deepxde.nn.paddle

deepxde.nn.paddle.deeponet module

class deepxde.nn.paddle.deeponet.DeepONet(layer_sizes_branch, layer_sizes_trunk, activation, kernel_initializer, use_bias=True)

Bases: NN

Deep operator network.

Lu et al. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nat Mach Intell, 2021.

Parameters:

• layer_sizes_branch – A list of integers as the width of a fully connected network, or (dim, f) where dim is the input dimension and f is a network function. The width of the last layer in the branch and trunk net should be equal.

• layer_sizes_trunk (list) – A list of integers as the width of a fully connected network.

• activation – If activation is a string, then the same activation is used in both trunk and branch nets. If activation is a dict, then the trunk net uses the activation activation[“trunk”], and the branch net uses activation[“branch”].

forward(inputs)

Defines the computation performed at every call. Should be overridden by all subclasses.

Parameters:

• *inputs (tuple) – unpacked tuple arguments

• **kwargs (dict) – unpacked dict arguments

class deepxde.nn.paddle.deeponet.DeepONetCartesianProd(layer_sizes_branch, layer_sizes_trunk, activation, kernel_initializer, num_outputs=1, multi_output_strategy=None)

Bases: NN

Deep operator network for dataset in the format of Cartesian product.

Parameters:

• layer_sizes_branch – A list of integers as the width of a fully connected network, or (dim, f) where dim is the input dimension and f is a network function. The width of the last layer in the branch and trunk net should be the same for all strategies except “split_branch” and “split_trunk”.

• layer_sizes_trunk (list) – A list of integers as the width of a fully connected network.

• activation – If activation is a string, then the same activation is used in both trunk and branch nets. If activation is a dict, then the trunk net uses the activation activation[“trunk”], and the branch net uses activation[“branch”].

• num_outputs (integer) – Number of outputs. In case of multiple outputs, i.e., num_outputs > 1, multi_output_strategy below should be set.

• multi_output_strategy (str or None) –

  None, “independent”, “split_both”, “split_branch” or “split_trunk”. It makes sense to set in case of multiple outputs.

  • None

  Classical implementation of DeepONet with a single output. Cannot be used with num_outputs > 1.

  • independent

  Use num_outputs independent DeepONets, and each DeepONet outputs only one function.

  • split_both

  Split the outputs of both the branch net and the trunk net into num_outputs groups, and then the kth group outputs the kth solution.

  • split_branch

  Split the branch net and share the trunk net. The width of the last layer in the branch net should be equal to the one in the trunk net multiplied by the number of outputs.

  • split_trunk

  Split the trunk net and share the branch net. The width of the last layer in the trunk net should be equal to the one in the branch net multiplied by the number of outputs.

build_branch_net(layer_sizes_branch)

build_trunk_net(layer_sizes_trunk)

static concatenate_outputs(ys)

forward(inputs)

Defines the computation performed at every call. Should be overridden by all subclasses.

Parameters:

• *inputs (tuple) – unpacked tuple arguments

• **kwargs (dict) – unpacked dict arguments

merge_branch_trunk(x_func, x_loc, index)

deepxde.nn.paddle.fnn module

class deepxde.nn.paddle.fnn.FNN(layer_sizes, activation, kernel_initializer, regularization=None, dropout_rate=0)

Bases: NN

Fully-connected neural network.

forward(inputs)

Defines the computation performed at every call. Should be overridden by all subclasses.

Parameters:

• *inputs (tuple) – unpacked tuple arguments

• **kwargs (dict) – unpacked dict arguments

class deepxde.nn.paddle.fnn.PFNN(layer_sizes, activation, kernel_initializer, regularization=None)

Bases: NN

Parallel fully-connected network that uses independent sub-networks for each network output.

Parameters:

• layer_sizes – A nested list that defines the architecture of the neural network (how the layers are connected). If layer_sizes[i] is an int, it represents one layer shared by all the outputs; if layer_sizes[i] is a list, it represents len(layer_sizes[i]) sub-layers, each of which is exclusively used by one output. Note that len(layer_sizes[i]) should equal the number of outputs. Every number specifies the number of neurons in that layer.

• activation – A string represent activation used in fully-connected net.

• kernel_initializer – Initializer for the kernel weights matrix.

forward(inputs)

Defines the computation performed at every call. Should be overridden by all subclasses.

Parameters:

• *inputs (tuple) – unpacked tuple arguments

• **kwargs (dict) – unpacked dict arguments

deepxde.nn.paddle.msffn module

class deepxde.nn.paddle.msffn.MsFFN(layer_sizes, activation, kernel_initializer, sigmas, dropout_rate=0)

Bases: NN

Multi-scale fourier feature networks.

Parameters:

sigmas – List of standard deviation of the distribution of fourier feature embeddings.

References

S. Wang, H. Wang, & P. Perdikaris. On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 384, 113938, 2021.

forward(inputs)

Defines the computation performed at every call. Should be overridden by all subclasses.

Parameters:

• *inputs (tuple) – unpacked tuple arguments

• **kwargs (dict) – unpacked dict arguments

class deepxde.nn.paddle.msffn.STMsFFN(layer_sizes, activation, kernel_initializer, sigmas_x, sigmas_t, dropout_rate=0)

Bases: MsFFN

Spatio-temporal multi-scale fourier feature networks.

References

S. Wang, H. Wang, & P. Perdikaris. On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 384, 113938, 2021.

forward(inputs)

Defines the computation performed at every call. Should be overridden by all subclasses.

Parameters:

• *inputs (tuple) – unpacked tuple arguments

• **kwargs (dict) – unpacked dict arguments

deepxde.nn.paddle.nn module

class deepxde.nn.paddle.nn.NN

Bases: Layer

Base class for all neural network modules.

apply_feature_transform(transform)

Compute the features by appling a transform to the network inputs, i.e., features = transform(inputs). Then, outputs = network(features).

apply_output_transform(transform)

Apply a transform to the network outputs, i.e., outputs = transform(inputs, outputs).