""
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Computes the physics loss for the PINN solver based on given
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samples and equation.
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:param LabelTensor samples: The samples to evaluate the physics loss.
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:param EquationInterface equation: The governing equation
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representing the physics.
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:return: The physics loss calculated based on given
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samples and equation.
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:rtype: LabelTensor
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"""
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residual = self.compute_residual(samples=samples, equation=equation)
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loss_value = self.loss(
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torch.zeros_like(residual, requires_grad=True), residual
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)
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self.store_log(loss_value=float(loss_value))
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return loss_value
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def configure_optimizers(self):
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"""
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Optimizer configuration for the PINN
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solver.
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:return: The optimizers and the schedulers
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:rtype: tuple(list, list)
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"""
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# if the problem is an InverseProblem, add the unknown parameters
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# to the parameters that the optimizer needs to optimize
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if isinstance(self.problem, InverseProblem):
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self.optimizers[0].add_param_group(
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{
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"params": [
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self._params[var]
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for var in self.problem.unknown_variables
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]
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}
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)
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return self.optimizers, [self.scheduler]
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@property
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def scheduler(self):
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"""
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Scheduler for the PINN training.
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"""
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return self._scheduler
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@property
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def neural_net(self):
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"""
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Neural network for the PINN training.
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"""
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return self._neural_net
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