DeepONet#

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

Bases: MIONet

DeepONet model class.

The MIONet is a general architecture for learning operators, which map functions to functions. It can be trained with both Supervised and Physics-Informed 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 operator. Nat Mach Intell 3, 218-229 (2021). DOI: 10.1038/s42256-021-00302-5

Initialization of the DeepONet class.

Parameters:

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

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

  • input_indeces_branch_net (list[int] | list[str]) – List of indeces to extract from the input variable of 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 LabelTensor are extracted.

  • input_indeces_trunk_net (list[int] | list[str]) – List of indeces to extract from the input variable of 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 LabelTensor are extracted.

  • aggregator (str or Callable) – The aggregator to be used to aggregate component-wise partial results from the modules in networks. Available aggregators include: sum: +, product: *, mean: mean, min: min, max: max. Default is *.

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

  • scale (bool) – If True, the final output is scaled before being returned in the forward pass. Default is True.

  • translation (bool) – If True, the final output is translated before being returned in the forward pass. Default is 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.

Warning

No checks are performed in the forward pass to verify if the input is instance of either LabelTensor or torch.Tensor. In general, in case of a LabelTensor, both a list[int] or a list[str] can be passed as input_indeces_branch_net and input_indeces_trunk_net. Differently, in case of a torch.Tensor, only a list[int] can be passed.

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]#

Forward pass for the DeepONet model.

Parameters:

x (LabelTensor | torch.Tensor) – The input tensor.

Returns:

The output tensor.

Return type:

LabelTensor | torch.Tensor

property branch_net#

The branch net of the DeepONet.

Returns:

The branch net.

Return type:

torch.nn.Module

property trunk_net#

The trunk net of the DeepONet.

Returns:

The trunk net.

Return type:

torch.nn.Module