* Fourier feature embedding added, and modify typos in doc Periodic Boundary Embedding.
* Fixing doc for Periodic Boundary Embedding. * Creating doc for Fourier Feature Embedding.
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Nicola Demo
Nicola Demo
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@@ -10,6 +10,7 @@ __all__ = [
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"FourierBlock3D",
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"PODBlock",
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"PeriodicBoundaryEmbedding",
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"FourierFeatureEmbedding",
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"AVNOBlock",
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"LowRankBlock",
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]
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@@ -23,6 +24,6 @@ from .spectral import (
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)
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from .fourier import FourierBlock1D, FourierBlock2D, FourierBlock3D
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from .pod import PODBlock
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from .embedding import PeriodicBoundaryEmbedding
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from .embedding import PeriodicBoundaryEmbedding, FourierFeatureEmbedding
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from .avno_layer import AVNOBlock
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from .lowrank_layer import LowRankBlock
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@@ -1,7 +1,8 @@
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""" Periodic Boundary Embedding modulus. """
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""" Embedding modulus. """
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import torch
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from pina.utils import check_consistency
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from typing import Union, Sequence
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class PeriodicBoundaryEmbedding(torch.nn.Module):
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@@ -100,7 +101,7 @@ class PeriodicBoundaryEmbedding(torch.nn.Module):
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Forward pass to compute the periodic boundary conditions embedding.
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:param torch.Tensor x: Input tensor.
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:return: Fourier embeddings of the input.
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:return: Periodic embedding of the input.
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:rtype: torch.Tensor
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"""
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omega = torch.stack(
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@@ -155,3 +156,112 @@ class PeriodicBoundaryEmbedding(torch.nn.Module):
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The period of the periodic function to approximate.
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"""
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return self._period
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class FourierFeatureEmbedding(torch.nn.Module):
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def __init__(self,
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input_dimension : int,
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output_dimension : int,
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sigmas : Union[float, int, Sequence[float], Sequence[int]],
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embedding_output_dimension : int = None):
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r"""
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Fourier Feature Embedding class for encoding input features
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using random Fourier features.This class applies a Fourier
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transformation to the input features,
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which can help in learning high-frequency variations in data.
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If multiple sigmas are provided, the class
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supports multiscale feature embedding, creating embeddings for
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each scale specified by the sigmas.
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The :obj:`FourierFeatureEmbedding` augments the input
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by the following formula (3.10 of original paper):
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.. math::
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\mathbf{x} \rightarrow \tilde{\mathbf{x}} = \left[
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\cos\left( \mathbf{B} \mathbf{x} \right),
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\sin\left( \mathbf{B} \mathbf{x} \right)\right],
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where :math:`\mathbf{B}_{ij} \sim \mathcal{N}(0, \sigma^2)`.
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In case multiple ``sigmas`` are passed, the resulting embeddings
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are concateneted:
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.. math::
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\mathbf{x} \rightarrow \tilde{\mathbf{x}} = \left[
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\cos\left( \mathbf{B}^1 \mathbf{x} \right),
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\sin\left( \mathbf{B}^1 \mathbf{x} \right),
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\cos\left( \mathbf{B}^2 \mathbf{x} \right),
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\sin\left( \mathbf{B}^3 \mathbf{x} \right),
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\dots,
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\cos\left( \mathbf{B}^M \mathbf{x} \right),
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\sin\left( \mathbf{B}^M \mathbf{x} \right)\right],
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where :math:`\mathbf{B}^k_{ij} \sim \mathcal{N}(0, \sigma_k^2) \quad
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k \in (1, \dots, M)`.
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.. seealso::
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**Original reference**:
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Wang, Sifan, Hanwen Wang, and Paris Perdikaris. *On the eigenvector
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bias of Fourier feature networks: From regression to solving
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multi-scale PDEs with physics-informed neural networks.*
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Computer Methods in Applied Mechanics and
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Engineering 384 (2021): 113938.
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DOI: `10.1016/j.cma.2021.113938.
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<https://doi.org/10.1016/j.cma.2021.113938>`_
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:param int input_dimension: The input vector dimension of the layer.
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:param int output_dimension: The output dimension of the layer.
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:param sigmas: The standard deviation(s) used for the Fourier embedding.
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This can be a single float or integer, or a sequence of floats
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or integers. If a sequence is provided, the embedding will be
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computed for each sigma separately, enabling multiscale embeddings.
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:type sigmas: Union[float, int, Sequence[float], Sequence[int]]
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:param int output_dimension: The emebedding output dimension of the
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random matrix use to compute the fourier feature. If ``None``, it
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will be the same as ``output_dimension``, default ``None``.
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"""
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super().__init__()
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# check consistency
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check_consistency(sigmas, (int, float))
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if isinstance(sigmas, (int, float)):
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sigmas = [sigmas]
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check_consistency(output_dimension, int)
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check_consistency(input_dimension, int)
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if embedding_output_dimension is None:
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embedding_output_dimension = output_dimension
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check_consistency(embedding_output_dimension, int)
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# assign
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self.sigmas = sigmas
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# create non-trainable matrices
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self._matrices = [
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torch.rand(
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size = (input_dimension,
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embedding_output_dimension),
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requires_grad = False) * sigma for sigma in sigmas
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]
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# create linear layer to map to the output dimension
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self._linear = torch.nn.Linear(
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in_features=2*len(sigmas)*embedding_output_dimension,
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out_features=output_dimension)
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def forward(self, x):
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"""
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Forward pass to compute the fourier embedding.
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:param torch.Tensor x: Input tensor.
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:return: Fourier embeddings of the input.
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:rtype: torch.Tensor
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"""
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# compute random matrix multiplication
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out = torch.cat([torch.mm(x, m) for m in self._matrices], dim=-1)
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# compute cos/sin emebedding
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out = torch.cat([torch.cos(out), torch.sin(out)], dim=-1)
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# return linear layer mapping
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return self._linear(out)
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