392 lines
14 KiB
Python
392 lines
14 KiB
Python
"""Module for Self-Adaptive PINN."""
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import torch
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from copy import deepcopy
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from pina.utils import check_consistency
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from pina.problem import InverseProblem
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from ..solver import MultiSolverInterface
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from .pinn_interface import PINNInterface
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class Weights(torch.nn.Module):
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"""
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This class aims to implements the mask model for the
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self-adaptive weights of the Self-Adaptive PINN solver.
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"""
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def __init__(self, func):
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"""
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:param torch.nn.Module func: the mask module of SAPINN.
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"""
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super().__init__()
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check_consistency(func, torch.nn.Module)
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self.sa_weights = torch.nn.Parameter(torch.Tensor())
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self.func = func
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def forward(self):
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"""
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Forward pass implementation for the mask module.
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It returns the function on the weights evaluation.
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:return: evaluation of self adaptive weights through the mask.
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:rtype: torch.Tensor
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"""
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return self.func(self.sa_weights)
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class SelfAdaptivePINN(PINNInterface, MultiSolverInterface):
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r"""
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Self Adaptive Physics Informed Neural Network (SelfAdaptivePINN)
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solver class. This class implements Self-Adaptive 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 Self Adapive Physics Informed Neural 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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integrating the pointwise loss evaluation through a mask :math:`m` and
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self adaptive weights that permit to focus the loss function on
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specific training samples.
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The loss function to solve the problem is
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.. math::
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\mathcal{L}_{\rm{problem}} = \frac{1}{N} \sum_{i=1}^{N_\Omega} m
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\left( \lambda_{\Omega}^{i} \right) \mathcal{L} \left( \mathcal{A}
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[\mathbf{u}](\mathbf{x}) \right) + \frac{1}{N}
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\sum_{i=1}^{N_{\partial\Omega}}
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m \left( \lambda_{\partial\Omega}^{i} \right) \mathcal{L}
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\left( \mathcal{B}[\mathbf{u}](\mathbf{x})
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\right),
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denoting the self adaptive weights as
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:math:`\lambda_{\Omega}^1, \dots, \lambda_{\Omega}^{N_\Omega}` and
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:math:`\lambda_{\partial \Omega}^1, \dots,
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\lambda_{\Omega}^{N_\partial \Omega}`
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for :math:`\Omega` and :math:`\partial \Omega`, respectively.
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Self Adaptive Physics Informed Neural Network identifies the solution
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and appropriate self adaptive weights by solving the following problem
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.. math::
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\min_{w} \max_{\lambda_{\Omega}^k, \lambda_{\partial \Omega}^s}
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\mathcal{L} ,
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where :math:`w` denotes the network parameters, and
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:math:`\mathcal{L}` is a specific loss
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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**: McClenny, Levi D., and Ulisses M. Braga-Neto.
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"Self-adaptive physics-informed neural networks."
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Journal of Computational Physics 474 (2023): 111722.
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DOI: `10.1016/
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j.jcp.2022.111722 <https://doi.org/10.1016/j.jcp.2022.111722>`_.
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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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weight_function=torch.nn.Sigmoid(),
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optimizer_model=None,
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optimizer_weights=None,
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scheduler_model=None,
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scheduler_weights=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 AbstractProblem problem: The formulation of the problem.
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:param torch.nn.Module model: The neural network model to use for
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the model.
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:param torch.nn.Module weight_function: The neural network model
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related to the Self-Adaptive PINN mask; default `torch.nn.Sigmoid()`
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:param torch.optim.Optimizer optimizer_model: The neural network
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optimizer to use for the model network; default `None`.
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:param torch.optim.Optimizer optimizer_weights: The neural network
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optimizer to use for mask model; default `None`.
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:param torch.optim.LRScheduler scheduler_model: Learning rate scheduler
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for the model; default `None`.
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:param torch.optim.LRScheduler scheduler_weights: Learning rate
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scheduler for the mask model; 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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# check consistency weitghs_function
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check_consistency(weight_function, torch.nn.Module)
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# create models for weights
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weights_dict = {}
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for condition_name in problem.conditions:
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weights_dict[condition_name] = Weights(weight_function)
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weights_dict = torch.nn.ModuleDict(weights_dict)
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super().__init__(
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models=[model, weights_dict],
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problem=problem,
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optimizers=[optimizer_model, optimizer_weights],
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schedulers=[scheduler_model, scheduler_weights],
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weighting=weighting,
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loss=loss,
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)
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# Set automatic optimization to False
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self.automatic_optimization = False
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self._vectorial_loss = deepcopy(self.loss)
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self._vectorial_loss.reduction = "none"
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def forward(self, x):
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"""
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Forward pass implementation for the PINN
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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 SAPINN 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.
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:rtype: LabelTensor
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"""
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return self.model(x)
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def training_step(self, batch):
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"""
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Solver training step, overridden to perform manual optimization.
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:param batch: The batch element in the dataloader.
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:type batch: tuple
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:return: The sum of the loss functions.
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:rtype: LabelTensor
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"""
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# Weights optimization
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self.optimizer_weights.instance.zero_grad()
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loss = super().training_step(batch)
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self.manual_backward(-loss)
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self.optimizer_weights.instance.step()
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# Model optimization
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self.optimizer_model.instance.zero_grad()
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loss = super().training_step(batch)
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self.manual_backward(loss)
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self.optimizer_model.instance.step()
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return loss
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def configure_optimizers(self):
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"""
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Optimizer configuration for the SelfAdaptive 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_model.hook(self.model.parameters())
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self.optimizer_weights.hook(self.weights_dict.parameters())
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if isinstance(self.problem, InverseProblem):
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self.optimizer_model.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_model.hook(self.optimizer_model)
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self.scheduler_weights.hook(self.optimizer_weights)
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return (
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[self.optimizer_model.instance, self.optimizer_weights.instance],
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[self.scheduler_model.instance, self.scheduler_weights.instance],
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)
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def on_train_batch_end(self, outputs, batch, batch_idx):
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"""
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This method is called at the end of each training batch, and ovverides
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the PytorchLightining implementation for logging the checkpoints.
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:param torch.Tensor outputs: The output from the model for the
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current batch.
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:param tuple batch: The current batch of data.
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:param int batch_idx: The index of the current batch.
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:return: Whatever is returned by the parent
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method ``on_train_batch_end``.
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:rtype: Any
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"""
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# increase by one the counter of optimization to save loggers
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(
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self.trainer.fit_loop.epoch_loop.manual_optimization.optim_step_progress.total.completed
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) += 1
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return super().on_train_batch_end(outputs, batch, batch_idx)
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def on_train_start(self):
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"""
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This method is called at the start of the training for setting
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the self adaptive weights as parameters of the mask model.
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:return: Whatever is returned by the parent
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method ``on_train_start``.
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:rtype: Any
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"""
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if self.trainer.batch_size is not None:
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raise NotImplementedError(
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"SelfAdaptivePINN only works with full "
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"batch size, set batch_size=None inside "
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"the Trainer to use the solver."
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)
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device = torch.device(
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self.trainer._accelerator_connector._accelerator_flag
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)
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# Initialize the self adaptive weights only for training points
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for (
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condition_name,
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tensor,
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) in self.trainer.data_module.train_dataset.input_points.items():
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self.weights_dict[condition_name].sa_weights.data = torch.rand(
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(tensor.shape[0], 1), device=device
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)
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return super().on_train_start()
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def on_load_checkpoint(self, checkpoint):
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"""
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Override the Pytorch Lightning ``on_load_checkpoint`` to handle
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checkpoints for Self-Adaptive Weights. This method should not be
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overridden if not intentionally.
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:param dict checkpoint: Pytorch Lightning checkpoint dict.
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"""
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# First initialize self-adaptive weights with correct shape,
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# then load the values from the checkpoint.
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for condition_name, _ in self.problem.input_pts.items():
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shape = checkpoint["state_dict"][
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f"_pina_models.1.{condition_name}.sa_weights"
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].shape
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self.weights_dict[condition_name].sa_weights.data = torch.rand(
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shape
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)
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return super().on_load_checkpoint(checkpoint)
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def loss_phys(self, samples, equation):
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"""
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Computation of the physical loss for SelfAdaptive PINN solver.
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:param LabelTensor samples: Input samples to evaluate the physics loss.
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:param EquationInterface equation: the governing equation representing
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the physics.
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:return: tuple with weighted and not weighted scalar loss
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:rtype: List[LabelTensor, LabelTensor]
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"""
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residual = self.compute_residual(samples, equation)
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weights = self.weights_dict[self.current_condition_name].forward()
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loss_value = self._vectorial_loss(
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torch.zeros_like(residual, requires_grad=True), residual
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)
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return self._vect_to_scalar(weights * loss_value)
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def _vect_to_scalar(self, loss_value):
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"""
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Elaboration of the pointwise loss through the mask model and the
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self adaptive weights
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:param LabelTensor loss_value: the matrix of pointwise loss
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:return: the scalar loss
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:rtype LabelTensor
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"""
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if self.loss.reduction == "mean":
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ret = torch.mean(loss_value)
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elif self.loss.reduction == "sum":
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ret = torch.sum(loss_value)
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else:
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raise RuntimeError(
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f"Invalid reduction, got {self.loss.reduction} "
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"but expected mean or sum."
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)
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return ret
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@property
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def model(self):
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"""
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Return the mask models associate to the application of
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the mask to the self adaptive weights for each loss that
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compones the global loss of the problem.
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:return: The ModuleDict for mask models.
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:rtype: torch.nn.ModuleDict
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"""
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return self.models[0]
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@property
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def weights_dict(self):
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"""
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Return the mask models associate to the application of
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the mask to the self adaptive weights for each loss that
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compones the global loss of the problem.
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:return: The ModuleDict for mask models.
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:rtype: torch.nn.ModuleDict
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"""
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return self.models[1]
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@property
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def scheduler_model(self):
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"""
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Returns the scheduler associated with the neural network model.
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:return: The scheduler for the neural network model.
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:rtype: torch.optim.lr_scheduler._LRScheduler
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"""
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return self.schedulers[0]
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@property
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def scheduler_weights(self):
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"""
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Returns the scheduler associated with the mask model (if applicable).
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:return: The scheduler for the mask model.
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:rtype: torch.optim.lr_scheduler._LRScheduler
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"""
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return self.schedulers[1]
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@property
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def optimizer_model(self):
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"""
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Returns the optimizer associated with the neural network model.
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:return: The optimizer for the neural network model.
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:rtype: torch.optim.Optimizer
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"""
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return self.optimizers[0]
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@property
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def optimizer_weights(self):
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"""
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Returns the optimizer associated with the mask model (if applicable).
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:return: The optimizer for the mask model.
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:rtype: torch.optim.Optimizer
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"""
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return self.optimizers[1]
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