Refactoring solvers (#541)
* Refactoring solvers * Simplify logic compile * Improve and update doc * Create SupervisedSolverInterface * Specialize SupervisedSolver and ReducedOrderModelSolver * Create EnsembleSolverInterface + EnsembleSupervisedSolver * Create tests ensemble solvers * formatter * codacy * fix issues + speedup test
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Dario Coscia
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pina/solver/ensemble_solver/ensemble_pinn.py
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pina/solver/ensemble_solver/ensemble_pinn.py
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"""Module for the DeepEnsemble physics solver."""
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import torch
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from .ensemble_solver_interface import DeepEnsembleSolverInterface
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from ..physics_informed_solver import PINNInterface
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from ...problem import InverseProblem
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class DeepEnsemblePINN(PINNInterface, DeepEnsembleSolverInterface):
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r"""
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Deep Ensemble Physics Informed Solver class. This class implements a
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Deep Ensemble for Physics Informed Neural Networks using user
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specified ``model``s to solve a specific ``problem``.
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An ensemble model is constructed by combining multiple models that solve
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the same type of problem. Mathematically, this creates an implicit
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distribution :math:`p(\mathbf{u} \mid \mathbf{s})` over the possible
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outputs :math:`\mathbf{u}`, given the original input :math:`\mathbf{s}`.
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The models :math:`\mathcal{M}_{i\in (1,\dots,r)}` in
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the ensemble work collaboratively to capture different
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aspects of the data or task, with each model contributing a distinct
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prediction :math:`\mathbf{y}_{i}=\mathcal{M}_i(\mathbf{u} \mid \mathbf{s})`.
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By aggregating these predictions, the ensemble
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model can achieve greater robustness and accuracy compared to individual
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models, leveraging the diversity of the models to reduce overfitting and
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improve generalization. Furthemore, statistical metrics can
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be computed, e.g. the ensemble mean and variance:
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.. math::
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\mathbf{\mu} = \frac{1}{N}\sum_{i=1}^r \mathbf{y}_{i}
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.. math::
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\mathbf{\sigma^2} = \frac{1}{N}\sum_{i=1}^r
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(\mathbf{y}_{i} - \mathbf{\mu})^2
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During training the PINN loss is minimized by each ensemble model:
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.. math::
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\mathcal{L}_{\rm{problem}} = \frac{1}{N}\sum_{i=1}^4
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\mathcal{L}(\mathcal{A}[\mathbf{u}](\mathbf{x}_i)) +
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\frac{1}{N}\sum_{i=1}^N
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\mathcal{L}(\mathcal{B}[\mathbf{u}](\mathbf{x}_i)),
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for the differential system:
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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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:math:`\mathcal{L}` indicates a specific loss function, typically the MSE:
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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**: Zou, Z., Wang, Z., & Karniadakis, G. E. (2025).
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*Learning and discovering multiple solutions using physics-informed
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neural networks with random initialization and deep ensemble*.
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DOI: `arXiv:2503.06320 <https://arxiv.org/abs/2503.06320>`_.
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.. warning::
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This solver does not work with inverse problem. Hence in the ``problem``
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definition must not inherit from
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:class:`~pina.problem.inverse_problem.InverseProblem`.
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"""
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def __init__(
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self,
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problem,
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models,
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loss=None,
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optimizers=None,
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schedulers=None,
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weighting=None,
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ensemble_dim=0,
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):
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"""
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Initialization of the :class:`DeepEnsemblePINN` class.
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:param AbstractProblem problem: The problem to be solved.
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:param torch.nn.Module models: The neural network models to be used.
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:param torch.nn.Module loss: The loss function to be minimized.
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If ``None``, the :class:`torch.nn.MSELoss` loss is used.
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Default is ``None``.
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:param Optimizer optimizer: The optimizer to be used.
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If ``None``, the :class:`torch.optim.Adam` optimizer is used.
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Default is ``None``.
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:param Scheduler scheduler: Learning rate scheduler.
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If ``None``, the :class:`torch.optim.lr_scheduler.ConstantLR`
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scheduler is used. Default is ``None``.
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:param WeightingInterface weighting: The weighting schema to be used.
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If ``None``, no weighting schema is used. Default is ``None``.
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:param int ensemble_dim: The dimension along which the ensemble
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outputs are stacked. Default is 0.
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:raises NotImplementedError: If an inverse problem is passed.
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"""
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if isinstance(problem, InverseProblem):
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raise NotImplementedError(
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"DeepEnsemblePINN can not be used to solve inverse problems."
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)
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super().__init__(
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problem=problem,
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models=models,
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loss=loss,
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optimizers=optimizers,
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schedulers=schedulers,
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weighting=weighting,
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ensemble_dim=ensemble_dim,
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)
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def loss_data(self, input, target):
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"""
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Compute the data loss for the ensemble PINN solver by evaluating
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the loss between the network's output and the true solution for each
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model. This method should not be overridden, if not intentionally.
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:param input: The input to the neural network.
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:type input: LabelTensor | torch.Tensor | Graph | Data
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:param target: The target to compare with the network's output.
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:type target: LabelTensor | torch.Tensor | Graph | Data
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:return: The supervised loss, averaged over the number of observations.
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:rtype: torch.Tensor
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"""
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predictions = self.forward(input)
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loss = sum(
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self._loss_fn(predictions[idx], target)
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for idx in range(self.num_ensemble)
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)
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return loss / self.num_ensemble
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def loss_phys(self, samples, equation):
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"""
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Computes the physics loss for the ensemble PINN solver by evaluating
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the loss between the network's output and the true solution for each
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model. This method should not be overridden, if not intentionally.
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:param LabelTensor samples: The samples to evaluate the physics loss.
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:param EquationInterface equation: The governing equation.
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:return: The computed physics loss.
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:rtype: LabelTensor
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"""
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return self._residual_loss(samples, equation)
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def _residual_loss(self, samples, equation):
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"""
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Computes the physics loss for the physics-informed solver based on the
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provided samples and equation. This method should never be overridden
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by the user, if not intentionally,
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since it is used internally to compute validation loss. It overrides the
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:obj:`~pina.solver.physics_informed_solver.PINNInterface._residual_loss`
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method.
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:param LabelTensor samples: The samples to evaluate the loss.
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:param EquationInterface equation: The governing equation.
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:return: The residual loss.
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:rtype: torch.Tensor
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"""
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loss = 0
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predictions = self.forward(samples)
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for idx in range(self.num_ensemble):
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residuals = equation.residual(samples, predictions[idx])
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target = torch.zeros_like(residuals, requires_grad=True)
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loss = loss + self._loss_fn(residuals, target)
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return loss / self.num_ensemble
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