Source code for pina.solvers.rom
""" Module for ReducedOrderModelSolver """
import torch
from pina.solvers import SupervisedSolver
[docs]
class ReducedOrderModelSolver(SupervisedSolver):
r"""
ReducedOrderModelSolver solver class. This class implements a
Reduced Order Model solver, using user specified ``reduction_network`` and
``interpolation_network`` to solve a specific ``problem``.
The Reduced Order Model approach aims to find
the solution :math:`\mathbf{u}:\Omega\rightarrow\mathbb{R}^m`
of the differential problem:
.. math::
\begin{cases}
\mathcal{A}[\mathbf{u}(\mu)](\mathbf{x})=0\quad,\mathbf{x}\in\Omega\\
\mathcal{B}[\mathbf{u}(\mu)](\mathbf{x})=0\quad,
\mathbf{x}\in\partial\Omega
\end{cases}
This is done by using two neural networks. The ``reduction_network``, which
contains an encoder :math:`\mathcal{E}_{\rm{net}}`, a decoder
:math:`\mathcal{D}_{\rm{net}}`; and an ``interpolation_network``
:math:`\mathcal{I}_{\rm{net}}`. The input is assumed to be discretised in
the spatial dimensions.
The following loss function is minimized during training
.. math::
\mathcal{L}_{\rm{problem}} = \frac{1}{N}\sum_{i=1}^N
\mathcal{L}(\mathcal{E}_{\rm{net}}[\mathbf{u}(\mu_i)] -
\mathcal{I}_{\rm{net}}[\mu_i]) +
\mathcal{L}(
\mathcal{D}_{\rm{net}}[\mathcal{E}_{\rm{net}}[\mathbf{u}(\mu_i)]] -
\mathbf{u}(\mu_i))
where :math:`\mathcal{L}` is a specific loss function, default Mean Square Error:
.. math::
\mathcal{L}(v) = \| v \|^2_2.
.. seealso::
**Original reference**: Hesthaven, Jan S., and Stefano Ubbiali.
"Non-intrusive reduced order modeling of nonlinear problems
using neural networks." Journal of Computational
Physics 363 (2018): 55-78.
DOI `10.1016/j.jcp.2018.02.037
<https://doi.org/10.1016/j.jcp.2018.02.037>`_.
.. note::
The specified ``reduction_network`` must contain two methods,
namely ``encode`` for input encoding and ``decode`` for decoding the
former result. The ``interpolation_network`` network ``forward`` output
represents the interpolation of the latent space obtain with
``reduction_network.encode``.
.. note::
This solver uses the end-to-end training strategy, i.e. the
``reduction_network`` and ``interpolation_network`` are trained
simultaneously. For reference on this trainig strategy look at:
Pichi, Federico, Beatriz Moya, and Jan S. Hesthaven.
"A graph convolutional autoencoder approach to model order reduction
for parametrized PDEs." Journal of
Computational Physics 501 (2024): 112762.
DOI
`10.1016/j.jcp.2024.112762 <https://doi.org/10.1016/
j.jcp.2024.112762>`_.
.. warning::
This solver works only for data-driven model. Hence in the ``problem``
definition the codition must only contain ``input_points``
(e.g. coefficient parameters, time parameters), and ``output_points``.
.. warning::
This solver does not currently support the possibility to pass
``extra_feature``.
"""
def __init__(
self,
problem,
reduction_network,
interpolation_network,
loss=torch.nn.MSELoss(),
optimizer=torch.optim.Adam,
optimizer_kwargs={"lr": 0.001},
scheduler=torch.optim.lr_scheduler.ConstantLR,
scheduler_kwargs={"factor": 1, "total_iters": 0},
):
"""
:param AbstractProblem problem: The formualation of the problem.
:param torch.nn.Module reduction_network: The reduction network used
for reducing the input space. It must contain two methods,
namely ``encode`` for input encoding and ``decode`` for decoding the
former result.
:param torch.nn.Module interpolation_network: The interpolation network
for interpolating the control parameters to latent space obtain by
the ``reduction_network`` encoding.
:param torch.nn.Module loss: The loss function used as minimizer,
default :class:`torch.nn.MSELoss`.
:param torch.nn.Module extra_features: The additional input
features to use as augmented input.
:param torch.optim.Optimizer optimizer: The neural network optimizer to
use; default is :class:`torch.optim.Adam`.
:param dict optimizer_kwargs: Optimizer constructor keyword args.
:param float lr: The learning rate; default is 0.001.
:param torch.optim.LRScheduler scheduler: Learning
rate scheduler.
:param dict scheduler_kwargs: LR scheduler constructor keyword args.
"""
model = torch.nn.ModuleDict(
{
"reduction_network": reduction_network,
"interpolation_network": interpolation_network,
}
)
super().__init__(
model=model,
problem=problem,
loss=loss,
optimizer=optimizer,
optimizer_kwargs=optimizer_kwargs,
scheduler=scheduler,
scheduler_kwargs=scheduler_kwargs,
)
# assert reduction object contains encode/ decode
if not hasattr(self.neural_net["reduction_network"], "encode"):
raise SyntaxError(
"reduction_network must have encode method. "
"The encode method should return a lower "
"dimensional representation of the input."
)
if not hasattr(self.neural_net["reduction_network"], "decode"):
raise SyntaxError(
"reduction_network must have decode method. "
"The decode method should return a high "
"dimensional representation of the encoding."
)
[docs]
def forward(self, x):
"""
Forward pass implementation for the solver. It finds the encoder
representation by calling ``interpolation_network.forward`` on the
input, and maps this representation to output space by calling
``reduction_network.decode``.
:param torch.Tensor x: Input tensor.
:return: Solver solution.
:rtype: torch.Tensor
"""
reduction_network = self.neural_net["reduction_network"]
interpolation_network = self.neural_net["interpolation_network"]
return reduction_network.decode(interpolation_network(x))
[docs]
def loss_data(self, input_pts, output_pts):
"""
The data loss for the ReducedOrderModelSolver solver.
It computes the loss between
the network output against the true solution. This function
should not be override if not intentionally.
:param LabelTensor input_tensor: The input to the neural networks.
:param LabelTensor output_tensor: The true solution to compare the
network solution.
:return: The residual loss averaged on the input coordinates
:rtype: torch.Tensor
"""
# extract networks
reduction_network = self.neural_net["reduction_network"]
interpolation_network = self.neural_net["interpolation_network"]
# encoded representations loss
encode_repr_inter_net = interpolation_network(input_pts)
encode_repr_reduction_network = reduction_network.encode(output_pts)
loss_encode = self.loss(
encode_repr_inter_net, encode_repr_reduction_network
)
# reconstruction loss
loss_reconstruction = self.loss(
reduction_network.decode(encode_repr_reduction_network), output_pts
)
return loss_encode + loss_reconstruction
@property
def neural_net(self):
"""
Neural network for training. It returns a :obj:`~torch.nn.ModuleDict`
containing the ``reduction_network`` and ``interpolation_network``.
"""
return self._neural_net.torchmodel
