"""Module for DeepONet model"""
import torch
import torch.nn as nn
from ..utils import check_consistency, is_function
from functools import partial
[docs]
class MIONet(torch.nn.Module):
"""
The PINA implementation of MIONet network.
MIONet is a general architecture for learning Operators defined
on the tensor product of Banach spaces. Unlike traditional machine
learning methods MIONet is designed to map entire functions to other functions.
It can be trained both with Physics Informed or Supervised learning strategies.
.. seealso::
**Original reference**: Jin, Pengzhan, Shuai Meng, and Lu Lu.
*MIONet: Learning multiple-input operators via tensor product.*
SIAM Journal on Scientific Computing 44.6 (2022): A3490-A351
DOI: `10.1137/22M1477751
<https://doi.org/10.1137/22M1477751>`_
"""
def __init__(
self,
networks,
aggregator="*",
reduction="+",
scale=True,
translation=True,
):
"""
:param dict networks: The neural networks to use as
models. The ``dict`` takes as key a neural network, and
as value the list of indeces to extract from the input variable
in the forward pass of the neural network. If a list of ``int`` is passed,
the corresponding columns of the inner most entries are extracted.
If a list of ``str`` is passed the variables of the corresponding :py:obj:`pina.label_tensor.LabelTensor`
are extracted. The ``torch.nn.Module`` model has to take as input a
:py:obj:`pina.label_tensor.LabelTensor` or :class:`torch.Tensor`.
Default implementation consist of different branch nets and one trunk nets.
:param str or Callable aggregator: Aggregator to be used to aggregate
partial results from the modules in `nets`. Partial results are
aggregated component-wise. Available aggregators include
sum: ``+``, product: ``*``, mean: ``mean``, min: ``min``, max: ``max``.
:param str or Callable reduction: Reduction to be used to reduce
the aggregated result of the modules in `nets` to the desired output
dimension. Available reductions include
sum: ``+``, product: ``*``, mean: ``mean``, min: ``min``, max: ``max``.
:param bool or Callable scale: Scaling the final output before returning the
forward pass, default ``True``.
:param bool or Callable translation: Translating the final output before
returning the forward pass, default ``True``.
.. warning::
In the forward pass we do not check if the input is instance of
:py:obj:`pina.label_tensor.LabelTensor` or :class:`torch.Tensor`. A general rule is
that for a :py:obj:`pina.label_tensor.LabelTensor` input both list of integers and
list of strings can be passed for ``input_indeces_branch_net``
and ``input_indeces_trunk_net``. Differently, for a :class:`torch.Tensor`
only a list of integers can be passed for ``input_indeces_branch_net``
and ``input_indeces_trunk_net``.
:Example:
>>> branch_net1 = FeedForward(input_dimensons=1, output_dimensions=10)
>>> branch_net2 = FeedForward(input_dimensons=2, output_dimensions=10)
>>> trunk_net = FeedForward(input_dimensons=1, output_dimensions=10)
>>> networks = {branch_net1 : ['x'],
branch_net2 : ['x', 'y'],
... trunk_net : ['z']}
>>> model = MIONet(networks=networks,
... reduction='+',
... aggregator='*')
>>> model
MIONet(
(models): ModuleList(
(0): FeedForward(
(model): Sequential(
(0): Linear(in_features=1, out_features=20, bias=True)
(1): Tanh()
(2): Linear(in_features=20, out_features=20, bias=True)
(3): Tanh()
(4): Linear(in_features=20, out_features=10, bias=True)
)
)
(1): FeedForward(
(model): Sequential(
(0): Linear(in_features=2, out_features=20, bias=True)
(1): Tanh()
(2): Linear(in_features=20, out_features=20, bias=True)
(3): Tanh()
(4): Linear(in_features=20, out_features=10, bias=True)
)
)
(2): FeedForward(
(model): Sequential(
(0): Linear(in_features=1, out_features=20, bias=True)
(1): Tanh()
(2): Linear(in_features=20, out_features=20, bias=True)
(3): Tanh()
(4): Linear(in_features=20, out_features=10, bias=True)
)
)
)
)
"""
super().__init__()
# check type consistency
check_consistency(networks, dict)
check_consistency(scale, bool)
check_consistency(translation, bool)
# check trunk branch nets consistency
shapes = []
for key, value in networks.items():
check_consistency(value, (str, int))
check_consistency(key, torch.nn.Module)
input_ = torch.rand(10, len(value))
shapes.append(key(input_).shape[-1])
if not all(map(lambda x: x == shapes[0], shapes)):
raise ValueError(
"The passed networks have not the same " "output dimension."
)
# assign trunk and branch net with their input indeces
self.models = torch.nn.ModuleList(networks.keys())
self._indeces = networks.values()
# initializie aggregation
self._init_aggregator(aggregator=aggregator)
self._init_reduction(reduction=reduction)
# scale and translation
self._scale = (
torch.nn.Parameter(torch.tensor([1.0]))
if scale
else torch.tensor([1.0])
)
self._trasl = (
torch.nn.Parameter(torch.tensor([1.0]))
if translation
else torch.tensor([1.0])
)
@staticmethod
def _symbol_functions(**kwargs):
"""
Return a dictionary of functions that can be used as aggregators or
reductions.
"""
return {
"+": partial(torch.sum, **kwargs),
"*": partial(torch.prod, **kwargs),
"mean": partial(torch.mean, **kwargs),
"min": lambda x: torch.min(x, **kwargs).values,
"max": lambda x: torch.max(x, **kwargs).values,
}
def _init_aggregator(self, aggregator):
aggregator_funcs = DeepONet._symbol_functions(dim=2)
if aggregator in aggregator_funcs:
aggregator_func = aggregator_funcs[aggregator]
elif isinstance(aggregator, nn.Module) or is_function(aggregator):
aggregator_func = aggregator
else:
raise ValueError(f"Unsupported aggregation: {str(aggregator)}")
self._aggregator = aggregator_func
self._aggregator_type = aggregator
def _init_reduction(self, reduction):
reduction_funcs = DeepONet._symbol_functions(dim=-1)
if reduction in reduction_funcs:
reduction_func = reduction_funcs[reduction]
elif isinstance(reduction, nn.Module) or is_function(reduction):
reduction_func = reduction
else:
raise ValueError(f"Unsupported reduction: {reduction}")
self._reduction = reduction_func
self._reduction_type = reduction
def _get_vars(self, x, indeces):
if isinstance(indeces[0], str):
try:
return x.extract(indeces)
except AttributeError:
raise RuntimeError(
"Not possible to extract input variables from tensor."
" Ensure that the passed tensor is a LabelTensor or"
" pass list of integers to extract variables. For"
" more information refer to warning in the documentation."
)
elif isinstance(indeces[0], int):
return x[..., indeces]
else:
raise RuntimeError(
"Not able to extract right indeces for tensor."
" For more information refer to warning in the documentation."
)
[docs]
def forward(self, x):
"""
Defines the computation performed at every call.
:param LabelTensor or torch.Tensor x: The input tensor for the forward call.
:return: The output computed by the DeepONet model.
:rtype: LabelTensor or torch.Tensor
"""
# forward pass
output_ = [
model(self._get_vars(x, indeces))
for model, indeces in zip(self.models, self._indeces)
]
# aggregation
aggregated = self._aggregator(torch.dstack(output_))
# reduce
output_ = self._reduction(aggregated)
if self._reduction_type in DeepONet._symbol_functions(dim=-1):
output_ = output_.reshape(-1, 1)
# scale and translate
output_ *= self._scale
output_ += self._trasl
return output_
@property
def aggregator(self):
"""
The aggregator function.
"""
return self._aggregator
@property
def reduction(self):
"""
The translation factor.
"""
return self._reduction
@property
def scale(self):
"""
The scale factor.
"""
return self._scale
@property
def translation(self):
"""
The translation factor for MIONet.
"""
return self._trasl
@property
def indeces_variables_extracted(self):
"""
The input indeces for each model in form of list.
"""
return self._indeces
@property
def model(self):
"""
The models in form of list.
"""
return self._indeces
[docs]
class DeepONet(MIONet):
"""
The PINA implementation of DeepONet network.
DeepONet is a general architecture for learning Operators. Unlike
traditional machine learning methods DeepONet is designed to map
entire functions to other functions. It can be trained both with
Physics Informed or Supervised learning strategies.
.. seealso::
**Original reference**: Lu, L., Jin, P., Pang, G. et al. *Learning
nonlinear operators via DeepONet based on the universal approximation
theorem of operators*. Nat Mach Intell 3, 218–229 (2021).
DOI: `10.1038/s42256-021-00302-5
<https://doi.org/10.1038/s42256-021-00302-5>`_
"""
def __init__(
self,
branch_net,
trunk_net,
input_indeces_branch_net,
input_indeces_trunk_net,
aggregator="*",
reduction="+",
scale=True,
translation=True,
):
"""
:param torch.nn.Module branch_net: The neural network to use as branch
model. It has to take as input a :py:obj:`pina.label_tensor.LabelTensor`
or :class:`torch.Tensor`. The number of dimensions of the output has
to be the same of the ``trunk_net``.
:param torch.nn.Module trunk_net: The neural network to use as trunk
model. It has to take as input a :py:obj:`pina.label_tensor.LabelTensor`
or :class:`torch.Tensor`. The number of dimensions of the output
has to be the same of the ``branch_net``.
:param list(int) or list(str) input_indeces_branch_net: List of indeces
to extract from the input variable in the forward pass for the
branch net. If a list of ``int`` is passed, the corresponding columns
of the inner most entries are extracted. If a list of ``str`` is passed
the variables of the corresponding :py:obj:`pina.label_tensor.LabelTensor` are extracted.
:param list(int) or list(str) input_indeces_trunk_net: List of indeces
to extract from the input variable in the forward pass for the
trunk net. If a list of ``int`` is passed, the corresponding columns
of the inner most entries are extracted. If a list of ``str`` is passed
the variables of the corresponding :py:obj:`pina.label_tensor.LabelTensor` are extracted.
:param str or Callable aggregator: Aggregator to be used to aggregate
partial results from the modules in `nets`. Partial results are
aggregated component-wise. Available aggregators include
sum: ``+``, product: ``*``, mean: ``mean``, min: ``min``, max: ``max``.
:param str or Callable reduction: Reduction to be used to reduce
the aggregated result of the modules in `nets` to the desired output
dimension. Available reductions include
sum: ``+``, product: ``*``, mean: ``mean``, min: ``min``, max: ``max``.
:param bool or Callable scale: Scaling the final output before returning the
forward pass, default True.
:param bool or Callable translation: Translating the final output before
returning the forward pass, default True.
.. warning::
In the forward pass we do not check if the input is instance of
:py:obj:`pina.label_tensor.LabelTensor` or :class:`torch.Tensor`. A general rule is
that for a :py:obj:`pina.label_tensor.LabelTensor` input both list of integers and
list of strings can be passed for ``input_indeces_branch_net``
and ``input_indeces_trunk_net``. Differently, for a :class:`torch.Tensor`
only a list of integers can be passed for ``input_indeces_branch_net``
and ``input_indeces_trunk_net``.
:Example:
>>> branch_net = FeedForward(input_dimensons=1, output_dimensions=10)
>>> trunk_net = FeedForward(input_dimensons=1, output_dimensions=10)
>>> model = DeepONet(branch_net=branch_net,
... trunk_net=trunk_net,
... input_indeces_branch_net=['x'],
... input_indeces_trunk_net=['t'],
... reduction='+',
... aggregator='*')
>>> model
DeepONet(
(trunk_net): FeedForward(
(model): Sequential(
(0): Linear(in_features=1, out_features=20, bias=True)
(1): Tanh()
(2): Linear(in_features=20, out_features=20, bias=True)
(3): Tanh()
(4): Linear(in_features=20, out_features=10, bias=True)
)
)
(branch_net): FeedForward(
(model): Sequential(
(0): Linear(in_features=1, out_features=20, bias=True)
(1): Tanh()
(2): Linear(in_features=20, out_features=20, bias=True)
(3): Tanh()
(4): Linear(in_features=20, out_features=10, bias=True)
)
)
)
"""
networks = {
branch_net: input_indeces_branch_net,
trunk_net: input_indeces_trunk_net,
}
super().__init__(
networks=networks,
aggregator=aggregator,
reduction=reduction,
scale=scale,
translation=translation,
)
[docs]
def forward(self, x):
"""
Defines the computation performed at every call.
:param LabelTensor or torch.Tensor x: The input tensor for the forward call.
:return: The output computed by the DeepONet model.
:rtype: LabelTensor or torch.Tensor
"""
return super().forward(x)
@property
def branch_net(self):
"""
The branch net for DeepONet.
"""
return self.models[0]
@property
def trunk_net(self):
"""
The trunk net for DeepONet.
"""
return self.models[1]
