DeepONet#

class DeepONet(branch_net, trunk_net, input_indeces_branch_net, input_indeces_trunk_net, aggregator='*', reduction='+', scale=True, translation=True)[source]#

Bases: MIONet

The PINA implementation of DeepONet network.

DeepONet is a general architecture for learning Operators. Unlike traditional machine learning methods DeepONet is designed to map entire functions to other functions. It can be trained both with Physics Informed or Supervised learning strategies.

See also

Original reference: Lu, L., Jin, P., Pang, G. et al. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nat Mach Intell 3, 218–229 (2021). DOI: 10.1038/s42256-021-00302-5

Parameters:

  • branch_net (torch.nn.Module) – The neural network to use as branch model. It has to take as input a pina.label_tensor.LabelTensor or torch.Tensor. The number of dimensions of the output has to be the same of the trunk_net.

  • trunk_net (torch.nn.Module) – The neural network to use as trunk model. It has to take as input a pina.label_tensor.LabelTensor or torch.Tensor. The number of dimensions of the output has to be the same of the branch_net.

  • input_indeces_branch_net (list(int) or list(str)) – List of indeces to extract from the input variable in the forward pass for the branch net. If a list of int is passed, the corresponding columns of the inner most entries are extracted. If a list of str is passed the variables of the corresponding pina.label_tensor.LabelTensor are extracted.

  • input_indeces_trunk_net (list(int) or list(str)) – List of indeces to extract from the input variable in the forward pass for the trunk net. If a list of int is passed, the corresponding columns of the inner most entries are extracted. If a list of str is passed the variables of the corresponding pina.label_tensor.LabelTensor are extracted.

  • aggregator (str or Callable) – Aggregator to be used to aggregate partial results from the modules in nets. Partial results are aggregated component-wise. Available aggregators include sum: +, product: *, mean: mean, min: min, max: max.

  • reduction (str or Callable) – Reduction to be used to reduce the aggregated result of the modules in nets to the desired output dimension. Available reductions include sum: +, product: *, mean: mean, min: min, max: max.

  • scale (bool or Callable) – Scaling the final output before returning the forward pass, default True.

  • translation (bool or Callable) – Translating the final output before returning the forward pass, default True.

Warning

In the forward pass we do not check if the input is instance of pina.label_tensor.LabelTensor or torch.Tensor. A general rule is that for a pina.label_tensor.LabelTensor input both list of integers and list of strings can be passed for input_indeces_branch_net and input_indeces_trunk_net. Differently, for a torch.Tensor only a list of integers can be passed for input_indeces_branch_net and input_indeces_trunk_net.

Example:
>>> branch_net = FeedForward(input_dimensons=1, output_dimensions=10)
>>> trunk_net = FeedForward(input_dimensons=1, output_dimensions=10)
>>> model = DeepONet(branch_net=branch_net,
...                  trunk_net=trunk_net,
...                  input_indeces_branch_net=['x'],
...                  input_indeces_trunk_net=['t'],
...                  reduction='+',
...                  aggregator='*')
>>> model
DeepONet(
(trunk_net): FeedForward(
    (model): Sequential(
    (0): Linear(in_features=1, out_features=20, bias=True)
    (1): Tanh()
    (2): Linear(in_features=20, out_features=20, bias=True)
    (3): Tanh()
    (4): Linear(in_features=20, out_features=10, bias=True)
    )
)
(branch_net): FeedForward(
    (model): Sequential(
    (0): Linear(in_features=1, out_features=20, bias=True)
    (1): Tanh()
    (2): Linear(in_features=20, out_features=20, bias=True)
    (3): Tanh()
    (4): Linear(in_features=20, out_features=10, bias=True)
    )
)
)
forward(x)[source]#

Defines the computation performed at every call.

Parameters:

x (LabelTensor or torch.Tensor) – The input tensor for the forward call.

Returns:

The output computed by the DeepONet model.

Return type:

LabelTensor or torch.Tensor

property branch_net#

The branch net for DeepONet.

property trunk_net#

The trunk net for DeepONet.