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PINN variants addition and Solvers Update (#263)

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* gpinn/basepinn new classes, pinn restructure
* codacy fix gpinn/basepinn/pinn
* inverse problem fix
* Causal PINN (#267)
* fix GPU training in inverse problem (#283)
* Create a `compute_residual` attribute for `PINNInterface`
* Modify dataloading in solvers (#286)
* Modify PINNInterface by removing _loss_phys, _loss_data
* Adding in PINNInterface a variable to track the current condition during training
* Modify GPINN,PINN,CausalPINN to match changes in PINNInterface
* Competitive Pinn Addition (#288)
* fixing after rebase/ fix loss
* fixing final issues

---------

Co-authored-by: Dario Coscia <dariocoscia@Dario-Coscia.local>

* Modify min max formulation to max min for paper consistency
* Adding SAPINN solver (#291)
* rom solver
* fix import

---------

Co-authored-by: Dario Coscia <dariocoscia@Dario-Coscia.local>
Co-authored-by: Anna Ivagnes <75523024+annaivagnes@users.noreply.github.com>
Co-authored-by: valc89 <103250118+valc89@users.noreply.github.com>
Co-authored-by: Monthly Tag bot <mtbot@noreply.github.com>
Co-authored-by: Nicola Demo <demo.nicola@gmail.com>
This commit is contained in:
Dario Coscia
2024-05-10 14:07:01 +02:00
committed by GitHub
parent 39dc6c4d86
commit e0429bb445
29 changed files with 3837 additions and 357 deletions
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21
pina/solvers/__init__.py
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@@ -1,6 +1,19 @@
__all__ = ["PINN", "GAROM", "SupervisedSolver", "SolverInterface"]
__all__ = [
"SolverInterface",
"PINNInterface",
"PINN",
"GPINN",
"CausalPINN",
"CompetitivePINN",
"SAPINN",
"SupervisedSolver",
"ReducedOrderModelSolver",
"GAROM",
]
from .garom import GAROM
from .pinn import PINN
from .supervised import SupervisedSolver
from .solver import SolverInterface
from .pinns import *
from .supervised import SupervisedSolver
from .rom import ReducedOrderModelSolver
from .garom import GAROM

9
pina/solvers/garom.py
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@@ -253,18 +253,11 @@ class GAROM(SolverInterface):
:rtype: LabelTensor
"""
dataloader = self.trainer.train_dataloader
condition_idx = batch["condition"]
for condition_id in range(condition_idx.min(), condition_idx.max() + 1):
if sys.version_info >= (3, 8):
condition_name = dataloader.condition_names[condition_id]
else:
condition_name = dataloader.loaders.condition_names[
condition_id
]
condition_name = self._dataloader.condition_names[condition_id]
condition = self.problem.conditions[condition_name]
pts = batch["pts"].detach()
out = batch["output"]

232
pina/solvers/pinn.py
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@@ -1,232 +0,0 @@
""" Module for PINN """
import torch
try:
from torch.optim.lr_scheduler import LRScheduler # torch >= 2.0
except ImportError:
from torch.optim.lr_scheduler import (
_LRScheduler as LRScheduler,
) # torch < 2.0
import sys
from torch.optim.lr_scheduler import ConstantLR
from .solver import SolverInterface
from ..label_tensor import LabelTensor
from ..utils import check_consistency
from ..loss import LossInterface
from ..problem import InverseProblem
from torch.nn.modules.loss import _Loss
torch.pi = torch.acos(torch.zeros(1)).item() * 2 # which is 3.1415927410125732
class PINN(SolverInterface):
"""
PINN solver class. This class implements Physics Informed Neural
Network solvers, using a user specified ``model`` to solve a specific
``problem``. It can be used for solving both forward and inverse problems.
.. seealso::
**Original reference**: Karniadakis, G. E., Kevrekidis, I. G., Lu, L.,
Perdikaris, P., Wang, S., & Yang, L. (2021).
Physics-informed machine learning. Nature Reviews Physics, 3(6), 422-440.
<https://doi.org/10.1038/s42254-021-00314-5>`_.
"""
def __init__(
self,
problem,
model,
extra_features=None,
loss=torch.nn.MSELoss(),
optimizer=torch.optim.Adam,
optimizer_kwargs={"lr": 0.001},
scheduler=ConstantLR,
scheduler_kwargs={"factor": 1, "total_iters": 0},
):
"""
:param AbstractProblem problem: The formulation of the problem.
:param torch.nn.Module model: The neural network model to use.
: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 torch.optim.LRScheduler scheduler: Learning
rate scheduler.
:param dict scheduler_kwargs: LR scheduler constructor keyword args.
"""
super().__init__(
models=[model],
problem=problem,
optimizers=[optimizer],
optimizers_kwargs=[optimizer_kwargs],
extra_features=extra_features,
)
# check consistency
check_consistency(scheduler, LRScheduler, subclass=True)
check_consistency(scheduler_kwargs, dict)
check_consistency(loss, (LossInterface, _Loss), subclass=False)
# assign variables
self._scheduler = scheduler(self.optimizers[0], **scheduler_kwargs)
self._loss = loss
self._neural_net = self.models[0]
# inverse problem handling
if isinstance(self.problem, InverseProblem):
self._params = self.problem.unknown_parameters
else:
self._params = None
def forward(self, x):
"""
Forward pass implementation for the PINN
solver.
:param torch.Tensor x: Input tensor.
:return: PINN solution.
:rtype: torch.Tensor
"""
return self.neural_net(x)
def configure_optimizers(self):
"""
Optimizer configuration for the PINN
solver.
:return: The optimizers and the schedulers
:rtype: tuple(list, list)
"""
# if the problem is an InverseProblem, add the unknown parameters
# to the parameters that the optimizer needs to optimize
if isinstance(self.problem, InverseProblem):
self.optimizers[0].add_param_group(
{
"params": [
self._params[var]
for var in self.problem.unknown_variables
]
}
)
return self.optimizers, [self.scheduler]
def _clamp_inverse_problem_params(self):
for v in self._params:
self._params[v].data.clamp_(
self.problem.unknown_parameter_domain.range_[v][0],
self.problem.unknown_parameter_domain.range_[v][1],
)
def _loss_data(self, input, output):
return self.loss(self.forward(input), output)
def _loss_phys(self, samples, equation):
try:
residual = equation.residual(samples, self.forward(samples))
except (
TypeError
): # this occurs when the function has three inputs, i.e. inverse problem
residual = equation.residual(
samples, self.forward(samples), self._params
)
return self.loss(
torch.zeros_like(residual, requires_grad=True), residual
)
def training_step(self, batch, batch_idx):
"""
PINN solver training step.
:param batch: The batch element in the dataloader.
:type batch: tuple
:param batch_idx: The batch index.
:type batch_idx: int
:return: The sum of the loss functions.
:rtype: LabelTensor
"""
dataloader = self.trainer.train_dataloader
condition_losses = []
condition_idx = batch["condition"]
for condition_id in range(condition_idx.min(), condition_idx.max() + 1):
if sys.version_info >= (3, 8):
condition_name = dataloader.condition_names[condition_id]
else:
condition_name = dataloader.loaders.condition_names[
condition_id
]
condition = self.problem.conditions[condition_name]
pts = batch["pts"]
if len(batch) == 2:
samples = pts[condition_idx == condition_id]
loss = self._loss_phys(samples, condition.equation)
elif len(batch) == 3:
samples = pts[condition_idx == condition_id]
ground_truth = batch["output"][condition_idx == condition_id]
loss = self._loss_data(samples, ground_truth)
else:
raise ValueError("Batch size not supported")
# TODO for users this us hard to remember when creating a new solver, to fix in a smarter way
loss = loss.as_subclass(torch.Tensor)
# # add condition losses and accumulate logging for each epoch
condition_losses.append(loss * condition.data_weight)
self.log(
condition_name + "_loss",
float(loss),
prog_bar=True,
logger=True,
on_epoch=True,
on_step=False,
)
# clamp unknown parameters of the InverseProblem to their domain ranges (if needed)
if isinstance(self.problem, InverseProblem):
self._clamp_inverse_problem_params()
# TODO Fix the bug, tot_loss is a label tensor without labels
# we need to pass it as a torch tensor to make everything work
total_loss = sum(condition_losses)
self.log(
"mean_loss",
float(total_loss / len(condition_losses)),
prog_bar=True,
logger=True,
on_epoch=True,
on_step=False,
)
return total_loss
@property
def scheduler(self):
"""
Scheduler for the PINN training.
"""
return self._scheduler
@property
def neural_net(self):
"""
Neural network for the PINN training.
"""
return self._neural_net
@property
def loss(self):
"""
Loss for the PINN training.
"""
return self._loss

15
pina/solvers/pinns/__init__.py Normal file
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@@ -0,0 +1,15 @@
__all__ = [
"PINNInterface",
"PINN",
"GPINN",
"CausalPINN",
"CompetitivePINN",
"SAPINN",
]
from .basepinn import PINNInterface
from .pinn import PINN
from .gpinn import GPINN
from .causalpinn import CausalPINN
from .competitive_pinn import CompetitivePINN
from .sapinn import SAPINN

247
pina/solvers/pinns/basepinn.py Normal file
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@@ -0,0 +1,247 @@
""" Module for PINN """
import sys
from abc import ABCMeta, abstractmethod
import torch
from ...solvers.solver import SolverInterface
from pina.utils import check_consistency
from pina.loss import LossInterface
from pina.problem import InverseProblem
from torch.nn.modules.loss import _Loss
torch.pi = torch.acos(torch.zeros(1)).item() * 2 # which is 3.1415927410125732
class PINNInterface(SolverInterface, metaclass=ABCMeta):
"""
Base PINN solver class. This class implements the Solver Interface
for Physics Informed Neural Network solvers.
This class can be used to
define PINNs with multiple ``optimizers``, and/or ``models``.
By default it takes
an :class:`~pina.problem.abstract_problem.AbstractProblem`, so it is up
to the user to choose which problem the implemented solver inheriting from
this class is suitable for.
"""
def __init__(
self,
models,
problem,
optimizers,
optimizers_kwargs,
extra_features,
loss,
):
"""
:param models: Multiple torch neural network models instances.
:type models: list(torch.nn.Module)
:param problem: A problem definition instance.
:type problem: AbstractProblem
:param list(torch.optim.Optimizer) optimizer: A list of neural network
optimizers to use.
:param list(dict) optimizer_kwargs: A list of optimizer constructor
keyword args.
:param list(torch.nn.Module) extra_features: The additional input
features to use as augmented input. If ``None`` no extra features
are passed. If it is a list of :class:`torch.nn.Module`,
the extra feature list is passed to all models. If it is a list
of extra features' lists, each single list of extra feature
is passed to a model.
:param torch.nn.Module loss: The loss function used as minimizer,
default :class:`torch.nn.MSELoss`.
"""
super().__init__(
models=models,
problem=problem,
optimizers=optimizers,
optimizers_kwargs=optimizers_kwargs,
extra_features=extra_features,
)
# check consistency
check_consistency(loss, (LossInterface, _Loss), subclass=False)
# assign variables
self._loss = loss
# inverse problem handling
if isinstance(self.problem, InverseProblem):
self._params = self.problem.unknown_parameters
self._clamp_params = self._clamp_inverse_problem_params
else:
self._params = None
self._clamp_params = lambda : None
# variable used internally to store residual losses at each epoch
# this variable save the residual at each iteration (not weighted)
self.__logged_res_losses = []
# variable used internally in pina for logging. This variable points to
# the current condition during the training step and returns the
# condition name. Whenever :meth:`store_log` is called the logged
# variable will be stored with name = self.__logged_metric
self.__logged_metric = None
def training_step(self, batch, _):
"""
The Physics Informed Solver Training Step. This function takes care
of the physics informed training step, and it must not be override
if not intentionally. It handles the batching mechanism, the workload
division for the various conditions, the inverse problem clamping,
and loggers.
:param tuple batch: The batch element in the dataloader.
:param int batch_idx: The batch index.
:return: The sum of the loss functions.
:rtype: LabelTensor
"""
condition_losses = []
condition_idx = batch["condition"]
for condition_id in range(condition_idx.min(), condition_idx.max() + 1):
condition_name = self._dataloader.condition_names[condition_id]
condition = self.problem.conditions[condition_name]
pts = batch["pts"]
# condition name is logged (if logs enabled)
self.__logged_metric = condition_name
if len(batch) == 2:
samples = pts[condition_idx == condition_id]
loss = self.loss_phys(samples, condition.equation)
elif len(batch) == 3:
samples = pts[condition_idx == condition_id]
ground_truth = batch["output"][condition_idx == condition_id]
loss = self.loss_data(samples, ground_truth)
else:
raise ValueError("Batch size not supported")
# add condition losses for each epoch
condition_losses.append(loss * condition.data_weight)
# clamp unknown parameters in InverseProblem (if needed)
self._clamp_params()
# total loss (must be a torch.Tensor)
total_loss = sum(condition_losses)
return total_loss.as_subclass(torch.Tensor)
def loss_data(self, input_tensor, output_tensor):
"""
The data loss for the PINN 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
"""
loss_value = self.loss(self.forward(input_tensor), output_tensor)
self.store_log(loss_value=float(loss_value))
return self.loss(self.forward(input_tensor), output_tensor)
@abstractmethod
def loss_phys(self, samples, equation):
"""
Computes the physics loss for the physics informed solver based on given
samples and equation. This method must be override by all inherited
classes and it is the core to define a new physics informed solver.
:param LabelTensor samples: The samples to evaluate the physics loss.
:param EquationInterface equation: The governing equation
representing the physics.
:return: The physics loss calculated based on given
samples and equation.
:rtype: LabelTensor
"""
pass
def compute_residual(self, samples, equation):
"""
Compute the residual for Physics Informed learning. This function
returns the :obj:`~pina.equation.equation.Equation` specified in the
:obj:`~pina.condition.Condition` evaluated at the ``samples`` points.
:param LabelTensor samples: The samples to evaluate the physics loss.
:param EquationInterface equation: The governing equation
representing the physics.
:return: The residual of the neural network solution.
:rtype: LabelTensor
"""
try:
residual = equation.residual(samples, self.forward(samples))
except (
TypeError
): # this occurs when the function has three inputs, i.e. inverse problem
residual = equation.residual(
samples, self.forward(samples), self._params
)
return residual
def store_log(self, loss_value):
"""
Stores the loss value in the logger. This function should be
called for all conditions. It automatically handles the storing
conditions names. It must be used
anytime a specific variable wants to be stored for a specific condition.
A simple example is to use the variable to store the residual.
:param str name: The name of the loss.
:param torch.Tensor loss_value: The value of the loss.
"""
self.log(
self.__logged_metric+'_loss',
loss_value,
prog_bar=True,
logger=True,
on_epoch=True,
on_step=False,
)
self.__logged_res_losses.append(loss_value)
def on_train_epoch_end(self):
"""
At the end of each epoch we free the stored losses. This function
should not be override if not intentionally.
"""
if self.__logged_res_losses:
# storing mean loss
self.__logged_metric = 'mean'
self.store_log(
sum(self.__logged_res_losses)/len(self.__logged_res_losses)
)
# free the logged losses
self.__logged_res_losses = []
return super().on_train_epoch_end()
def _clamp_inverse_problem_params(self):
"""
Clamps the parameters of the inverse problem
solver to the specified ranges.
"""
for v in self._params:
self._params[v].data.clamp_(
self.problem.unknown_parameter_domain.range_[v][0],
self.problem.unknown_parameter_domain.range_[v][1],
)
@property
def loss(self):
"""
Loss used for training.
"""
return self._loss
@property
def current_condition_name(self):
"""
Returns the condition name. This function can be used inside the
:meth:`loss_phys` to extract the condition at which the loss is
computed.
"""
return self.__logged_metric

221
pina/solvers/pinns/causalpinn.py Normal file
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""" Module for CausalPINN """
import torch
from torch.optim.lr_scheduler import ConstantLR
from .pinn import PINN
from pina.problem import TimeDependentProblem
from pina.utils import check_consistency
class CausalPINN(PINN):
r"""
Causal Physics Informed Neural Network (PINN) solver class.
This class implements Causal Physics Informed Neural
Network solvers, using a user specified ``model`` to solve a specific
``problem``. It can be used for solving both forward and inverse problems.
The Causal Physics Informed Network aims to find
the solution :math:`\mathbf{u}:\Omega\rightarrow\mathbb{R}^m`
of the differential problem:
.. math::
\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}
minimizing the loss function
.. math::
\mathcal{L}_{\rm{problem}} = \frac{1}{N_t}\sum_{i=1}^{N_t}
\omega_{i}\mathcal{L}_r(t_i),
where:
.. math::
\mathcal{L}_r(t) = \frac{1}{N}\sum_{i=1}^N
\mathcal{L}(\mathcal{A}[\mathbf{u}](\mathbf{x}_i, t)) +
\frac{1}{N}\sum_{i=1}^N
\mathcal{L}(\mathcal{B}[\mathbf{u}](\mathbf{x}_i, t))
and,
.. math::
\omega_i = \exp\left(\epsilon \sum_{k=1}^{i-1}\mathcal{L}_r(t_k)\right).
:math:`\epsilon` is an hyperparameter, default set to :math:`100`, while
:math:`\mathcal{L}` is a specific loss function,
default Mean Square Error:
.. math::
\mathcal{L}(v) = \| v \|^2_2.
.. seealso::
**Original reference**: Wang, Sifan, Shyam Sankaran, and Paris
Perdikaris. "Respecting causality for training physics-informed
neural networks." Computer Methods in Applied Mechanics
and Engineering 421 (2024): 116813.
DOI `10.1016 <https://doi.org/10.1016/j.cma.2024.116813>`_.
.. note::
This class can only work for problems inheriting
from at least
:class:`~pina.problem.timedep_problem.TimeDependentProblem` class.
"""
def __init__(
self,
problem,
model,
extra_features=None,
loss=torch.nn.MSELoss(),
optimizer=torch.optim.Adam,
optimizer_kwargs={"lr": 0.001},
scheduler=ConstantLR,
scheduler_kwargs={"factor": 1, "total_iters": 0},
eps=100,
):
"""
:param AbstractProblem problem: The formulation of the problem.
:param torch.nn.Module model: The neural network model to use.
: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 torch.optim.LRScheduler scheduler: Learning
rate scheduler.
:param dict scheduler_kwargs: LR scheduler constructor keyword args.
:param int | float eps: The exponential decay parameter. Note that this
value is kept fixed during the training, but can be changed by means
of a callback, e.g. for annealing.
"""
super().__init__(
problem=problem,
model=model,
extra_features=extra_features,
loss=loss,
optimizer=optimizer,
optimizer_kwargs=optimizer_kwargs,
scheduler=scheduler,
scheduler_kwargs=scheduler_kwargs,
)
# checking consistency
check_consistency(eps, (int,float))
self._eps = eps
if not isinstance(self.problem, TimeDependentProblem):
raise ValueError('Casual PINN works only for problems'
'inheritig from TimeDependentProblem.')
def loss_phys(self, samples, equation):
"""
Computes the physics loss for the Causal PINN solver based on given
samples and equation.
:param LabelTensor samples: The samples to evaluate the physics loss.
:param EquationInterface equation: The governing equation
representing the physics.
:return: The physics loss calculated based on given
samples and equation.
:rtype: LabelTensor
"""
# split sequentially ordered time tensors into chunks
chunks, labels = self._split_tensor_into_chunks(samples)
# compute residuals - this correspond to ordered loss functions
# values for each time step. We apply `flatten` such that after
# concataning the residuals we obtain a tensor of shape #chunks
time_loss = []
for chunk in chunks:
chunk.labels = labels
# classical PINN loss
residual = self.compute_residual(samples=chunk, equation=equation)
loss_val = self.loss(
torch.zeros_like(residual, requires_grad=True), residual
)
time_loss.append(loss_val)
# store results
self.store_log(loss_value=float(sum(time_loss)/len(time_loss)))
# concatenate residuals
time_loss = torch.stack(time_loss)
# compute weights (without the gradient storing)
with torch.no_grad():
weights = self._compute_weights(time_loss)
return (weights * time_loss).mean()
@property
def eps(self):
"""
The exponential decay parameter.
"""
return self._eps
@eps.setter
def eps(self, value):
"""
Setter method for the eps parameter.
:param float value: The exponential decay parameter.
"""
check_consistency(value, float)
self._eps = value
def _sort_label_tensor(self, tensor):
"""
Sorts the label tensor based on time variables.
:param LabelTensor tensor: The label tensor to be sorted.
:return: The sorted label tensor based on time variables.
:rtype: LabelTensor
"""
# labels input tensors
labels = tensor.labels
# extract time tensor
time_tensor = tensor.extract(self.problem.temporal_domain.variables)
# sort the time tensors (this is very bad for GPU)
_, idx = torch.sort(time_tensor.tensor.flatten())
tensor = tensor[idx]
tensor.labels = labels
return tensor
def _split_tensor_into_chunks(self, tensor):
"""
Splits the label tensor into chunks based on time.
:param LabelTensor tensor: The label tensor to be split.
:return: Tuple containing the chunks and the original labels.
:rtype: Tuple[List[LabelTensor], List]
"""
# labels input tensors
labels = tensor.labels
# labels input tensors
tensor = self._sort_label_tensor(tensor)
# extract time tensor
time_tensor = tensor.extract(self.problem.temporal_domain.variables)
# count unique tensors in time
_, idx_split = time_tensor.unique(return_counts=True)
# splitting
chunks = torch.split(tensor, tuple(idx_split))
return chunks, labels # return chunks
def _compute_weights(self, loss):
"""
Computes the weights for the physics loss based on the cumulative loss.
:param LabelTensor loss: The physics loss values.
:return: The computed weights for the physics loss.
:rtype: LabelTensor
"""
# compute comulative loss and multiply by epsilos
cumulative_loss = self._eps * torch.cumsum(loss, dim=0)
# return the exponential of the weghited negative cumulative sum
return torch.exp(-cumulative_loss)

360
pina/solvers/pinns/competitive_pinn.py Normal file
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""" Module for CompetitivePINN """
import torch
import copy
try:
from torch.optim.lr_scheduler import LRScheduler # torch >= 2.0
except ImportError:
from torch.optim.lr_scheduler import (
_LRScheduler as LRScheduler,
) # torch < 2.0
from torch.optim.lr_scheduler import ConstantLR
from .basepinn import PINNInterface
from pina.utils import check_consistency
from pina.problem import InverseProblem
class CompetitivePINN(PINNInterface):
r"""
Competitive Physics Informed Neural Network (PINN) solver class.
This class implements Competitive Physics Informed Neural
Network solvers, using a user specified ``model`` to solve a specific
``problem``. It can be used for solving both forward and inverse problems.
The Competitive Physics Informed Network aims to find
the solution :math:`\mathbf{u}:\Omega\rightarrow\mathbb{R}^m`
of the differential problem:
.. math::
\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}
with a minimization (on ``model`` parameters) maximation (
on ``discriminator`` parameters) of the loss function
.. math::
\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 tries to find the points
where the network performs worst, and :math:`\mathcal{L}` is a specific loss
function, default Mean Square Error:
.. math::
\mathcal{L}(v) = \| v \|^2_2.
.. seealso::
**Original reference**: Zeng, Qi, et al.
"Competitive physics informed networks." International Conference on
Learning Representations, ICLR 2022
`OpenReview Preprint <https://openreview.net/forum?id=z9SIj-IM7tn>`_.
.. warning::
This solver does not currently support the possibility to pass
``extra_feature``.
"""
def __init__(
self,
problem,
model,
discriminator=None,
loss=torch.nn.MSELoss(),
optimizer_model=torch.optim.Adam,
optimizer_model_kwargs={"lr": 0.001},
optimizer_discriminator=torch.optim.Adam,
optimizer_discriminator_kwargs={"lr": 0.001},
scheduler_model=ConstantLR,
scheduler_model_kwargs={"factor": 1, "total_iters": 0},
scheduler_discriminator=ConstantLR,
scheduler_discriminator_kwargs={"factor": 1, "total_iters": 0},
):
"""
:param AbstractProblem problem: The formualation of the problem.
:param torch.nn.Module model: The neural network model to use
for the model.
:param torch.nn.Module discriminator: The neural network model to use
for the discriminator. If ``None``, the discriminator network will
have the same architecture as the model network.
:param torch.nn.Module loss: The loss function used as minimizer,
default :class:`torch.nn.MSELoss`.
:param torch.optim.Optimizer optimizer_model: The neural
network optimizer to use for the model network
, default is `torch.optim.Adam`.
:param dict optimizer_model_kwargs: Optimizer constructor keyword
args. for the model.
:param torch.optim.Optimizer optimizer_discriminator: The neural
network optimizer to use for the discriminator network
, default is `torch.optim.Adam`.
:param dict optimizer_discriminator_kwargs: Optimizer constructor
keyword args. for the discriminator.
:param torch.optim.LRScheduler scheduler_model: Learning
rate scheduler for the model.
:param dict scheduler_model_kwargs: LR scheduler constructor
keyword args.
:param torch.optim.LRScheduler scheduler_discriminator: Learning
rate scheduler for the discriminator.
"""
if discriminator is None:
discriminator = copy.deepcopy(model)
super().__init__(
models=[model, discriminator],
problem=problem,
optimizers=[optimizer_model, optimizer_discriminator],
optimizers_kwargs=[
optimizer_model_kwargs,
optimizer_discriminator_kwargs,
],
extra_features=None, # CompetitivePINN doesn't take extra features
loss=loss
)
# set automatic optimization for GANs
self.automatic_optimization = False
# check consistency
check_consistency(scheduler_model, LRScheduler, subclass=True)
check_consistency(scheduler_model_kwargs, dict)
check_consistency(scheduler_discriminator, LRScheduler, subclass=True)
check_consistency(scheduler_discriminator_kwargs, dict)
# assign schedulers
self._schedulers = [
scheduler_model(
self.optimizers[0], **scheduler_model_kwargs
),
scheduler_discriminator(
self.optimizers[1], **scheduler_discriminator_kwargs
),
]
self._model = self.models[0]
self._discriminator = self.models[1]
def forward(self, x):
r"""
Forward pass implementation for the PINN solver. It returns the function
evaluation :math:`\mathbf{u}(\mathbf{x})` at the control points
:math:`\mathbf{x}`.
:param LabelTensor x: Input tensor for the PINN solver. It expects
a tensor :math:`N \times D`, where :math:`N` the number of points
in the mesh, :math:`D` the dimension of the problem,
:return: PINN solution evaluated at contro points.
:rtype: LabelTensor
"""
return self.neural_net(x)
def loss_phys(self, samples, equation):
"""
Computes the physics loss for the Competitive PINN solver based on given
samples and equation.
:param LabelTensor samples: The samples to evaluate the physics loss.
:param EquationInterface equation: The governing equation
representing the physics.
:return: The physics loss calculated based on given
samples and equation.
:rtype: LabelTensor
"""
# train one step of the model
with torch.no_grad():
discriminator_bets = self.discriminator(samples)
loss_val = self._train_model(samples, equation, discriminator_bets)
self.store_log(loss_value=float(loss_val))
# detaching samples from the computational graph to erase it and setting
# the gradient to true to create a new computational graph.
# In alternative set `retain_graph=True`.
samples = samples.detach()
samples.requires_grad = True
# train one step of discriminator
discriminator_bets = self.discriminator(samples)
self._train_discriminator(samples, equation, discriminator_bets)
return loss_val
def loss_data(self, input_tensor, output_tensor):
"""
The data loss for the PINN solver. It computes the loss between the
network output against the true solution.
:param LabelTensor input_tensor: The input to the neural networks.
:param LabelTensor output_tensor: The true solution to compare the
network solution.
:return: The computed data loss.
:rtype: torch.Tensor
"""
self.optimizer_model.zero_grad()
loss_val = super().loss_data(
input_tensor, output_tensor).as_subclass(torch.Tensor)
loss_val.backward()
self.optimizer_model.step()
return loss_val
def configure_optimizers(self):
"""
Optimizer configuration for the Competitive PINN solver.
:return: The optimizers and the schedulers
:rtype: tuple(list, list)
"""
# if the problem is an InverseProblem, add the unknown parameters
# to the parameters that the optimizer needs to optimize
if isinstance(self.problem, InverseProblem):
self.optimizer_model.add_param_group(
{
"params": [
self._params[var]
for var in self.problem.unknown_variables
]
}
)
return self.optimizers, self._schedulers
def on_train_batch_end(self,outputs, batch, batch_idx):
"""
This method is called at the end of each training batch, and ovverides
the PytorchLightining implementation for logging the checkpoints.
:param torch.Tensor outputs: The output from the model for the
current batch.
:param tuple batch: The current batch of data.
:param int batch_idx: The index of the current batch.
:return: Whatever is returned by the parent
method ``on_train_batch_end``.
:rtype: Any
"""
# increase by one the counter of optimization to save loggers
self.trainer.fit_loop.epoch_loop.manual_optimization.optim_step_progress.total.completed += 1
return super().on_train_batch_end(outputs, batch, batch_idx)
def _train_discriminator(self, samples, equation, discriminator_bets):
"""
Trains the discriminator network of the Competitive PINN.
:param LabelTensor samples: Input samples to evaluate the physics loss.
:param EquationInterface equation: The governing equation representing
the physics.
:param Tensor discriminator_bets: Predictions made by the discriminator
network.
"""
# manual optimization
self.optimizer_discriminator.zero_grad()
# compute residual, we detach because the weights of the generator
# model are fixed
residual = self.compute_residual(samples=samples,
equation=equation).detach()
# compute competitive residual, the minus is because we maximise
competitive_residual = residual * discriminator_bets
loss_val = - self.loss(
torch.zeros_like(competitive_residual, requires_grad=True),
competitive_residual
).as_subclass(torch.Tensor)
# backprop
self.manual_backward(loss_val)
self.optimizer_discriminator.step()
return
def _train_model(self, samples, equation, discriminator_bets):
"""
Trains the model network of the Competitive PINN.
:param LabelTensor samples: Input samples to evaluate the physics loss.
:param EquationInterface equation: The governing equation representing
the physics.
:param Tensor discriminator_bets: Predictions made by the discriminator.
network.
:return: The computed data loss.
:rtype: torch.Tensor
"""
# manual optimization
self.optimizer_model.zero_grad()
# compute residual (detached for discriminator) and log
residual = self.compute_residual(samples=samples, equation=equation)
# store logging
with torch.no_grad():
loss_residual = self.loss(
torch.zeros_like(residual),
residual
)
# compute competitive residual, discriminator_bets are detached becase
# we optimize only the generator model
competitive_residual = residual * discriminator_bets.detach()
loss_val = self.loss(
torch.zeros_like(competitive_residual, requires_grad=True),
competitive_residual
).as_subclass(torch.Tensor)
# backprop
self.manual_backward(loss_val)
self.optimizer_model.step()
return loss_residual
@property
def neural_net(self):
"""
Returns the neural network model.
:return: The neural network model.
:rtype: torch.nn.Module
"""
return self._model
@property
def discriminator(self):
"""
Returns the discriminator model (if applicable).
:return: The discriminator model.
:rtype: torch.nn.Module
"""
return self._discriminator
@property
def optimizer_model(self):
"""
Returns the optimizer associated with the neural network model.
:return: The optimizer for the neural network model.
:rtype: torch.optim.Optimizer
"""
return self.optimizers[0]
@property
def optimizer_discriminator(self):
"""
Returns the optimizer associated with the discriminator (if applicable).
:return: The optimizer for the discriminator.
:rtype: torch.optim.Optimizer
"""
return self.optimizers[1]
@property
def scheduler_model(self):
"""
Returns the scheduler associated with the neural network model.
:return: The scheduler for the neural network model.
:rtype: torch.optim.lr_scheduler._LRScheduler
"""
return self._schedulers[0]
@property
def scheduler_discriminator(self):
"""
Returns the scheduler associated with the discriminator (if applicable).
:return: The scheduler for the discriminator.
:rtype: torch.optim.lr_scheduler._LRScheduler
"""
return self._schedulers[1]

134
pina/solvers/pinns/gpinn.py Normal file
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@@ -0,0 +1,134 @@
""" Module for GPINN """
import torch
from torch.optim.lr_scheduler import ConstantLR
from .pinn import PINN
from pina.operators import grad
from pina.problem import SpatialProblem
class GPINN(PINN):
r"""
Gradient Physics Informed Neural Network (GPINN) solver class.
This class implements Gradient Physics Informed Neural
Network solvers, using a user specified ``model`` to solve a specific
``problem``. It can be used for solving both forward and inverse problems.
The Gradient Physics Informed Network aims to find
the solution :math:`\mathbf{u}:\Omega\rightarrow\mathbb{R}^m`
of the differential problem:
.. math::
\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}
minimizing the loss function
.. math::
\mathcal{L}_{\rm{problem}} =& \frac{1}{N}\sum_{i=1}^N
\mathcal{L}(\mathcal{A}[\mathbf{u}](\mathbf{x}_i)) +
\frac{1}{N}\sum_{i=1}^N
\mathcal{L}(\mathcal{B}[\mathbf{u}](\mathbf{x}_i)) + \\
&\frac{1}{N}\sum_{i=1}^N
\nabla_{\mathbf{x}}\mathcal{L}(\mathcal{A}[\mathbf{u}](\mathbf{x}_i)) +
\frac{1}{N}\sum_{i=1}^N
\nabla_{\mathbf{x}}\mathcal{L}(\mathcal{B}[\mathbf{u}](\mathbf{x}_i))
where :math:`\mathcal{L}` is a specific loss function, default Mean Square Error:
.. math::
\mathcal{L}(v) = \| v \|^2_2.
.. seealso::
**Original reference**: Yu, Jeremy, et al. "Gradient-enhanced
physics-informed neural networks for forward and inverse
PDE problems." Computer Methods in Applied Mechanics
and Engineering 393 (2022): 114823.
DOI: `10.1016 <https://doi.org/10.1016/j.cma.2022.114823>`_.
.. note::
This class can only work for problems inheriting
from at least :class:`~pina.problem.spatial_problem.SpatialProblem`
class.
"""
def __init__(
self,
problem,
model,
extra_features=None,
loss=torch.nn.MSELoss(),
optimizer=torch.optim.Adam,
optimizer_kwargs={"lr": 0.001},
scheduler=ConstantLR,
scheduler_kwargs={"factor": 1, "total_iters": 0},
):
"""
:param AbstractProblem problem: The formulation of the problem. It must
inherit from at least
:class:`~pina.problem.spatial_problem.SpatialProblem` in order to
compute the gradient of the loss.
:param torch.nn.Module model: The neural network model to use.
: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 torch.optim.LRScheduler scheduler: Learning
rate scheduler.
:param dict scheduler_kwargs: LR scheduler constructor keyword args.
"""
super().__init__(
problem=problem,
model=model,
extra_features=extra_features,
loss=loss,
optimizer=optimizer,
optimizer_kwargs=optimizer_kwargs,
scheduler=scheduler,
scheduler_kwargs=scheduler_kwargs,
)
if not isinstance(self.problem, SpatialProblem):
raise ValueError('Gradient PINN computes the gradient of the '
'PINN loss with respect to the spatial '
'coordinates, thus the PINA problem must be '
'a SpatialProblem.')
def loss_phys(self, samples, equation):
"""
Computes the physics loss for the GPINN solver based on given
samples and equation.
:param LabelTensor samples: The samples to evaluate the physics loss.
:param EquationInterface equation: The governing equation
representing the physics.
:return: The physics loss calculated based on given
samples and equation.
:rtype: LabelTensor
"""
# classical PINN loss
residual = self.compute_residual(samples=samples, equation=equation)
loss_value = self.loss(
torch.zeros_like(residual, requires_grad=True), residual
)
self.store_log(loss_value=float(loss_value))
# gradient PINN loss
loss_value = loss_value.reshape(-1, 1)
loss_value.labels = ['__LOSS']
loss_grad = grad(loss_value, samples, d=self.problem.spatial_variables)
g_loss_phys = self.loss(
torch.zeros_like(loss_grad, requires_grad=True), loss_grad
)
return loss_value + g_loss_phys

170
pina/solvers/pinns/pinn.py Normal file
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""" Module for Physics Informed Neural Network. """
import torch
try:
from torch.optim.lr_scheduler import LRScheduler # torch >= 2.0
except ImportError:
from torch.optim.lr_scheduler import (
_LRScheduler as LRScheduler,
) # torch < 2.0
from torch.optim.lr_scheduler import ConstantLR
from .basepinn import PINNInterface
from pina.utils import check_consistency
from pina.problem import InverseProblem
class PINN(PINNInterface):
r"""
Physics Informed Neural Network (PINN) solver class.
This class implements Physics Informed Neural
Network solvers, using a user specified ``model`` to solve a specific
``problem``. It can be used for solving both forward and inverse problems.
The Physics Informed Network aims to find
the solution :math:`\mathbf{u}:\Omega\rightarrow\mathbb{R}^m`
of the differential problem:
.. math::
\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}
minimizing the loss function
.. math::
\mathcal{L}_{\rm{problem}} = \frac{1}{N}\sum_{i=1}^N
\mathcal{L}(\mathcal{A}[\mathbf{u}](\mathbf{x}_i)) +
\frac{1}{N}\sum_{i=1}^N
\mathcal{L}(\mathcal{B}[\mathbf{u}](\mathbf{x}_i))
where :math:`\mathcal{L}` is a specific loss function, default Mean Square Error:
.. math::
\mathcal{L}(v) = \| v \|^2_2.
.. seealso::
**Original reference**: Karniadakis, G. E., Kevrekidis, I. G., Lu, L.,
Perdikaris, P., Wang, S., & Yang, L. (2021).
Physics-informed machine learning. Nature Reviews Physics, 3, 422-440.
DOI: `10.1038 <https://doi.org/10.1038/s42254-021-00314-5>`_.
"""
def __init__(
self,
problem,
model,
extra_features=None,
loss=torch.nn.MSELoss(),
optimizer=torch.optim.Adam,
optimizer_kwargs={"lr": 0.001},
scheduler=ConstantLR,
scheduler_kwargs={"factor": 1, "total_iters": 0},
):
"""
:param AbstractProblem problem: The formulation of the problem.
:param torch.nn.Module model: The neural network model to use.
: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 torch.optim.LRScheduler scheduler: Learning
rate scheduler.
:param dict scheduler_kwargs: LR scheduler constructor keyword args.
"""
super().__init__(
models=[model],
problem=problem,
optimizers=[optimizer],
optimizers_kwargs=[optimizer_kwargs],
extra_features=extra_features,
loss=loss
)
# check consistency
check_consistency(scheduler, LRScheduler, subclass=True)
check_consistency(scheduler_kwargs, dict)
# assign variables
self._scheduler = scheduler(self.optimizers[0], **scheduler_kwargs)
self._neural_net = self.models[0]
def forward(self, x):
r"""
Forward pass implementation for the PINN solver. It returns the function
evaluation :math:`\mathbf{u}(\mathbf{x})` at the control points
:math:`\mathbf{x}`.
:param LabelTensor x: Input tensor for the PINN solver. It expects
a tensor :math:`N \times D`, where :math:`N` the number of points
in the mesh, :math:`D` the dimension of the problem,
:return: PINN solution evaluated at contro points.
:rtype: LabelTensor
"""
return self.neural_net(x)
def loss_phys(self, samples, equation):
"""
Computes the physics loss for the PINN solver based on given
samples and equation.
:param LabelTensor samples: The samples to evaluate the physics loss.
:param EquationInterface equation: The governing equation
representing the physics.
:return: The physics loss calculated based on given
samples and equation.
:rtype: LabelTensor
"""
residual = self.compute_residual(samples=samples, equation=equation)
loss_value = self.loss(
torch.zeros_like(residual, requires_grad=True), residual
)
self.store_log(loss_value=float(loss_value))
return loss_value
def configure_optimizers(self):
"""
Optimizer configuration for the PINN
solver.
:return: The optimizers and the schedulers
:rtype: tuple(list, list)
"""
# if the problem is an InverseProblem, add the unknown parameters
# to the parameters that the optimizer needs to optimize
if isinstance(self.problem, InverseProblem):
self.optimizers[0].add_param_group(
{
"params": [
self._params[var]
for var in self.problem.unknown_variables
]
}
)
return self.optimizers, [self.scheduler]
@property
def scheduler(self):
"""
Scheduler for the PINN training.
"""
return self._scheduler
@property
def neural_net(self):
"""
Neural network for the PINN training.
"""
return self._neural_net

494
pina/solvers/pinns/sapinn.py Normal file
View File

@@ -0,0 +1,494 @@
import torch
from copy import deepcopy
try:
from torch.optim.lr_scheduler import LRScheduler # torch >= 2.0
except ImportError:
from torch.optim.lr_scheduler import (
_LRScheduler as LRScheduler,
) # torch < 2.0
from .basepinn import PINNInterface
from pina.utils import check_consistency
from pina.problem import InverseProblem
from torch.optim.lr_scheduler import ConstantLR
class Weights(torch.nn.Module):
"""
This class aims to implements the mask model for
self adaptive weights of the Self-Adaptive
PINN solver.
"""
def __init__(self, func):
"""
:param torch.nn.Module func: the mask module of SAPINN
"""
super().__init__()
check_consistency(func, torch.nn.Module)
self.sa_weights = torch.nn.Parameter(
torch.Tensor()
)
self.func = func
def forward(self):
"""
Forward pass implementation for the mask module.
It returns the function on the weights
evaluation.
:return: evaluation of self adaptive weights through the mask.
:rtype: torch.Tensor
"""
return self.func(self.sa_weights)
class SAPINN(PINNInterface):
r"""
Self Adaptive Physics Informed Neural Network (SAPINN) solver class.
This class implements Self-Adaptive Physics Informed Neural
Network solvers, using a user specified ``model`` to solve a specific
``problem``. It can be used for solving both forward and inverse problems.
The Self Adapive Physics Informed Neural Network aims to find
the solution :math:`\mathbf{u}:\Omega\rightarrow\mathbb{R}^m`
of the differential problem:
.. math::
\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}
integrating the pointwise loss evaluation through a mask :math:`m` and
self adaptive weights that permit to focus the loss function on
specific training samples.
The loss function to solve the problem is
.. math::
\mathcal{L}_{\rm{problem}} = \frac{1}{N} \sum_{i=1}^{N_\Omega} m
\left( \lambda_{\Omega}^{i} \right) \mathcal{L} \left( \mathcal{A}
[\mathbf{u}](\mathbf{x}) \right) + \frac{1}{N}
\sum_{i=1}^{N_{\partial\Omega}}
m \left( \lambda_{\partial\Omega}^{i} \right) \mathcal{L}
\left( \mathcal{B}[\mathbf{u}](\mathbf{x})
\right),
denoting the self adaptive weights as
:math:`\lambda_{\Omega}^1, \dots, \lambda_{\Omega}^{N_\Omega}` and
:math:`\lambda_{\partial \Omega}^1, \dots,
\lambda_{\Omega}^{N_\partial \Omega}`
for :math:`\Omega` and :math:`\partial \Omega`, respectively.
Self Adaptive Physics Informed Neural Network identifies the solution
and appropriate self adaptive weights by solving the following problem
.. math::
\min_{w} \max_{\lambda_{\Omega}^k, \lambda_{\partial \Omega}^s}
\mathcal{L} ,
where :math:`w` denotes the network parameters, and
:math:`\mathcal{L}` is a specific loss
function, default Mean Square Error:
.. math::
\mathcal{L}(v) = \| v \|^2_2.
.. seealso::
**Original reference**: McClenny, Levi D., and Ulisses M. Braga-Neto.
"Self-adaptive physics-informed neural networks."
Journal of Computational Physics 474 (2023): 111722.
DOI: `10.1016/
j.jcp.2022.111722 <https://doi.org/10.1016/j.jcp.2022.111722>`_.
"""
def __init__(
self,
problem,
model,
weights_function=torch.nn.Sigmoid(),
extra_features=None,
loss=torch.nn.MSELoss(),
optimizer_model=torch.optim.Adam,
optimizer_model_kwargs={"lr" : 0.001},
optimizer_weights=torch.optim.Adam,
optimizer_weights_kwargs={"lr" : 0.001},
scheduler_model=ConstantLR,
scheduler_model_kwargs={"factor" : 1, "total_iters" : 0},
scheduler_weights=ConstantLR,
scheduler_weights_kwargs={"factor" : 1, "total_iters" : 0}
):
"""
:param AbstractProblem problem: The formualation of the problem.
:param torch.nn.Module model: The neural network model to use
for the model.
:param torch.nn.Module weights_function: The neural network model
related to the mask of SAPINN.
default :obj:`~torch.nn.Sigmoid`.
:param list(torch.nn.Module) extra_features: The additional input
features to use as augmented input. If ``None`` no extra features
are passed. If it is a list of :class:`torch.nn.Module`,
the extra feature list is passed to all models. If it is a list
of extra features' lists, each single list of extra feature
is passed to a model.
:param torch.nn.Module loss: The loss function used as minimizer,
default :class:`torch.nn.MSELoss`.
:param torch.optim.Optimizer optimizer_model: The neural
network optimizer to use for the model network
, default is `torch.optim.Adam`.
:param dict optimizer_model_kwargs: Optimizer constructor keyword
args. for the model.
:param torch.optim.Optimizer optimizer_weights: The neural
network optimizer to use for mask model model,
default is `torch.optim.Adam`.
:param dict optimizer_weights_kwargs: Optimizer constructor
keyword args. for the mask module.
:param torch.optim.LRScheduler scheduler_model: Learning
rate scheduler for the model.
:param dict scheduler_model_kwargs: LR scheduler constructor
keyword args.
:param torch.optim.LRScheduler scheduler_weights: Learning
rate scheduler for the mask model.
:param dict scheduler_model_kwargs: LR scheduler constructor
keyword args.
"""
# check consistency weitghs_function
check_consistency(weights_function, torch.nn.Module)
# create models for weights
weights_dict = {}
for condition_name in problem.conditions:
weights_dict[condition_name] = Weights(weights_function)
weights_dict = torch.nn.ModuleDict(weights_dict)
super().__init__(
models=[model, weights_dict],
problem=problem,
optimizers=[optimizer_model, optimizer_weights],
optimizers_kwargs=[
optimizer_model_kwargs,
optimizer_weights_kwargs
],
extra_features=extra_features,
loss=loss
)
# set automatic optimization
self.automatic_optimization = False
# check consistency
check_consistency(scheduler_model, LRScheduler, subclass=True)
check_consistency(scheduler_model_kwargs, dict)
check_consistency(scheduler_weights, LRScheduler, subclass=True)
check_consistency(scheduler_weights_kwargs, dict)
# assign schedulers
self._schedulers = [
scheduler_model(
self.optimizers[0], **scheduler_model_kwargs
),
scheduler_weights(
self.optimizers[1], **scheduler_weights_kwargs
),
]
self._model = self.models[0]
self._weights = self.models[1]
self._vectorial_loss = deepcopy(loss)
self._vectorial_loss.reduction = "none"
def forward(self, x):
"""
Forward pass implementation for the PINN
solver. It returns the function
evaluation :math:`\mathbf{u}(\mathbf{x})` at the control points
:math:`\mathbf{x}`.
:param LabelTensor x: Input tensor for the SAPINN solver. It expects
a tensor :math:`N \\times D`, where :math:`N` the number of points
in the mesh, :math:`D` the dimension of the problem,
:return: PINN solution.
:rtype: LabelTensor
"""
return self.neural_net(x)
def loss_phys(self, samples, equation):
"""
Computes the physics loss for the SAPINN solver based on given
samples and equation.
:param LabelTensor samples: The samples to evaluate the physics loss.
:param EquationInterface equation: The governing equation
representing the physics.
:return: The physics loss calculated based on given
samples and equation.
:rtype: torch.Tensor
"""
# train weights
self.optimizer_weights.zero_grad()
weighted_loss, _ = self._loss_phys(samples, equation)
loss_value = - weighted_loss.as_subclass(torch.Tensor)
self.manual_backward(loss_value)
self.optimizer_weights.step()
# detaching samples from the computational graph to erase it and setting
# the gradient to true to create a new computational graph.
# In alternative set `retain_graph=True`.
samples = samples.detach()
samples.requires_grad = True
# train model
self.optimizer_model.zero_grad()
weighted_loss, loss = self._loss_phys(samples, equation)
loss_value = weighted_loss.as_subclass(torch.Tensor)
self.manual_backward(loss_value)
self.optimizer_model.step()
# store loss without weights
self.store_log(loss_value=float(loss))
return loss_value
def loss_data(self, input_tensor, output_tensor):
"""
Computes the data loss for the SAPINN solver based on input and
output. It computes the loss between the
network output against the true solution.
:param LabelTensor input_tensor: The input to the neural networks.
:param LabelTensor output_tensor: The true solution to compare the
network solution.
:return: The computed data loss.
:rtype: torch.Tensor
"""
# train weights
self.optimizer_weights.zero_grad()
weighted_loss, _ = self._loss_data(input_tensor, output_tensor)
loss_value = - weighted_loss.as_subclass(torch.Tensor)
self.manual_backward(loss_value)
self.optimizer_weights.step()
# detaching samples from the computational graph to erase it and setting
# the gradient to true to create a new computational graph.
# In alternative set `retain_graph=True`.
input_tensor = input_tensor.detach()
input_tensor.requires_grad = True
# train model
self.optimizer_model.zero_grad()
weighted_loss, loss = self._loss_data(input_tensor, output_tensor)
loss_value = weighted_loss.as_subclass(torch.Tensor)
self.manual_backward(loss_value)
self.optimizer_model.step()
# store loss without weights
self.store_log(loss_value=float(loss))
return loss_value
def configure_optimizers(self):
"""
Optimizer configuration for the SAPINN
solver.
:return: The optimizers and the schedulers
:rtype: tuple(list, list)
"""
# if the problem is an InverseProblem, add the unknown parameters
# to the parameters that the optimizer needs to optimize
if isinstance(self.problem, InverseProblem):
self.optimizers[0].add_param_group(
{
"params": [
self._params[var]
for var in self.problem.unknown_variables
]
}
)
return self.optimizers, self._schedulers
def on_train_batch_end(self,outputs, batch, batch_idx):
"""
This method is called at the end of each training batch, and ovverides
the PytorchLightining implementation for logging the checkpoints.
:param torch.Tensor outputs: The output from the model for the
current batch.
:param tuple batch: The current batch of data.
:param int batch_idx: The index of the current batch.
:return: Whatever is returned by the parent
method ``on_train_batch_end``.
:rtype: Any
"""
# increase by one the counter of optimization to save loggers
self.trainer.fit_loop.epoch_loop.manual_optimization.optim_step_progress.total.completed += 1
return super().on_train_batch_end(outputs, batch, batch_idx)
def on_train_start(self):
"""
This method is called at the start of the training for setting
the self adaptive weights as parameters of the mask model.
:return: Whatever is returned by the parent
method ``on_train_start``.
:rtype: Any
"""
device = torch.device(
self.trainer._accelerator_connector._accelerator_flag
)
for condition_name, tensor in self.problem.input_pts.items():
self.weights_dict.torchmodel[condition_name].sa_weights.data = torch.rand(
(tensor.shape[0], 1),
device = device
)
return super().on_train_start()
def on_load_checkpoint(self, checkpoint):
"""
Overriding the Pytorch Lightning ``on_load_checkpoint`` to handle
checkpoints for Self Adaptive Weights. This method should not be
overridden if not intentionally.
:param dict checkpoint: Pytorch Lightning checkpoint dict.
"""
for condition_name, tensor in self.problem.input_pts.items():
self.weights_dict.torchmodel[condition_name].sa_weights.data = torch.rand(
(tensor.shape[0], 1)
)
return super().on_load_checkpoint(checkpoint)
def _loss_phys(self, samples, equation):
"""
Elaboration of the physical loss for the SAPINN solver.
:param LabelTensor samples: Input samples to evaluate the physics loss.
:param EquationInterface equation: the governing equation representing
the physics.
:return: tuple with weighted and not weighted scalar loss
:rtype: List[LabelTensor, LabelTensor]
"""
residual = self.compute_residual(samples, equation)
return self._compute_loss(residual)
def _loss_data(self, input_tensor, output_tensor):
"""
Elaboration of the loss related to data for the SAPINN solver.
:param LabelTensor input_tensor: The input to the neural networks.
:param LabelTensor output_tensor: The true solution to compare the
network solution.
:return: tuple with weighted and not weighted scalar loss
:rtype: List[LabelTensor, LabelTensor]
"""
residual = self.forward(input_tensor) - output_tensor
return self._compute_loss(residual)
def _compute_loss(self, residual):
"""
Elaboration of the pointwise loss through the mask model and the
self adaptive weights
:param LabelTensor residual: the matrix of residuals that have to
be weighted
:return: tuple with weighted and not weighted loss
:rtype List[LabelTensor, LabelTensor]
"""
weights = self.weights_dict.torchmodel[
self.current_condition_name].forward()
loss_value = self._vectorial_loss(torch.zeros_like(
residual, requires_grad=True), residual)
return (
self._vect_to_scalar(weights * loss_value),
self._vect_to_scalar(loss_value)
)
def _vect_to_scalar(self, loss_value):
"""
Elaboration of the pointwise loss through the mask model and the
self adaptive weights
:param LabelTensor loss_value: the matrix of pointwise loss
:return: the scalar loss
:rtype LabelTensor
"""
if self.loss.reduction == "mean":
ret = torch.mean(loss_value)
elif self.loss.reduction == "sum":
ret = torch.sum(loss_value)
else:
raise RuntimeError(f"Invalid reduction, got {self.loss.reduction} "
"but expected mean or sum.")
return ret
@property
def neural_net(self):
"""
Returns the neural network model.
:return: The neural network model.
:rtype: torch.nn.Module
"""
return self.models[0]
@property
def weights_dict(self):
"""
Return the mask models associate to the application of
the mask to the self adaptive weights for each loss that
compones the global loss of the problem.
:return: The ModuleDict for mask models.
:rtype: torch.nn.ModuleDict
"""
return self.models[1]
@property
def scheduler_model(self):
"""
Returns the scheduler associated with the neural network model.
:return: The scheduler for the neural network model.
:rtype: torch.optim.lr_scheduler._LRScheduler
"""
return self._scheduler[0]
@property
def scheduler_weights(self):
"""
Returns the scheduler associated with the mask model (if applicable).
:return: The scheduler for the mask model.
:rtype: torch.optim.lr_scheduler._LRScheduler
"""
return self._scheduler[1]
@property
def optimizer_model(self):
"""
Returns the optimizer associated with the neural network model.
:return: The optimizer for the neural network model.
:rtype: torch.optim.Optimizer
"""
return self.optimizers[0]
@property
def optimizer_weights(self):
"""
Returns the optimizer associated with the mask model (if applicable).
:return: The optimizer for the mask model.
:rtype: torch.optim.Optimizer
"""
return self.optimizers[1]

190
pina/solvers/rom.py Normal file
View File

@@ -0,0 +1,190 @@
""" Module for ReducedOrderModelSolver """
import torch
from pina.solvers import SupervisedSolver
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.')
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))
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

15
pina/solvers/solver.py
View File

@@ -6,6 +6,7 @@ import pytorch_lightning
from ..utils import check_consistency
from ..problem import AbstractProblem
import torch
import sys
class SolverInterface(pytorch_lightning.LightningModule, metaclass=ABCMeta):
@@ -141,6 +142,20 @@ class SolverInterface(pytorch_lightning.LightningModule, metaclass=ABCMeta):
"""
The problem formulation."""
return self._pina_problem
def on_train_start(self):
"""
On training epoch start this function is call to do global checks for
the different solvers.
"""
# 1. Check the verison for dataloader
dataloader = self.trainer.train_dataloader
if sys.version_info < (3, 8):
dataloader = dataloader.loaders
self._dataloader = dataloader
return super().on_train_start()
# @model.setter
# def model(self, new_model):

54
pina/solvers/supervised.py
View File

@@ -1,7 +1,6 @@
""" Module for SupervisedSolver """
import torch
import sys
try:
from torch.optim.lr_scheduler import LRScheduler # torch >= 2.0
@@ -20,9 +19,32 @@ from torch.nn.modules.loss import _Loss
class SupervisedSolver(SolverInterface):
"""
r"""
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 :math:`\mathbf{s}:\Omega\rightarrow\mathbb{R}^m`
and the output :math:`\mathbf{u}:\Omega\rightarrow\mathbb{R}^m`. The input
can be discretised in space (as in :obj:`~pina.solvers.rom.ROMe2eSolver`),
or not (e.g. when training Neural Operators).
Given a model :math:`\mathcal{M}`, the following loss function is
minimized during training:
.. math::
\mathcal{L}_{\rm{problem}} = \frac{1}{N}\sum_{i=1}^N
\mathcal{L}(\mathbf{u}_i - \mathcal{M}(\mathbf{v}_i))
where :math:`\mathcal{L}` is a specific loss function,
default Mean Square Error:
.. math::
\mathcal{L}(v) = \| v \|^2_2.
In this context :math:`\mathbf{u}_i` and :math:`\mathbf{v}_i` means that
we are seeking to approximate multiple (discretised) functions given
multiple (discretised) input functions.
"""
def __init__(
@@ -96,18 +118,12 @@ class SupervisedSolver(SolverInterface):
:return: The sum of the loss functions.
:rtype: LabelTensor
"""
dataloader = self.trainer.train_dataloader
condition_idx = batch["condition"]
for condition_id in range(condition_idx.min(), condition_idx.max() + 1):
if sys.version_info >= (3, 8):
condition_name = dataloader.condition_names[condition_id]
else:
condition_name = dataloader.loaders.condition_names[
condition_id
]
condition_name = self._dataloader.condition_names[condition_id]
condition = self.problem.conditions[condition_name]
pts = batch["pts"]
out = batch["output"]
@@ -118,14 +134,14 @@ class SupervisedSolver(SolverInterface):
# for data driven mode
if not hasattr(condition, "output_points"):
raise NotImplementedError(
"Supervised solver works only in data-driven mode."
f"{type(self).__name__} works only in data-driven mode."
)
output_pts = out[condition_idx == condition_id]
input_pts = pts[condition_idx == condition_id]
loss = (
self.loss(self.forward(input_pts), output_pts)
self.loss_data(input_pts=input_pts, output_pts=output_pts)
* condition.data_weight
)
loss = loss.as_subclass(torch.Tensor)
@@ -133,6 +149,20 @@ class SupervisedSolver(SolverInterface):
self.log("mean_loss", float(loss), prog_bar=True, logger=True)
return loss
def loss_data(self, input_pts, output_pts):
"""
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.
: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
"""
return self.loss(self.forward(input_pts), output_pts)
@property
def scheduler(self):
"""