CompetitivePINN

class CompetitivePINN(problem, model, discriminator=None, optimizer_model=None, optimizer_discriminator=None, scheduler_model=None, scheduler_discriminator=None, weighting=None, loss=None)

Bases: PINNInterface, MultiSolverInterface

Competitive Physics-Informed Neural Network (CompetitivePINN) solver class. This class implements the Competitive Physics-Informed Neural Network solver, using a user specified model to solve a specific problem. It can be used to solve both forward and inverse problems.

The Competitive Physics-Informed Neural Network solver aims to find the solution \(\mathbf{u}:\Omega\rightarrow\mathbb{R}^m\) of a differential problem:

\[\begin{split}\begin{cases} \mathcal{A}[\mathbf{u}](\mathbf{x})=0\quad,\mathbf{x}\in\Omega\\ \mathcal{B}[\mathbf{u}](\mathbf{x})=0\quad, \mathbf{x}\in\partial\Omega \end{cases}\end{split}\]

minimizing the loss function with respect to the model parameters, while maximizing it with respect to the discriminator parameters:

\[\mathcal{L}_{\rm{problem}} = \frac{1}{N}\sum_{i=1}^N \mathcal{L}(D(\mathbf{x}_i)\mathcal{A}[\mathbf{u}](\mathbf{x}_i))+ \frac{1}{N}\sum_{i=1}^N \mathcal{L}(D(\mathbf{x}_i)\mathcal{B}[\mathbf{u}](\mathbf{x}_i)),\]

where :math:D is the discriminator network, which identifies the points where the model performs worst, and :math:mathcal{L} is a specific loss function, typically the MSE:

\[\mathcal{L}(v) = \| v \|^2_2.\]

See also

Original reference: Zeng, Qi, et al. Competitive physics informed networks. International Conference on Learning Representations, ICLR 2022 OpenReview Preprint.

Initialization of the CompetitivePINN class.

Parameters:

• problem (AbstractProblem) – The problem to be solved.

• model (torch.nn.Module) – The neural network model to be used.

• discriminator (torch.nn.Module) – The discriminator to be used. If None, the discriminator is a deepcopy of the model. Default is None.

• optimizer_model (torch.optim.Optimizer) – The optimizer of the model. If None, the torch.optim.Adam optimizer is used. Default is None.

• optimizer_discriminator (torch.optim.Optimizer) – The optimizer of the discriminator. If None, the torch.optim.Adam optimizer is used. Default is None.

• scheduler_model (Scheduler) – Learning rate scheduler for the model. If None, the torch.optim.lr_scheduler.ConstantLR scheduler is used. Default is None.

• scheduler_discriminator (Scheduler) – Learning rate scheduler for the discriminator. If None, the torch.optim.lr_scheduler.ConstantLR scheduler is used. Default is None.

• weighting (WeightingInterface) – The weighting schema to be used. If None, no weighting schema is used. Default is None.

• loss (torch.nn.Module) – The loss function to be minimized. If None, the torch.nn.MSELoss loss is used. Default is None.

forward(x)

Forward pass.

Parameters:

x (LabelTensor) – Input tensor.

Returns:

The output of the neural network.

Return type:

LabelTensor

training_step(batch)

Solver training step, overridden to perform manual optimization.

Parameters:

batch (list[tuple[str, dict]]) – A batch of data. Each element is a tuple containing a condition name and a dictionary of points.

Returns:

The aggregated loss.

Return type:

LabelTensor

loss_phys(samples, equation)

Computes the physics loss for the physics-informed solver based on the provided samples and equation.

Parameters:

• samples (LabelTensor) – The samples to evaluate the physics loss.

• equation (EquationInterface) – The governing equation.

Returns:

The computed physics loss.

Return type:

LabelTensor

loss_data(input, target)

Compute the data loss for the PINN solver by evaluating the loss between the network’s output and the true solution. This method should not be overridden, if not intentionally.

Parameters:

• input (LabelTensor) – The input to the neural network.

• target (LabelTensor) – The target to compare with the network’s output.

Returns:

The supervised loss, averaged over the number of observations.

Return type:

LabelTensor

configure_optimizers()

Optimizer configuration.

Returns:

The optimizers and the schedulers

Return type:

tuple[list[Optimizer], list[Scheduler]]

property neural_net

The model.

Returns:

The model.

Return type:

torch.nn.Module

property discriminator

The discriminator.

Returns:

The discriminator.

Return type:

torch.nn.Module

property optimizer_model

The optimizer associated to the model.

Returns:

The optimizer for the model.

Return type:

Optimizer

property optimizer_discriminator

The optimizer associated to the discriminator.

Returns:

The optimizer for the discriminator.

Return type:

Optimizer

property scheduler_model

The scheduler associated to the model.

Returns:

The scheduler for the model.

Return type:

Scheduler

property scheduler_discriminator

The scheduler associated to the discriminator.

Returns:

The scheduler for the discriminator.

Return type:

Scheduler