MIONet

class MIONet(networks, aggregator='*', reduction='+', scale=True, translation=True)

Bases: Module

The PINA implementation of MIONet network.

MIONet is a general architecture for learning Operators defined on the tensor product of Banach spaces. Unlike traditional machine learning methods MIONet 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: Jin, Pengzhan, Shuai Meng, and Lu Lu. MIONet: Learning multiple-input operators via tensor product. SIAM Journal on Scientific Computing 44.6 (2022): A3490-A351 DOI: 10.1137/22M1477751

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 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. The torch.nn.Module model has to take as input a pina.label_tensor.LabelTensor or torch.Tensor. Default implementation consist of different branch nets and one trunk nets.

• 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_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)

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 aggregator

The aggregator function.

property reduction

The translation factor.

property scale

The scale factor.

property translation

The translation factor for MIONet.

property indeces_variables_extracted

The input indeces for each model in form of list.

property model

The models in form of list.