MIONet#

class MIONet(networks, aggregator='*', reduction='+', scale=True, translation=True)[source]#

Bases: Module

MIONet 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: Jin, P., Meng, S., and Lu L. (2022). MIONet: Learning multiple-input operators via tensor product. SIAM Journal on Scientific Computing 44.6 (2022): A3490-A351 DOI: 10.1137/22M1477751

Initialization of the MIONet class.

Parameters:

networks (dict) – The neural networks to use as models. The dict takes as key a neural network, and as value the list of indeces to extract from the input variable in the forward pass of the neural network. If a list[int] is passed, the corresponding columns of the inner most entries are extracted. If a list[str] is passed the variables of the corresponding LabelTensor are extracted. Each torch.nn.Module model has to take as input either a LabelTensor or a torch.Tensor. Default implementation consists of several branch nets and one trunk nets.
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.

Raises:

ValueError – If the passed networks have not the same output dimension.

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 networks dict values. Differently, in case of a torch.Tensor, only a list[int] can be passed as networks dict values.

Example:

>>> branch_net1 = FeedForward(input_dimensons=1,
... output_dimensions=10)
>>> branch_net2 = FeedForward(input_dimensons=2,
... output_dimensions=10)
>>> trunk_net = FeedForward(input_dimensons=1, output_dimensions=10)
>>> networks = {branch_net1 : ['x'],
                branch_net2 : ['x', 'y'],
...             trunk_net : ['z']}
>>> model = MIONet(networks=networks,
...                reduction='+',
...                aggregator='*')
>>> model
MIONet(
(models): ModuleList(
    (0): 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)
    )
    )
    (1): FeedForward(
    (model): Sequential(
        (0): Linear(in_features=2, 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)
    )
    )
    (2): 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 MIONet model.

Parameters:: x (LabelTensor | torch.Tensor) – The input tensor.
Returns:: The output tensor.
Return type:: LabelTensor | torch.Tensor

property aggregator#

The aggregator function.

Returns:: The aggregator function.
Return type:: str or Callable

property reduction#

The reduction function.

Returns:: The reduction function.
Return type:: str or Callable

property scale#

The scale factor.

Returns:: The scale factor.
Return type:: torch.Tensor

property translation#

The translation factor.

Returns:: The translation factor.
Return type:: torch.Tensor

property indeces_variables_extracted#

The input indeces for each model in form of list.

Returns:: The indeces for each model.
Return type:: list

property model#

The models in form of list.

Returns:: The models.
Return type:: list[torch.nn.Module]

MIONet#

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