API Documentation

rom.gradients module

rom.gradients.local_linear_gradients(X, Y, n=None)[source]

Estimates gradients via local linear approximations.

Note

This code follows that used in: https://github.com/paulcon/active_subspaces

Parameters

X (ndarray) – M-by-d 2D numpy array containing input training samples
Y (ndarray) – M length 1D numpy array containing the 1D output training samples
n (int) – number of nearest neighbors to use for local linear approximation

Returns

M-by-d 2D numpy array containing local linear approximation of gradients for each training sample

Return type

DY (ndarray)

rom.surr_model module

class rom.surr_model.NN_alt(U, dim_layers, lr=0.001, lr_decay=0.9, alpha=0.001)[source]

Bases: object

Shallow ReLU Network with alternating minimization surrogate model.

net: two layer ReLU network

optimizer: optimizer for network

loss_func: loss function for network

lr

learning rate

Type: float

lr_decay

learning rate decay

Type: float

alpha

regularization parameter (ell 2 regularizer)

Type: float

U

d-by-k 2D numpy array to reduce input dimension

Type: ndarray

loss_train

contains training loss values at each epoch

Type: list

loss_val

contains validation loss values at each epoch

Type: list

predict(X)[source]

Calculates output of trained NN model.

Parameters: X (ndarray) – ?-by-d 2D numpy array containing input data
Returns: ?-by-d2 2D numpy array containing output data
Return type: Y (ndarray)

rel_error_tensor(Y_true, Y_calc)[source]

Calculates relative error (via ell 2 norm) between 2 PyTorch tensors.

Parameters

Y_true (ndarray) – numpy array containing true values
Y_calc (ndarray) – numpy array containing calculated/predicted values

Returns

relative error between Y_true and Y_calc

Return type

(float)

sub_dres(U, X_train, Y_train)[source]

Defines derivative of cost function w.r.t. U.

Note

This function is defined for the pymanopt optimization problem. Must take in U as variable.

Parameters

U (ndarray) – d-by-k 2D numpy array containing reduced basis
X_train (ndarray) – M-by-d 2D numpy array containing input training data
Y_train (ndarray) – M-by-d2 2D numpy array containing output training data

Returns

d-by-k 2D numpy array containing reduced basis

Return type

(ndarray)

sub_res(U, X_train, Y_train)[source]

Defines cost function w.r.t. U.

Note

This function is defined for the pymanopt optimization problem. Must take in U as variable.

Parameters

U (ndarray) – d-by-k 2D numpy array containing reduced basis
X_train (ndarray) – M-by-d 2D numpy array containing input training data
Y_train (ndarray) – M-by-d2 2D numpy array containing output training data

Returns

cost value for given U

Return type

out (float)

train(dataset_train, dataset_val=None, num_outer=10, num_epoch=5000, batch_size=16, record=True, verbose=2)[source]

Trains NN model via alternating minimization scheme.

Parameters

dataset_train (tuple,ndarray) – [X_train,Y_train], numpy array containing input/output training data
dataset_val (tuple,ndarray) – [X_val,Y_val], numpy array containing input/output validation data
num_outer (int) – number of outer iterations to perform
num_epoch (int) – number of inner iterations for NN training to perform
batch_size (int) – number of training samples in each training batch
record (bool) – choose to record loss during training or not
verbose (int) – amount of information to print; 0 = nothing printed; 1 = loss values printed every 1000 epochs; 2 = loss values printed every 100 epochs; >2 = loss values printed every epoch

train_NN(dataset_train, dataset_val, num_epoch, batch_size, record, verbose)[source]

Trains and validates NN.

Parameters

dataset_train (tuple,ndarray) – [X_train,Y_train], numpy array containing input/output training data
dataset_val (tuple,ndarray) – [X_val,Y_val], numpy array containing input/output validation data
num_outer (int) – number of outer iterations to perform
num_epoch (int) – number of inner iterations for NN training to perform
batch_size (int) – number of training samples in each training batch
record (bool) – choose to record loss during training or not
verbose (int) – amount of information to print; 0 = nothing printed; 1 = loss values printed every 1000 epochs; 2 = loss values printed every 100 epochs; >2 = loss values printed every epoch

Returns

contains training loss at each epoch loss_val (list): contains validation loss at each epoch

Return type

loss_train (list)

train_sub(X_train, Y_train)[source]

Trains subspace U.

Parameters

X_train (ndarray) – M-by-d 2D numpy array containing input training data
Y_train (ndarray) – M-by-d2 2D numpy array containing output training data

class rom.surr_model.RF[source]

Bases: object

Random Feature Expansion surrogate model.

Note

All attributes are set after the “train” method is called.

c

N length 1D numpy array containing coefficients of learned RF model

Type: ndarray

Omega

N-by-d 2D numpy array containing weights of the RF model

Type: ndarray

bias

N length 1D numpy array containing biases of the RF model

Type: ndarray

scale_A_normalize

N length 1D numpy array to normalize columns of A_train (RF matrix with training data)

Type: ndarray

construct_A(X)[source]

Constructs random feature matrix A.

Parameters: X (ndarray) – ?-by-d 2D numpy array containing ? number of input data points
Returns: ?-by-N 2D numpy array representing the random feature matrix A
Return type: A (ndarray)

construct_weights(X_train, k, N, s)[source]

Constructs weights and biases for RF model.

Parameters

X_train (ndarray) – M-by-d 2D numpy array containing input training data
k (int) – dimension of input data
N (int) – number of weights to use for RF model
s (int) – sparsity for weights Omega

phi(nodes)[source]

Activation function phi for RF model.

Parameters: nodes (ndarray) – N length 1D numpy array containing nodal values
Returns: N length 1D numpy array containing nodes passed through activation function phi
Return type: out (ndarray)

predict(X)[source]

Calculates output of trained RF model.

Parameters: X (ndarray) – ?-by-d 2D numpy array containing ? number of input data points
Returns: ? length 1D numpy array containing predicted output values
Return type: Y (ndarray)

train(dataset_train, N=None, s=None, alpha=0.001)[source]

Trains RF model by learning coefficients c via ridge regression.

Note

Assumes output data is 1D.

Parameters

X_train (ndarray) – M-by-d 2D numpy array containing input training data
Y_train (ndarray) – M length 1D numpy array containing output training data
N (int) – number of weights to use for RF model
alpha (float) – regularizing hyperparameter for ridge regression model

rom.subspaces module

rom.subspaces.AS(DY, k)[source]

Constructs a reduced subspace via active subspaces.

Parameters

DY (ndarray) – M-by-d 2D numpy array containing gradients for each training sample
k (int) – reduced dimension size

Returns

d-by-k 2D numpy array containing reduced basis vectors

Return type

U (ndarray)

rom.subspaces.POD(X, k)[source]

Constructs a reduced subspace via active subspaces.

Parameters

X (ndarray) – M-by-d 2D numpy array containing gradients for each training sample
k (int) – reduced dimension size

Returns

d-by-k 2D numpy array containing reduced basis vectors

Return type

U (ndarray)

rom.utils module

rom.utils.check_1D(X)[source]

Enforces requirement that X be a 1D numpy array.

Parameters: X (ndarray) – ND numpy array containing data points
Returns: unaltered 1D numpy array
Return type: X (ndarray)

rom.utils.check_2D(X)[source]

Enforces requirement that X be a 2D numpy array.

Parameters: X (ndarray) – ND numpy array containing data points
Returns: unaltered 2D numpy array
Return type: X (ndarray)

rom.utils.print_epoch(verbose, epoch, num_epoch, loss_train, loss_val=None, overwrite=False)[source]

Prints training/validation error at given epoch.

Parameters

verbose (int) – amount of information to print; 0 = nothing printed; 1 = loss values printed every 1000 epochs; 2 = loss values printed every 100 epochs; >2 = loss values printed every epoch
epoch (int) – current epoch number
num_epoch (int) – total epoch number
loss_train (float) – current loss value for training data
loss_val (float) – current loss value for validation data
overwrite (boolean) – choose to overwrite previous line

rom.utils.rel_error(Y_true, Y_calc)[source]

Calculates relative error (via ell 2 norm) between 2 arrays.

Parameters

Y_true (ndarray) – numpy array containing true values
Y_calc (ndarray) – numpy array containing calculated/predicted values

Returns

relative error between Y_true and Y_calc

Return type

out (float)