120 lines
3.9 KiB
Python
120 lines
3.9 KiB
Python
"""Module for Physics Informed Neural Network."""
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import torch
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from .pinn_interface import PINNInterface
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from ..solver import SingleSolverInterface
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from ...problem import InverseProblem
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class PINN(PINNInterface, SingleSolverInterface):
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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 solver, 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,
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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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optimizer=None,
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scheduler=None,
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weighting=None,
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loss=None,
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):
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"""
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:param torch.nn.Module model: The neural network model to use.
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:param AbstractProblem problem: The formulation of the problem.
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:param torch.optim.Optimizer optimizer: The neural network optimizer to
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use; default `None`.
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:param torch.optim.LRScheduler scheduler: Learning rate scheduler;
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default `None`.
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:param WeightingInterface weighting: The weighting schema to use;
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default `None`.
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:param torch.nn.Module loss: The loss function to be minimized;
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default `None`.
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"""
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super().__init__(
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model=model,
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problem=problem,
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optimizer=optimizer,
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scheduler=scheduler,
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weighting=weighting,
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loss=loss,
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)
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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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return loss_value
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def configure_optimizers(self):
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"""
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Optimizer configuration for the PINN 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 to be optimized.
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self.optimizer.hook(self.model.parameters())
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if isinstance(self.problem, InverseProblem):
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self.optimizer.instance.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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self.scheduler.hook(self.optimizer)
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return ([self.optimizer.instance], [self.scheduler.instance])
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