""" Module for RBAPINN. """
from copy import deepcopy
import torch
from torch.optim.lr_scheduler import ConstantLR
from .pinn import PINN
from ...utils import check_consistency
[docs]
class RBAPINN(PINN):
r"""
Residual-based Attention PINN (RBAPINN) solver class.
This class implements Residual-based Attention 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 Residual-based Attention Physics Informed Neural 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_\Omega}
\lambda_{\Omega}^{i} \mathcal{L} \left( \mathcal{A}
[\mathbf{u}](\mathbf{x}) \right) + \frac{1}{N}
\sum_{i=1}^{N_{\partial\Omega}}
\lambda_{\partial\Omega}^{i} \mathcal{L}
\left( \mathcal{B}[\mathbf{u}](\mathbf{x})
\right),
denoting the weights as
:math:`\lambda_{\Omega}^1, \dots, \lambda_{\Omega}^{N_\Omega}` and
:math:`\lambda_{\partial \Omega}^1, \dots,
\lambda_{\Omega}^{N_\partial \Omega}`
for :math:`\Omega` and :math:`\partial \Omega`, respectively.
Residual-based Attention Physics Informed Neural Network computes
the weights by updating them at every epoch as follows
.. math::
\lambda_i^{k+1} \leftarrow \gamma\lambda_i^{k} +
\eta\frac{\lvert r_i\rvert}{\max_j \lvert r_j\rvert},
where :math:`r_i` denotes the residual at point :math:`i`,
:math:`\gamma` denotes the decay rate, and :math:`\eta` is
the learning rate for the weights' update.
.. seealso::
**Original reference**: Sokratis J. Anagnostopoulos, Juan D. Toscano,
Nikolaos Stergiopulos, and George E. Karniadakis.
"Residual-based attention and connection to information
bottleneck theory in PINNs".
Computer Methods in Applied Mechanics and Engineering 421 (2024): 116805
DOI: `10.1016/
j.cma.2024.116805 <https://doi.org/10.1016/j.cma.2024.116805>`_.
"""
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},
eta=0.001,
gamma=0.999,
):
"""
:param AbstractProblem problem: The formulation of the problem.
:param torch.nn.Module model: The neural network model to use.
:param torch.nn.Module extra_features: The additional input
features to use as augmented input.
:param torch.nn.Module loss: The loss function used as minimizer,
default :class:`torch.nn.MSELoss`.
: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.
:param float | int eta: The learning rate for the
weights of the residual.
:param float gamma: The decay parameter in the update of the weights
of the residual.
"""
super().__init__(
problem=problem,
model=model,
extra_features=extra_features,
loss=loss,
optimizer=optimizer,
optimizer_kwargs=optimizer_kwargs,
scheduler=scheduler,
scheduler_kwargs=scheduler_kwargs,
)
# check consistency
check_consistency(eta, (float, int))
check_consistency(gamma, float)
self.eta = eta
self.gamma = gamma
# initialize weights
self.weights = {}
for condition_name in problem.conditions:
self.weights[condition_name] = 0
# define vectorial loss
self._vectorial_loss = deepcopy(loss)
self._vectorial_loss.reduction = "none"
def _vect_to_scalar(self, loss_value):
"""
Elaboration of the pointwise loss.
:param LabelTensor loss_value: the matrix of pointwise loss.
:return: the scalar loss.
:rtype LabelTensor
"""
if self.loss.reduction == "mean":
ret = torch.mean(loss_value)
elif self.loss.reduction == "sum":
ret = torch.sum(loss_value)
else:
raise RuntimeError(
f"Invalid reduction, got {self.loss.reduction} "
"but expected mean or sum."
)
return ret
[docs]
def loss_phys(self, samples, equation):
"""
Computes the physics loss for the residual-based attention 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)
cond = self.current_condition_name
r_norm = (
self.eta
* torch.abs(residual)
/ (torch.max(torch.abs(residual)) + 1e-12)
)
self.weights[cond] = (self.gamma * self.weights[cond] + r_norm).detach()
loss_value = self._vectorial_loss(
torch.zeros_like(residual, requires_grad=True), residual
)
self.store_log(loss_value=float(self._vect_to_scalar(loss_value)))
return self._vect_to_scalar(self.weights[cond] ** 2 * loss_value)
