lasdi.latent_space

Attributes

act_dict

Classes

MultiLayerPerceptron	A standard multi-layer perceptron (MLP) module.
Autoencoder	A standard autoencoder using MLP.
MLPWithMask	Multi-layer perceptron with additional mask output.
AutoEncoderWithMask	Autoencoder class with additional mask output.

Functions

initial_condition_latent(param_grid, physics, autoencoder)

Outputs the initial condition in the latent space: Z0 = encoder(U0)

Module Contents

lasdi.latent_space.act_dict

lasdi.latent_space.initial_condition_latent(param_grid, physics, autoencoder)

Outputs the initial condition in the latent space: Z0 = encoder(U0)

Parameters:

• param_grid (numpy.array) – A 2d array of shape (n_param, param_dim) for parameter points to obtain initial condition.

• physics (lasdi.physics.Physics) – Physics class to generate initial condition.

• autoencoder (lasdi.latent_space.Autoencoder) – Autoencoder class to encode initial conditions into latent variables.

Returns:

Z0 – a torch tensor of size (n_param, n_z), where n_z is the latent variable dimension defined by autoencoder.

Return type:

torch.Tensor

class lasdi.latent_space.MultiLayerPerceptron(layer_sizes, act_type='sigmoid', reshape_index=None, reshape_shape=None, threshold=0.1, value=0.0, num_heads=1)

Bases: torch.nn.Module

A standard multi-layer perceptron (MLP) module.

n_layers

Depth of MLP including input, hidden, and output layers.

Type:

int

layer_sizes

Widths of each MLP layer, including input, hidden and output layers.

Type:

list(int)

fcs = []

torch module list of \((self.n\_layers-1)\) linear layers, connecting from input to output layers.

Type:

torch.nn.ModuleList

reshape_index = None

Index of the layer to reshape.

• 0: Input data is n-dimensional and will be squeezed into 1d tensor for MLP input.

• 1: Output data should be n-dimensional and MLP output will be reshaped as such.

Type:

int

reshape_shape = None

Shape of the layer to be reshaped.

• \((self.reshape_index=0)\): Shape of the input data that will be squeezed into 1d tensor for MLP input.

• \((self.reshape_index=1)\): Shape of the output data into which MLP output shall be reshaped.

Type:

list(int)

act_type = 'sigmoid'

type of activation function

Type:

str

use_multihead = False

switch to use multihead attention.

Warning:

this attribute is obsolete and will be removed in future.

Type:

bool

act = None

activation function

Type:

torch.nn.Module

forward(x)

Pass the input through the MLP layers.

Args:

x (torch.Tensor): n-dimensional torch.Tensor for input data.

Note:

• If self.reshape_index == 0, then the last n dimensions of x must match self.reshape_shape. In other words, list(x.shape[-len(self.reshape_shape):]) == self.reshape_shape

• If self.reshape_index == -1, then the last layer output z is reshaped into self.reshape_shape. In other words, list(z.shape[-len(self.reshape_shape):]) == self.reshape_shape

Returns:

n-dimensional torch.Tensor for output data.

apply_attention(x, act_idx)

init_weight()

Initialize the weights and biases of the linear layers.

Returns:

Does not return a value.

class lasdi.latent_space.Autoencoder(physics, config)

Bases: torch.nn.Module

A standard autoencoder using MLP.

Args:

physics (lasdi.physics.Physics): Physics class that specifies full-order model solution dimensions.

config: (dict): options for autoencoder. It must include the following keys and values.

• 'hidden_units': a list of integers for the widths of hidden layers.

• 'latent_dimension': integer for the latent space dimension.

• 'activation': string for type of activation function.

qgrid_size

space_dim

n_z

encoder

decoder

forward(x)

export()

load(dict_)

class lasdi.latent_space.MLPWithMask(mlp)

Bases: MultiLayerPerceptron

Multi-layer perceptron with additional mask output.

Args:

mlp (lasdi.latent_space.MultiLayerPerceptron): MultiLayerPerceptron class to copy. The same architecture, activation function, reshaping will be used.

n_layers

Depth of MLP including input, hidden, and output layers.

Type:

int

layer_sizes

Widths of each MLP layer, including input, hidden and output layers.

Type:

list(int)

fcs

torch module list of \((self.n\_layers-1)\) linear layers, connecting from input to output layers.

Type:

torch.nn.ModuleList

reshape_index

Index of the layer to reshape.

• 0: Input data is n-dimensional and will be squeezed into 1d tensor for MLP input.

• 1: Output data should be n-dimensional and MLP output will be reshaped as such.

Type:

int

reshape_shape

Shape of the layer to be reshaped.

• \((self.reshape_index=0)\): Shape of the input data that will be squeezed into 1d tensor for MLP input.

• \((self.reshape_index=1)\): Shape of the output data into which MLP output shall be reshaped.

Type:

list(int)

act_type

type of activation function

Type:

str

use_multihead

switch to use multihead attention.

Warning:

this attribute is obsolete and will be removed in future.

Type:

bool

act

activation function

Type:

torch.nn.Module

bool_d

additional linear layer to output a mask variable.

Type:

torch.nn.Linear

sigmoid

mask output passes through the sigmoid activation function to ensure \([0, 1]\).

Type:

torch.nn.Sigmoid

forward(x)

Pass the input through the MLP layers.

Args:

x (torch.Tensor): n-dimensional torch.Tensor for input data.

Note:

• If self.reshape_index == 0, then the last n dimensions of x must match self.reshape_shape. In other words, list(x.shape[-len(self.reshape_shape):]) == self.reshape_shape

• If self.reshape_index == -1, then the last layer outputs xval and xbool are reshaped into self.reshape_shape. In other words, list(xval.shape[-len(self.reshape_shape):]) == self.reshape_shape

Returns:

xval (torch.Tensor): n-dimensional torch.Tensor for output data. xbool (torch.Tensor): n-dimensional torch.Tensor for output mask.

class lasdi.latent_space.AutoEncoderWithMask(physics, config)

Bases: Autoencoder

Autoencoder class with additional mask output.

Its decoder is lasdi.latent_space.MLPWithMask, which has an additional mask output.

Note:

Unlike the standard autoencoder, the decoder output will have two outputs (with the same shape of the input of the encoder).

decoder