SupervisedSolver#

class SupervisedSolver(problem, model, extra_features=None, loss=MSELoss(), optimizer=<class 'torch.optim.adam.Adam'>, optimizer_kwargs={'lr': 0.001}, scheduler=<class 'torch.optim.lr_scheduler.ConstantLR'>, scheduler_kwargs={'factor': 1, 'total_iters': 0})[source]#

Bases: SolverInterface

SupervisedSolver solver class. This class implements a SupervisedSolver, using a user specified model to solve a specific problem.

The Supervised Solver class aims to find a map between the input \(\mathbf{s}:\Omega\rightarrow\mathbb{R}^m\) and the output \(\mathbf{u}:\Omega\rightarrow\mathbb{R}^m\). The input can be discretised in space (as in ROMe2eSolver), or not (e.g. when training Neural Operators).

Given a model \(\mathcal{M}\), the following loss function is minimized during training:

\[\mathcal{L}_{\rm{problem}} = \frac{1}{N}\sum_{i=1}^N \mathcal{L}(\mathbf{u}_i - \mathcal{M}(\mathbf{v}_i))\]

where \(\mathcal{L}\) is a specific loss function, default Mean Square Error:

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

In this context \(\mathbf{u}_i\) and \(\mathbf{v}_i\) means that we are seeking to approximate multiple (discretised) functions given multiple (discretised) input functions.

Parameters:

  • problem (AbstractProblem) – The formualation of the problem.

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

  • loss (torch.nn.Module) – The loss function used as minimizer, default torch.nn.MSELoss.

  • extra_features (torch.nn.Module) – The additional input features to use as augmented input.

  • optimizer (torch.optim.Optimizer) – The neural network optimizer to use; default is torch.optim.Adam.

  • optimizer_kwargs (dict) – Optimizer constructor keyword args.

  • lr (float) – The learning rate; default is 0.001.

  • scheduler (torch.optim.LRScheduler) – Learning rate scheduler.

  • scheduler_kwargs (dict) – LR scheduler constructor keyword args.

forward(x)[source]#

Forward pass implementation for the solver.

Parameters:

x (torch.Tensor) – Input tensor.

Returns:

Solver solution.

Return type:

torch.Tensor

configure_optimizers()[source]#

Optimizer configuration for the solver.

Returns:

The optimizers and the schedulers

Return type:

tuple(list, list)

training_step(batch, batch_idx)[source]#

Solver training step.

Parameters:

  • batch (tuple) – The batch element in the dataloader.

  • batch_idx (int) – The batch index.

Returns:

The sum of the loss functions.

Return type:

LabelTensor

loss_data(input_pts, output_pts)[source]#

The data loss for the Supervised solver. It computes the loss between the network output against the true solution. This function should not be override if not intentionally.

Parameters:

  • input_tensor (LabelTensor) – The input to the neural networks.

  • output_tensor (LabelTensor) – The true solution to compare the network solution.

Returns:

The residual loss averaged on the input coordinates

Return type:

torch.Tensor

property scheduler#

Scheduler for training.

property neural_net#

Neural network for training.

property loss#

Loss for training.