""" Module for Competitive PINN. """ import torch import copy from pina.problem import InverseProblem from .pinn_interface import PINNInterface from ..solver import MultiSolverInterface class CompetitivePINN(PINNInterface, MultiSolverInterface): r""" Competitive Physics Informed Neural Network (PINN) solver class. This class implements Competitive 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 Competitive 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} with a minimization (on ``model`` parameters) maximation ( on ``discriminator`` parameters) of the loss function .. math:: \mathcal{L}_{\rm{problem}} = \frac{1}{N}\sum_{i=1}^N \mathcal{L}(D(\mathbf{x}_i)\mathcal{A}[\mathbf{u}](\mathbf{x}_i))+ \frac{1}{N}\sum_{i=1}^N \mathcal{L}(D(\mathbf{x}_i)\mathcal{B}[\mathbf{u}](\mathbf{x}_i)) where :math:`D` is the discriminator network, which tries to find the points where the network performs worst, and :math:`\mathcal{L}` is a specific loss function, default Mean Square Error: .. math:: \mathcal{L}(v) = \| v \|^2_2. .. seealso:: **Original reference**: Zeng, Qi, et al. "Competitive physics informed networks." International Conference on Learning Representations, ICLR 2022 `OpenReview Preprint `_. .. warning:: This solver does not currently support the possibility to pass ``extra_feature``. """ def __init__(self, problem, model, discriminator=None, optimizer_model=None, optimizer_discriminator=None, scheduler_model=None, scheduler_discriminator=None, weighting=None, loss=None): """ :param AbstractProblem problem: The formulation of the problem. :param torch.nn.Module model: The neural network model to use for the model. :param torch.nn.Module discriminator: The neural network model to use for the discriminator. If ``None``, the discriminator network will have the same architecture as the model network. :param torch.optim.Optimizer optimizer_model: The neural network optimizer to use for the model network; default `None`. :param torch.optim.Optimizer optimizer_discriminator: The neural network optimizer to use for the discriminator network; default `None`. :param torch.optim.LRScheduler scheduler_model: Learning rate scheduler for the model; default `None`. :param torch.optim.LRScheduler scheduler_discriminator: Learning rate scheduler for the discriminator; default `None`. :param WeightingInterface weighting: The weighting schema to use; default `None`. :param torch.nn.Module loss: The loss function to be minimized; default `None`. """ if discriminator is None: discriminator = copy.deepcopy(model) super().__init__(models=[model, discriminator], problem=problem, optimizers=[optimizer_model, optimizer_discriminator], schedulers=[scheduler_model, scheduler_discriminator], weighting=weighting, loss=loss) # Set automatic optimization to False self.automatic_optimization = False 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) def training_step(self, batch): """ Solver training step, overridden to perform manual optimization. :param batch: The batch element in the dataloader. :type batch: tuple :return: The sum of the loss functions. :rtype: LabelTensor """ self.optimizer_model.instance.zero_grad() self.optimizer_discriminator.instance.zero_grad() loss = super().training_step(batch) self.optimizer_model.instance.step() self.optimizer_discriminator.instance.step() return loss def loss_phys(self, samples, equation): """ Computes the physics loss for the Competitive 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 """ # Train the model for one step with torch.no_grad(): discriminator_bets = self.discriminator(samples) loss_val = self._train_model(samples, equation, discriminator_bets) # Detach samples from the existing computational graph and # create a new one by setting requires_grad to True. # In alternative set `retain_graph=True`. samples = samples.detach() samples.requires_grad_() # Train the discriminator for one step discriminator_bets = self.discriminator(samples) self._train_discriminator(samples, equation, discriminator_bets) return loss_val def loss_data(self, input_pts, output_pts): """ The data loss for the CompetitivePINN solver. It computes the loss between the network output against the true solution. :param LabelTensor input_tensor: The input to the neural networks. :param LabelTensor output_tensor: The true solution to compare the network solution. :return: The computed data loss. :rtype: torch.Tensor """ loss_val = (super().loss_data(input_pts, output_pts)) # prepare for optimizer step called in training step loss_val.backward() return loss_val def configure_optimizers(self): """ Optimizer configuration for the Competitive PINN solver. :return: The optimizers and the schedulers :rtype: tuple(list, list) """ # If the problem is an InverseProblem, add the unknown parameters # to the parameters to be optimized self.optimizer_model.hook(self.neural_net.parameters()) self.optimizer_discriminator.hook(self.discriminator.parameters()) if isinstance(self.problem, InverseProblem): self.optimizer_model.instance.add_param_group( { "params": [ self._params[var] for var in self.problem.unknown_variables ] } ) self.scheduler_model.hook(self.optimizer_model) self.scheduler_discriminator.hook(self.optimizer_discriminator) return ( [self.optimizer_model.instance, self.optimizer_discriminator.instance], [self.scheduler_model.instance, self.scheduler_discriminator.instance] ) def on_train_batch_end(self, outputs, batch, batch_idx): """ This method is called at the end of each training batch, and ovverides the PytorchLightining implementation for logging the checkpoints. :param torch.Tensor outputs: The output from the model for the current batch. :param tuple batch: The current batch of data. :param int batch_idx: The index of the current batch. :return: Whatever is returned by the parent method ``on_train_batch_end``. :rtype: Any """ # increase by one the counter of optimization to save loggers ( self.trainer.fit_loop.epoch_loop.manual_optimization .optim_step_progress.total.completed ) += 1 return super().on_train_batch_end(outputs, batch, batch_idx) def _train_discriminator(self, samples, equation, discriminator_bets): """ Trains the discriminator network of the Competitive PINN. :param LabelTensor samples: Input samples to evaluate the physics loss. :param EquationInterface equation: The governing equation representing the physics. :param Tensor discriminator_bets: Predictions made by the discriminator network. """ # Compute residual. Detach since discriminator weights are fixed residual = self.compute_residual( samples=samples, equation=equation ).detach() # Compute competitive residual, then maximise the loss competitive_residual = residual * discriminator_bets loss_val = -self.loss( torch.zeros_like(competitive_residual, requires_grad=True), competitive_residual, ) # prepare for optimizer step called in training step self.manual_backward(loss_val) return def _train_model(self, samples, equation, discriminator_bets): """ Trains the model network of the Competitive PINN. :param LabelTensor samples: Input samples to evaluate the physics loss. :param EquationInterface equation: The governing equation representing the physics. :param Tensor discriminator_bets: Predictions made by the discriminator. network. :return: The computed data loss. :rtype: torch.Tensor """ # Compute residual residual = self.compute_residual(samples=samples, equation=equation) with torch.no_grad(): loss_residual = self.loss(torch.zeros_like(residual), residual) # Compute competitive residual. Detach discriminator_bets # to optimize only the generator model competitive_residual = residual * discriminator_bets.detach() loss_val = self.loss( torch.zeros_like(competitive_residual, requires_grad=True), competitive_residual, ) # prepare for optimizer step called in training step self.manual_backward(loss_val) return loss_residual @property def neural_net(self): """ Returns the neural network model. :return: The neural network model. :rtype: torch.nn.Module """ return self.models[0] @property def discriminator(self): """ Returns the discriminator model (if applicable). :return: The discriminator model. :rtype: torch.nn.Module """ return self.models[1] @property def optimizer_model(self): """ Returns the optimizer associated with the neural network model. :return: The optimizer for the neural network model. :rtype: torch.optim.Optimizer """ return self.optimizers[0] @property def optimizer_discriminator(self): """ Returns the optimizer associated with the discriminator (if applicable). :return: The optimizer for the discriminator. :rtype: torch.optim.Optimizer """ return self.optimizers[1] @property def scheduler_model(self): """ Returns the scheduler associated with the neural network model. :return: The scheduler for the neural network model. :rtype: torch.optim.lr_scheduler._LRScheduler """ return self.schedulers[0] @property def scheduler_discriminator(self): """ Returns the scheduler associated with the discriminator (if applicable). :return: The scheduler for the discriminator. :rtype: torch.optim.lr_scheduler._LRScheduler """ return self.schedulers[1]