SupervisedSolver

class SupervisedSolver(problem, model, loss=None, optimizer=None, scheduler=None, weighting=None, use_lt=True)

Bases: SupervisedSolverInterface, SingleSolverInterface

Supervised Solver solver class. This class implements a Supervised Solver, 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 \(\mathbf{u}:\Omega\rightarrow\mathbb{R}^m\).

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

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

where \(\mathcal{L}\) is a specific loss function, typically the MSE:

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

In this context, \(\mathbf{u}_i\) and \(\mathbf{s}_i\) indicates the will to approximate multiple (discretised) functions given multiple (discretised) input functions.

Initialization of the SupervisedSolver class.

Parameters:

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

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

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

• optimizer (Optimizer) – The optimizer to be used. If None, the torch.optim.Adam optimizer is used. Default is None.

• scheduler (Scheduler) – Learning rate scheduler. 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.

• use_lt (bool) – If True, the solver uses LabelTensors as input. Default is True.

loss_data(input, target)

Compute the data loss for the Supervised 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 | torch.Tensor | Graph | Data) – The input to the neural network.

• target (LabelTensor | torch.Tensor | Graph | Data) – The target to compare with the network’s output.

Returns:

The supervised loss, averaged over the number of observations.

Return type:

LabelTensor | torch.Tensor | Graph | Data