344 lines
13 KiB
Python
344 lines
13 KiB
Python
"""
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Module for the Fourier Neural Operator model class.
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"""
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import warnings
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import torch
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from torch import nn
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from ..label_tensor import LabelTensor
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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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Fourier Integral Kernel model class.
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This class implements the Fourier Integral Kernel network, which
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performs global convolution in the Fourier space.
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.. seealso::
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**Original reference**: Li, Z., Kovachki, N., Azizzadenesheli, K., Liu,
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B., Bhattacharya, K., Stuart, A., & Anandkumar, A. (2020).
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*Fourier neural operator for parametric partial 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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Initialization of the :class:`FourierIntegralKernel` class.
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:param int input_numb_fields: The number of input fields.
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:param int output_numb_fields: The number of output fields.
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:param n_modes: The number of modes.
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:type n_modes: int | list[int]
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:param int dimensions: The number of dimensions. It can be set to ``1``,
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``2``, or ``3``. Default is ``3``.
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:param int padding: The padding size. Default is ``8``.
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:param str padding_type: The padding strategy. Default is ``constant``.
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:param int inner_size: The inner size. Default is ``20``.
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:param int n_layers: The number of layers. Default is ``2``.
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:param func: The activation function. If a list is passed, it must have
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the same length as ``n_layers``. If a single function is passed, it
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is used for all layers, except for the last one.
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Default is :class:`torch.nn.Tanh`.
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:type func: torch.nn.Module | list[torch.nn.Module]
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:param list[int] layers: The list of the dimension of inner layers.
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If ``None``, ``n_layers`` of dimension ``inner_size`` are used.
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Otherwise, it overrides the values passed to ``n_layers`` and
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``inner_size``. Default is ``None``.
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:raises RuntimeError: If the number of layers and functions are
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inconsistent.
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:raises RunTimeError: If the number of layers and modes are
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inconsistent.
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"""
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super().__init__()
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# check type consistency
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self._check_consistency(
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dimensions,
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padding,
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padding_type,
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inner_size,
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n_layers,
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func,
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layers,
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n_modes,
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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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fourier_layer = self._get_fourier_block(dimensions)
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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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"Inconsistent 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("Inconsistent number of layers and modes.")
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if 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 = [input_numb_fields] + layers + [output_numb_fields]
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self._layers = nn.Sequential(
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*[
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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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for i in range(len(layers))
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]
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)
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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 pass for the :class:`FourierIntegralKernel` model.
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:param x: The input tensor for performing the computation. Depending
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on the ``dimensions`` in the initialization, it expects a tensor
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with the following shapes:
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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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:type x: torch.Tensor | LabelTensor
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:raises Warning: If a LabelTensor is passed as input.
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:return: The output tensor.
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:rtype: torch.Tensor
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"""
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if isinstance(x, LabelTensor):
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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, *list(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, *list(range(2, x.ndim)), 1]
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x = x.permute(permutation_idx)
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return x
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@staticmethod
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def _check_consistency(
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dimensions,
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padding,
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padding_type,
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inner_size,
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n_layers,
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func,
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layers,
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n_modes,
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):
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"""
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Check the consistency of the input parameters.
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:param int dimensions: The number of dimensions.
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:param int padding: The padding size.
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:param str padding_type: The padding strategy.
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:param int inner_size: The inner size.
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:param int n_layers: The number of layers.
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:param func: The activation function.
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:type func: torch.nn.Module | list[torch.nn.Module]
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:param list[int] layers: The list of the dimension of inner layers.
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:param n_modes: The number of modes.
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:type n_modes: int | list[int]
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:raises ValueError: If the input is not consistent.
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"""
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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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@staticmethod
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def _get_fourier_block(dimensions):
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"""
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Retrieve the Fourier Block class based on the number of dimensions.
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:param int dimensions: The number of dimensions.
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:raises NotImplementedError: If the number of dimensions is not 1, 2,
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or 3.
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:return: The Fourier Block class.
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:rtype: FourierBlock1D | FourierBlock2D | FourierBlock3D
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"""
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if dimensions == 1:
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return FourierBlock1D
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if dimensions == 2:
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return FourierBlock2D
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if dimensions == 3:
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return FourierBlock3D
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raise NotImplementedError("FNO implemented only for 1D/2D/3D data.")
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class FNO(KernelNeuralOperator):
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"""
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Fourier Neural Operator model class.
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The Fourier Neural Operator (FNO) is a general architecture for learning
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operators, which map functions to functions. It can be trained both with
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Supervised and Physics_Informed learning strategies. The Fourier Neural
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Operator performs global convolution in the Fourier space.
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.. seealso::
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**Original reference**: Li, Z., Kovachki, N., Azizzadenesheli, K.,
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Liu, B., Bhattacharya, K., Stuart, A., & Anandkumar, A. (2020).
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*Fourier neural operator for parametric partial 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 lifting neural network mapping
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the input to its hidden dimension.
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:param torch.nn.Module projecting_net: The projection neural network
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mapping the hidden representation to the output function.
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:param n_modes: The number of modes.
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:type n_modes: int | list[int]
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:param int dimensions: The number of dimensions. It can be set to ``1``,
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``2``, or ``3``. Default is ``3``.
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:param int padding: The padding size. Default is ``8``.
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:param str padding_type: The padding strategy. Default is ``constant``.
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:param int inner_size: The inner size. Default is ``20``.
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:param int n_layers: The number of layers. Default is ``2``.
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:param func: The activation function. If a list is passed, it must have
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the same length as ``n_layers``. If a single function is passed, it
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is used for all layers, except for the last one.
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Default is :class:`torch.nn.Tanh`.
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:type func: torch.nn.Module | list[torch.nn.Module]
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:param list[int] layers: The list of the dimension of inner layers.
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If ``None``, ``n_layers`` of dimension ``inner_size`` are used.
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Otherwise, it overrides the values passed to ``n_layers`` and
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``inner_size``. Default is ``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 pass for the :class:`FourierNeuralOperator` model.
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The ``lifting_net`` maps the input to the hidden dimension.
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Then, several layers of Fourier blocks are applied. Finally, the
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``projection_net`` maps the hidden representation to the output
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function.
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: param x: The input tensor for performing the computation. Depending
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on the ``dimensions`` in the initialization, it expects a tensor
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with the following shapes:
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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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:type x: torch.Tensor | LabelTensor
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:return: The output tensor.
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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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