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FilippoOlivo
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Nicola Demo
Nicola Demo
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886bd23fdb
commit
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275
pina/model/fourier_neural_operator.py
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275
pina/model/fourier_neural_operator.py
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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 ..label_tensor import LabelTensor
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import warnings
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from ..utils import check_consistency
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from .block.fourier_block import FourierBlock1D, FourierBlock2D, FourierBlock3D
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from .kernel_neural_operator import KernelNeuralOperator
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class FourierIntegralKernel(torch.nn.Module):
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"""
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Implementation of Fourier Integral Kernel network.
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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,
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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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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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"""
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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(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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else:
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raise ValueError("layers must be tuple or list of int.")
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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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# assign padding
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self._padding = padding
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# initialize fourier layer for each dimension
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if dimensions == 1:
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fourier_layer = FourierBlock1D
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elif dimensions == 2:
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fourier_layer = FourierBlock2D
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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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# 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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layers = [inner_size] * n_layers
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# 2. Assign activation functions for each FNO layer
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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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_functions = func
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else:
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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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raise RuntimeError(
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"Uncosistent number of layers and functions."
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)
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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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_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(
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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=_functions[i],
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)
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)
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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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padding = [padding] * dimensions
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self._ipad = [-pad if pad > 0 else None for pad in padding[:dimensions]]
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self._padding_type = padding_type
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self._pad = [
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val for pair in zip([0] * dimensions, padding) for val in pair
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]
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def forward(self, x):
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"""
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Forward computation for Fourier Neural Operator. It performs a
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lifting of the input by the ``lifting_net``. Then different layers
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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,
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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 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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warnings.warn(
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"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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# 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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# padding the input
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x = torch.nn.functional.pad(x, pad=self._pad, mode=self._padding_type)
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# apply fourier layers
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x = self._layers(x)
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# remove padding
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idxs = [slice(None), slice(None)] + [slice(pad) for pad in self._ipad]
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x = x[idxs]
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# permuting back [batch, x, y, ..., channels]
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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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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.
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Fourier Neural Operator (FNO) is a general architecture for
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learning Operators. Unlike traditional machine learning methods
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FNO is designed to map entire functions to other functions. It
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can be trained with Supervised learning strategies. FNO does global
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convolution by performing the operation on the Fourier space.
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.. seealso::
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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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"""
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:param torch.nn.Module lifting_net: The neural network for lifting
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the input.
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:param torch.nn.Module projecting_net: The neural network for
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projecting the output.
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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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lifting_operator_out = lifting_net(
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torch.rand(size=next(lifting_net.parameters()).size())
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).shape[-1]
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super().__init__(
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lifting_operator=lifting_net,
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projection_operator=projecting_net,
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integral_kernels=FourierIntegralKernel(
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input_numb_fields=lifting_operator_out,
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output_numb_fields=next(projecting_net.parameters()).size(),
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n_modes=n_modes,
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dimensions=dimensions,
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padding=padding,
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padding_type=padding_type,
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inner_size=inner_size,
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n_layers=n_layers,
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func=func,
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layers=layers,
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),
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)
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def forward(self, x):
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"""
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Forward computation for Fourier Neural Operator. It performs a
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lifting of the input by the ``lifting_net``. Then different layers
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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,
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depending on ``dimension`` in the initialization. In
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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 FNO.
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:rtype: torch.Tensor
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"""
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if isinstance(x, LabelTensor):
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x = x.as_subclass(torch.Tensor)
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return super().forward(x)
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