Averaging Neural Operator#

class AveragingNeuralOperator(lifting_net, projecting_net, field_indices, coordinates_indices, n_layers=4, func=<class 'torch.nn.modules.activation.GELU'>)[source]#

Bases: KernelNeuralOperator

Averaging Neural Operator model class.

The Averaging Neural Operator is a general architecture for learning operators, which map functions to functions. It can be trained both with Supervised and Physics-Informed learning strategies. The Averaging Neural Operator performs convolution by means of a field average.

See also

Original reference: Lanthaler S., Li, Z., Stuart, A. (2020). The Nonlocal Neural Operator: Universal Approximation. DOI: arXiv preprint arXiv:2304.13221.

Initialization of the AveragingNeuralOperator class.

Parameters:

  • lifting_net (torch.nn.Module) – The lifting neural network mapping the input to its hidden dimension. It must take as input the input field and the coordinates at which the input field is evaluated.

  • projecting_net (torch.nn.Module) – The projection neural network mapping the hidden representation to the output function. It must take as input the embedding dimension plus the dimension of the coordinates.

  • field_indices (list[str]) – The labels of the fields in the input tensor.

  • coordinates_indices (list[str]) – The labels of the coordinates in the input tensor.

  • n_layers (int) – The number of hidden layers. Default is 4.

  • func (torch.nn.Module) – The activation function to use. Default is torch.nn.GELU.

Raises:

  • ValueError – If the input dimension does not match with the labels of the fields and coordinates.

  • ValueError – If the input dimension of the projecting network does not match with the hidden dimension of the lifting network.

forward(x)[source]#

Forward pass for the AveragingNeuralOperator model.

The lifting_net maps the input to the hidden dimension. Then, several layers of AVNOBlock are applied. Finally, the projection_net maps the hidden representation to the output function.

Parameters:

x (LabelTensor) – The input tensor for performing the computation. It expects a tensor \(B \times N \times D\), where \(B\) is the batch_size, \(N\) the number of points in the mesh, \(D\) the dimension of the problem, i.e. the sum of len(coordinates_indices) and len(field_indices).

Returns:

The output tensor.

Return type:

torch.Tensor