Unifying integral kernel NO architectures (#239)
* Unify integral kernel NO architectures with NeuralKernelOperator * Implement FNO based on NeuralKernelOperator * modify doc for FNO and add for FourierIntegralKernel, NeuralKernelOperator * adding tests --------- Co-authored-by: Dario Coscia <dariocoscia@Dario-Coscia.local> Co-authored-by: Dario Coscia <dariocoscia@dhcp-015.eduroam.sissa.it>
This commit is contained in:
Dario Coscia
@@ -48,11 +48,13 @@ Models
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:maxdepth: 5
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Network <models/network.rst>
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KernelNeuralOperator <models/base_no.rst>
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FeedForward <models/fnn.rst>
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MultiFeedForward <models/multifeedforward.rst>
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ResidualFeedForward <models/fnn_residual.rst>
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DeepONet <models/deeponet.rst>
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MIONet <models/mionet.rst>
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FourierIntegralKernel <models/fourier_kernel.rst>
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FNO <models/fno.rst>
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Layers
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7
docs/source/_rst/models/base_no.rst
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7
docs/source/_rst/models/base_no.rst
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@@ -0,0 +1,7 @@
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KernelNeuralOperator
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=======================
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.. currentmodule:: pina.model.base_no
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.. autoclass:: KernelNeuralOperator
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:members:
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:show-inheritance:
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7
docs/source/_rst/models/fourier_kernel.rst
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7
docs/source/_rst/models/fourier_kernel.rst
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@@ -0,0 +1,7 @@
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FourierIntegralKernel
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=========================
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.. currentmodule:: pina.model.fno
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.. autoclass:: FourierIntegralKernel
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:members:
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:show-inheritance:
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@@ -1,13 +1,16 @@
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__all__ = [
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"FeedForward",
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"ResidualFeedForward",
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"MultiFeedForward",
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"DeepONet",
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"MIONet",
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"FNO",
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'FeedForward',
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'ResidualFeedForward',
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'MultiFeedForward',
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'DeepONet',
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'MIONet',
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'FNO',
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'FourierIntegralKernel',
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'KernelNeuralOperator'
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]
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from .feed_forward import FeedForward, ResidualFeedForward
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from .multi_feed_forward import MultiFeedForward
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from .deeponet import DeepONet, MIONet
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from .fno import FNO
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from .fno import FNO, FourierIntegralKernel
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from .base_no import KernelNeuralOperator
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136
pina/model/base_no.py
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136
pina/model/base_no.py
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@@ -0,0 +1,136 @@
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"""
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Kernel Neural Operator Module.
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"""
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import torch
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from pina.utils import check_consistency
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class KernelNeuralOperator(torch.nn.Module):
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r"""
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Base class for composing Neural Operators with integral kernels.
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This is a base class for composing neural operators with multiple
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integral kernels. All neural operator models defined in PINA inherit
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from this class. The structure is inspired by the work of Kovachki, N.
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et al. see Figure 2 of the reference for extra details. The Neural
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Operators inheriting from this class can be written as:
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.. math::
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G_\theta := P \circ K_m \circ \cdot \circ K_1 \circ L
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where:
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* :math:`G_\theta: \mathcal{A}\subset \mathbb{R}^{\rm{in}} \rightarrow
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\mathcal{D}\subset \mathbb{R}^{\rm{out}}` is the neural operator
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approximation of the unknown real operator :math:`G`, that is
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:math:`G \approx G_\theta`
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* :math:`L: \mathcal{A}\subset \mathbb{R}^{\rm{in}} \rightarrow
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\mathbb{R}^{\rm{emb}}` is a lifting operator mapping the input
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from its domain :math:`\mathcal{A}\subset \mathbb{R}^{\rm{in}}`
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to its embedding dimension :math:`\mathbb{R}^{\rm{emb}}`
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* :math:`\{K_i : \mathbb{R}^{\rm{emb}} \rightarrow
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\mathbb{R}^{\rm{emb}} \}_{i=1}^m` are :math:`m` integral kernels
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mapping each hidden representation to the next one.
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* :math:`P : \mathbb{R}^{\rm{emb}} \rightarrow \mathcal{D}\subset
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\mathbb{R}^{\rm{out}}` is a projection operator mapping the hidden
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representation to the output function.
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.. seealso::
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**Original reference**: Kovachki, N., Li, Z., Liu, B.,
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Azizzadenesheli, K., Bhattacharya, K., Stuart, A., & Anandkumar, A.
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(2023). *Neural operator: Learning maps between function
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spaces with applications to PDEs*. Journal of Machine Learning
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Research, 24(89), 1-97.
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"""
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def __init__(self, lifting_operator, integral_kernels, projection_operator):
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"""
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:param torch.nn.Module lifting_operator: The lifting operator
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mapping the input to its hidden dimension.
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:param torch.nn.Module integral_kernels: List of integral kernels
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mapping each hidden representation to the next one.
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:param torch.nn.Module projection_operator: The projection operator
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mapping the hidden representation to the output function.
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"""
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super().__init__()
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self._lifting_operator = lifting_operator
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self._integral_kernels = integral_kernels
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self._projection_operator = projection_operator
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@property
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def lifting_operator(self):
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"""
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The lifting operator property.
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"""
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return self._lifting_operator
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@lifting_operator.setter
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def lifting_operator(self, value):
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"""
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The lifting operator setter
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:param torch.nn.Module value: The lifting operator torch module.
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"""
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check_consistency(value, torch.nn.Module)
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self._lifting_operator = value
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@property
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def projection_operator(self):
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"""
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The projection operator property.
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"""
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return self._projection_operator
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@projection_operator.setter
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def projection_operator(self, value):
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"""
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The projection operator setter
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:param torch.nn.Module value: The projection operator torch module.
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"""
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check_consistency(value, torch.nn.Module)
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self._projection_operator = value
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@property
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def integral_kernels(self):
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"""
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The integral kernels operator property.
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"""
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return self._integral_kernels
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@integral_kernels.setter
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def integral_kernels(self, value):
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"""
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The integral kernels operator setter
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:param torch.nn.Module value: The integral kernels operator torch
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module.
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"""
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check_consistency(value, torch.nn.Module)
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self._integral_kernels = value
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def forward(self, x):
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r"""
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Forward computation for Base Neural Operator. It performs a
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lifting of the input by the ``lifting_operator``.
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Then different layers integral kernels are applied using
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``integral_kernels``. Finally the output is projected
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to the final dimensionality by the ``projection_operator``.
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:param torch.Tensor x: The input tensor for performing the
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computation. It expects a tensor :math:`B \times N \times D`,
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where :math:`B` is the batch_size, :math:`N` the number of points
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in the mesh, :math:`D` the dimension of the problem. In particular
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:math:`D` is the number of spatial/paramtric/temporal variables
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plus the field variables. For example for 2D problems with 2
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output\ variables :math:`D=4`.
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:return: The output tensor obtained from the NO.
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:rtype: torch.Tensor
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"""
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x = self.lifting_operator(x)
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x = self.integral_kernels(x)
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x = self.projection_operator(x)
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return x
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@@ -1,54 +1,66 @@
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"""
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Fourier Neural Operator Module.
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"""
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import torch
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import torch.nn as nn
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from ..utils import check_consistency
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from .layers.fourier import FourierBlock1D, FourierBlock2D, FourierBlock3D
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from pina import LabelTensor
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import warnings
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from ..utils import check_consistency
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from .layers.fourier import FourierBlock1D, FourierBlock2D, FourierBlock3D
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from .base_no import KernelNeuralOperator
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class FNO(torch.nn.Module):
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class FourierIntegralKernel(torch.nn.Module):
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"""
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The PINA implementation of Fourier Neural Operator network.
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Implementation of Fourier Integral Kernel network.
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Fourier Neural Operator (FNO) is a general architecture for learning Operators.
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Unlike traditional machine learning methods FNO is designed to map
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entire functions to other functions. It can be trained both with
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Supervised learning strategies. FNO does global convolution by performing the
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operation on the Fourier space.
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This class implements the Fourier Integral Kernel network, which is a
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PINA implementation of Fourier Neural Operator kernel network.
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It performs global convolution by operating in the Fourier space.
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.. seealso::
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**Original reference**: Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B.,
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Bhattacharya, K., Stuart, A., & Anandkumar, A. (2020). *Fourier neural operator for
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parametric partial differential equations*.
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**Original reference**: Li, Z., Kovachki, N., Azizzadenesheli,
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K., Liu, B., Bhattacharya, K., Stuart, A., & Anandkumar, A.
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(2020). *Fourier neural operator for parametric partial
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differential equations*.
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DOI: `arXiv preprint arXiv:2010.08895.
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<https://arxiv.org/abs/2010.08895>`_
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"""
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def __init__(
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self,
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lifting_net,
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projecting_net,
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n_modes,
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dimensions=3,
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padding=8,
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padding_type="constant",
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inner_size=20,
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n_layers=2,
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func=nn.Tanh,
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layers=None,
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):
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def __init__(self,
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input_numb_fields,
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output_numb_fields,
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n_modes,
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dimensions=3,
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padding=8,
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padding_type="constant",
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inner_size=20,
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n_layers=2,
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func=nn.Tanh,
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layers=None):
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"""
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:param int input_numb_fields: Number of input fields.
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:param int output_numb_fields: Number of output fields.
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:param int | list[int] n_modes: Number of modes.
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:param int dimensions: Number of dimensions (1, 2, or 3).
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:param int padding: Padding size, defaults to 8.
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:param str padding_type: Type of padding, defaults to "constant".
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:param int inner_size: Inner size, defaults to 20.
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:param int n_layers: Number of layers, defaults to 2.
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:param torch.nn.Module func: Activation function, defaults to nn.Tanh.
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:param list[int] layers: List of layer sizes, defaults to None.
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"""
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super().__init__()
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# check type consistency
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check_consistency(lifting_net, nn.Module)
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check_consistency(projecting_net, nn.Module)
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check_consistency(dimensions, int)
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check_consistency(padding, int)
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check_consistency(padding_type, str)
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check_consistency(inner_size, int)
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check_consistency(n_layers, int)
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check_consistency(func, nn.Module, subclass=True)
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if layers is not None:
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if isinstance(layers, (tuple, list)):
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check_consistency(layers, int)
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@@ -57,13 +69,9 @@ class FNO(torch.nn.Module):
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if not isinstance(n_modes, (list, tuple, int)):
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raise ValueError(
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"n_modes must be a int or list or tuple of valid modes."
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" More information on the official documentation."
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)
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" More information on the official documentation.")
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# assign variables
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# TODO check input lifting net and input projecting net
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self._lifting_net = lifting_net
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self._projecting_net = projecting_net
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# assign padding
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self._padding = padding
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# initialize fourier layer for each dimension
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@@ -74,9 +82,11 @@ class FNO(torch.nn.Module):
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elif dimensions == 3:
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fourier_layer = FourierBlock3D
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else:
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raise NotImplementedError("FNO implemented only for 1D/2D/3D data.")
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raise NotImplementedError(
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"FNO implemented only for 1D/2D/3D data."
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)
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# Here we build the FNO by stacking Fourier Blocks
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# Here we build the FNO kernels by stacking Fourier Blocks
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# 1. Assign output dimensions for each FNO layer
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if layers is None:
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@@ -86,43 +96,33 @@ class FNO(torch.nn.Module):
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if isinstance(func, list):
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if len(layers) != len(func):
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raise RuntimeError(
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"Uncosistent number of layers and functions."
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)
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self._functions = func
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'Uncosistent number of layers and functions.')
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_functions = func
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else:
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self._functions = [func for _ in range(len(layers))]
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_functions = [func for _ in range(len(layers) - 1)]
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_functions.append(torch.nn.Identity)
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# 3. Assign modes functions for each FNO layer
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if isinstance(n_modes, list):
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if all(isinstance(i, list) for i in n_modes) and len(layers) != len(
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n_modes
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):
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if all(isinstance(i, list)
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for i in n_modes) and len(layers) != len(n_modes):
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raise RuntimeError(
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"Uncosistent number of layers and functions."
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)
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"Uncosistent number of layers and functions.")
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elif all(isinstance(i, int) for i in n_modes):
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n_modes = [n_modes] * len(layers)
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else:
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n_modes = [n_modes] * len(layers)
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# 4. Build the FNO network
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tmp_layers = layers.copy()
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first_parameter = next(lifting_net.parameters())
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input_shape = first_parameter.size()
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out_feats = lifting_net(torch.rand(size=input_shape)).shape[-1]
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tmp_layers.insert(0, out_feats)
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self._layers = []
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for i in range(len(tmp_layers) - 1):
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self._layers.append(
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fourier_layer(
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input_numb_fields=tmp_layers[i],
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output_numb_fields=tmp_layers[i + 1],
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n_modes=n_modes[i],
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activation=self._functions[i],
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)
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)
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self._layers = nn.Sequential(*self._layers)
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_layers = []
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tmp_layers = [input_numb_fields] + layers + [output_numb_fields]
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for i in range(len(layers)):
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_layers.append(
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fourier_layer(input_numb_fields=tmp_layers[i],
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output_numb_fields=tmp_layers[i + 1],
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n_modes=n_modes[i],
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activation=_functions[i]))
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self._layers = nn.Sequential(*_layers)
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# 5. Padding values for spectral conv
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if isinstance(padding, int):
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@@ -140,23 +140,22 @@ class FNO(torch.nn.Module):
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of Fourier Blocks are applied. Finally the output is projected
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to the final dimensionality by the ``projecting_net``.
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:param torch.Tensor x: The input tensor for fourier block, depending on
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``dimension`` in the initialization. In particular it is expected
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:param torch.Tensor x: The input tensor for fourier block,
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depending on ``dimension`` in the initialization.
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In particular it is expected:
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* 1D tensors: ``[batch, X, channels]``
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* 2D tensors: ``[batch, X, Y, channels]``
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* 3D tensors: ``[batch, X, Y, Z, channels]``
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:return: The output tensor obtained from the FNO.
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:return: The output tensor obtained from the kernels convolution.
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:rtype: torch.Tensor
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"""
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if isinstance(x, LabelTensor): # TODO remove when Network is fixed
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if isinstance(x, LabelTensor): #TODO remove when Network is fixed
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warnings.warn(
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"LabelTensor passed as input is not allowed, casting LabelTensor to Torch.Tensor"
|
||||
'LabelTensor passed as input is not allowed,'
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' casting LabelTensor to Torch.Tensor'
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)
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x = x.as_subclass(torch.Tensor)
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# lifting the input in higher dimensional space
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x = self._lifting_net(x)
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# permuting the input [batch, channels, x, y, ...]
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permutation_idx = [0, x.ndim - 1, *[i for i in range(1, x.ndim - 1)]]
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x = x.permute(permutation_idx)
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@@ -175,5 +174,85 @@ class FNO(torch.nn.Module):
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permutation_idx = [0, *[i for i in range(2, x.ndim)], 1]
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x = x.permute(permutation_idx)
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# apply projecting operator and return
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return self._projecting_net(x)
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return x
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class FNO(KernelNeuralOperator):
|
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"""
|
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The PINA implementation of Fourier Neural Operator network.
|
||||
|
||||
Fourier Neural Operator (FNO) is a general architecture for
|
||||
learning Operators. Unlike traditional machine learning methods
|
||||
FNO is designed to map entire functions to other functions. It
|
||||
can be trained with Supervised learning strategies. FNO does global
|
||||
convolution by performing the operation on the Fourier space.
|
||||
|
||||
.. seealso::
|
||||
|
||||
**Original reference**: Li, Z., Kovachki, N., Azizzadenesheli,
|
||||
K., Liu, B., Bhattacharya, K., Stuart, A., & Anandkumar, A.
|
||||
(2020). *Fourier neural operator for parametric partial
|
||||
differential equations*.
|
||||
DOI: `arXiv preprint arXiv:2010.08895.
|
||||
<https://arxiv.org/abs/2010.08895>`_
|
||||
"""
|
||||
def __init__(self,
|
||||
lifting_net,
|
||||
projecting_net,
|
||||
n_modes,
|
||||
dimensions=3,
|
||||
padding=8,
|
||||
padding_type="constant",
|
||||
inner_size=20,
|
||||
n_layers=2,
|
||||
func=nn.Tanh,
|
||||
layers=None):
|
||||
"""
|
||||
:param torch.nn.Module lifting_net: The neural network for lifting
|
||||
the input.
|
||||
:param torch.nn.Module projecting_net: The neural network for
|
||||
projecting the output.
|
||||
:param int | list[int] n_modes: Number of modes.
|
||||
:param int dimensions: Number of dimensions (1, 2, or 3).
|
||||
:param int padding: Padding size, defaults to 8.
|
||||
:param str padding_type: Type of padding, defaults to `constant`.
|
||||
:param int inner_size: Inner size, defaults to 20.
|
||||
:param int n_layers: Number of layers, defaults to 2.
|
||||
:param torch.nn.Module func: Activation function, defaults to nn.Tanh.
|
||||
:param list[int] layers: List of layer sizes, defaults to None.
|
||||
"""
|
||||
lifting_operator_out = lifting_net(
|
||||
torch.rand(size=next(lifting_net.parameters()).size())).shape[-1]
|
||||
super().__init__(lifting_operator=lifting_net,
|
||||
projection_operator=projecting_net,
|
||||
integral_kernels=FourierIntegralKernel(
|
||||
input_numb_fields=lifting_operator_out,
|
||||
output_numb_fields=next(
|
||||
projecting_net.parameters()).size(),
|
||||
n_modes=n_modes,
|
||||
dimensions=dimensions,
|
||||
padding=padding,
|
||||
padding_type=padding_type,
|
||||
inner_size=inner_size,
|
||||
n_layers=n_layers,
|
||||
func=func,
|
||||
layers=layers))
|
||||
|
||||
def forward(self, x):
|
||||
"""
|
||||
Forward computation for Fourier Neural Operator. It performs a
|
||||
lifting of the input by the ``lifting_net``. Then different layers
|
||||
of Fourier Blocks are applied. Finally the output is projected
|
||||
to the final dimensionality by the ``projecting_net``.
|
||||
|
||||
:param torch.Tensor x: The input tensor for fourier block,
|
||||
depending on ``dimension`` in the initialization. In
|
||||
particular it is expected:
|
||||
|
||||
* 1D tensors: ``[batch, X, channels]``
|
||||
* 2D tensors: ``[batch, X, Y, channels]``
|
||||
* 3D tensors: ``[batch, X, Y, Z, channels]``
|
||||
:return: The output tensor obtained from FNO.
|
||||
:rtype: torch.Tensor
|
||||
"""
|
||||
return super().forward(x)
|
||||
|
||||
40
tests/test_model/test_base_no.py
Normal file
40
tests/test_model/test_base_no.py
Normal file
@@ -0,0 +1,40 @@
|
||||
import torch
|
||||
from pina.model import KernelNeuralOperator, FeedForward
|
||||
|
||||
input_dim = 2
|
||||
output_dim = 4
|
||||
embedding_dim = 24
|
||||
batch_size = 10
|
||||
numb = 256
|
||||
data = torch.rand(size=(batch_size, numb, input_dim), requires_grad=True)
|
||||
output_shape = torch.Size([batch_size, numb, output_dim])
|
||||
|
||||
|
||||
lifting_operator = FeedForward(input_dimensions=input_dim, output_dimensions=embedding_dim)
|
||||
projection_operator = FeedForward(input_dimensions=embedding_dim, output_dimensions=output_dim)
|
||||
integral_kernels = torch.nn.Sequential(FeedForward(input_dimensions=embedding_dim,
|
||||
output_dimensions=embedding_dim),
|
||||
FeedForward(input_dimensions=embedding_dim,
|
||||
output_dimensions=embedding_dim),)
|
||||
|
||||
def test_constructor():
|
||||
KernelNeuralOperator(lifting_operator=lifting_operator,
|
||||
integral_kernels=integral_kernels,
|
||||
projection_operator=projection_operator)
|
||||
|
||||
def test_forward():
|
||||
operator = KernelNeuralOperator(lifting_operator=lifting_operator,
|
||||
integral_kernels=integral_kernels,
|
||||
projection_operator=projection_operator)
|
||||
out = operator(data)
|
||||
assert out.shape == output_shape
|
||||
|
||||
def test_backward():
|
||||
operator = KernelNeuralOperator(lifting_operator=lifting_operator,
|
||||
integral_kernels=integral_kernels,
|
||||
projection_operator=projection_operator)
|
||||
out = operator(data)
|
||||
loss = torch.nn.functional.mse_loss(out, torch.zeros_like(out))
|
||||
loss.backward()
|
||||
grad = data.grad
|
||||
assert grad.shape == data.shape
|
||||
Reference in New Issue
Block a user