""" Module for Physics Informed Neural Network. """
import torch
try:
from torch.optim.lr_scheduler import LRScheduler # torch >= 2.0
except ImportError:
from torch.optim.lr_scheduler import (
_LRScheduler as LRScheduler,
) # torch < 2.0
from torch.optim.lr_scheduler import ConstantLR
from .basepinn import PINNInterface
from pina.utils import check_consistency
from pina.problem import InverseProblem
[docs]
class PINN(PINNInterface):
r"""
Physics Informed Neural Network (PINN) solver class.
This class implements Physics Informed Neural
Network solvers, using a user specified ``model`` to solve a specific
``problem``. It can be used for solving both forward and inverse problems.
The Physics Informed Network aims to find
the solution :math:`\mathbf{u}:\Omega\rightarrow\mathbb{R}^m`
of the differential problem:
.. math::
\begin{cases}
\mathcal{A}[\mathbf{u}](\mathbf{x})=0\quad,\mathbf{x}\in\Omega\\
\mathcal{B}[\mathbf{u}](\mathbf{x})=0\quad,
\mathbf{x}\in\partial\Omega
\end{cases}
minimizing the loss function
.. math::
\mathcal{L}_{\rm{problem}} = \frac{1}{N}\sum_{i=1}^N
\mathcal{L}(\mathcal{A}[\mathbf{u}](\mathbf{x}_i)) +
\frac{1}{N}\sum_{i=1}^N
\mathcal{L}(\mathcal{B}[\mathbf{u}](\mathbf{x}_i))
where :math:`\mathcal{L}` is a specific loss function, default Mean Square Error:
.. math::
\mathcal{L}(v) = \| v \|^2_2.
.. seealso::
**Original reference**: Karniadakis, G. E., Kevrekidis, I. G., Lu, L.,
Perdikaris, P., Wang, S., & Yang, L. (2021).
Physics-informed machine learning. Nature Reviews Physics, 3, 422-440.
DOI: `10.1038 <https://doi.org/10.1038/s42254-021-00314-5>`_.
"""
def __init__(
self,
problem,
model,
extra_features=None,
loss=torch.nn.MSELoss(),
optimizer=torch.optim.Adam,
optimizer_kwargs={"lr": 0.001},
scheduler=ConstantLR,
scheduler_kwargs={"factor": 1, "total_iters": 0},
):
"""
:param AbstractProblem problem: The formulation of the problem.
:param torch.nn.Module model: The neural network model to use.
:param torch.nn.Module loss: The loss function used as minimizer,
default :class:`torch.nn.MSELoss`.
:param torch.nn.Module extra_features: The additional input
features to use as augmented input.
:param torch.optim.Optimizer optimizer: The neural network optimizer to
use; default is :class:`torch.optim.Adam`.
:param dict optimizer_kwargs: Optimizer constructor keyword args.
:param torch.optim.LRScheduler scheduler: Learning
rate scheduler.
:param dict scheduler_kwargs: LR scheduler constructor keyword args.
"""
super().__init__(
models=[model],
problem=problem,
optimizers=[optimizer],
optimizers_kwargs=[optimizer_kwargs],
extra_features=extra_features,
loss=loss,
)
# check consistency
check_consistency(scheduler, LRScheduler, subclass=True)
check_consistency(scheduler_kwargs, dict)
# assign variables
self._scheduler = scheduler(self.optimizers[0], **scheduler_kwargs)
self._neural_net = self.models[0]
[docs]
def forward(self, x):
r"""
Forward pass implementation for the PINN solver. It returns the function
evaluation :math:`\mathbf{u}(\mathbf{x})` at the control points
:math:`\mathbf{x}`.
:param LabelTensor x: Input tensor for the PINN solver. It expects
a tensor :math:`N \times D`, where :math:`N` the number of points
in the mesh, :math:`D` the dimension of the problem,
:return: PINN solution evaluated at contro points.
:rtype: LabelTensor
"""
return self.neural_net(x)
[docs]
def loss_phys(self, samples, equation):
"""
Computes the physics loss for the PINN solver based on given
samples and equation.
:param LabelTensor samples: The samples to evaluate the physics loss.
:param EquationInterface equation: The governing equation
representing the physics.
:return: The physics loss calculated based on given
samples and equation.
:rtype: LabelTensor
"""
residual = self.compute_residual(samples=samples, equation=equation)
loss_value = self.loss(
torch.zeros_like(residual, requires_grad=True), residual
)
self.store_log(loss_value=float(loss_value))
return loss_value
@property
def scheduler(self):
"""
Scheduler for the PINN training.
"""
return self._scheduler
@property
def neural_net(self):
"""
Neural network for the PINN training.
"""
return self._neural_net