autompc package

autompc.sysid module

Just doing system id using multi-layer perceptron. The code is similar to GP / RNN. The configuration space has to be carefully considered

autompc.sysid.mlp.transform_input(xu_means, xu_std, XU)

autompc.sysid.mlp.transform_output(xu_means, xu_std, XU)

class autompc.sysid.mlp.ForwardNet(n_in, n_out, hidden_sizes, nonlintype)

Bases: Module

forward(x)

Defines the computation performed at every call.

Should be overridden by all subclasses.

Note

Although the recipe for forward pass needs to be defined within this function, one should call the Module instance afterwards instead of this since the former takes care of running the registered hooks while the latter silently ignores them.

training: bool

class autompc.sysid.mlp.SimpleDataset(x, y)

Bases: Dataset

class autompc.sysid.mlp.MLPFactory(*args, **kwargs)

Bases: ModelFactory

The multi-layer perceptron (MLP) model uses a feed-forward neural network architecutret to predict the system dynamics. The network size, activation function, and learning rate are tunable hyperparameters.

Parameters

• n_batch (Type: int, Default: 64): Training batch size of the neural net.

• n_train_iters (Type: int, Default: 50): Number of training epochs

Hyperparameters:

• n_hidden_layers (Type: str, Choices: [“1”, “2”, “3”, “4”], Default: “2”): The number of hidden layers in the network

• hidden_size_1 (Type int, Low: 16, High: 256, Default: 32): Size of hidden layer 1.

• hidden_size_2 (Type int, Low: 16, High: 256, Default: 32): Size of hidden layer 2. (Conditioned on n_hidden_layers >=2).

• hidden_size_3 (Type int, Low: 16, High: 256, Default: 32): Size of hidden layer 3. (Conditioned on n_hidden_layers >=3).

• hidden_size_4 (Type int, Low: 16, High: 256, Default: 32): Size of hidden layer 4. (Conditioned on n_hidden_layers >=4).

• nonlintype (Type: str, choices: [“relu”, “tanh”, “sigmoid”, “selu”], Default: “relu): Type of activation function.

• lr (Type: float, Low: 1e-5, High: 1, Default: 1e-3): Adam learning rate for the network.

get_configuration_space()

Returns the model configuration space.

class autompc.sysid.mlp.MLP(system, n_hidden_layers=3, hidden_size=128, nonlintype='relu', n_train_iters=50, n_batch=64, lr=0.001, hidden_size_1=None, hidden_size_2=None, hidden_size_3=None, hidden_size_4=None, seed=100, use_cuda=True)

Bases: Model

traj_to_state(traj)

Parameters:

traj (Trajectory) – State and control history up to present time

Returns:

state – Corresponding model state

Return type:

numpy array of size self.state_dim

update_state(state, new_ctrl, new_obs)

Parameters:

• state (numpy array of size self.state_dim) – Current model state

• new_ctrl (numpy array of size self.system.ctrl_dim) – New control input

• new_obs (numpy array of size self.system.obs_dim) – New observation

Returns:

state – Model state after observation and control

Return type:

numpy array of size self.state_dim

property state_dim

Returns the size of the model state

train(trajs, silent=False, seed=100)

Parameters:

• trajs (List of pairs (xs, us)) – Training set of trajectories

• silent (bool) – Silence progress bar output

Only implemented for trainable models.

pred(state, ctrl)

Run model prediction.

Parameters:

• state (Numpy array of size self.state_dim) – Model state at time t

• ctrl (Numpy array of size self.system.ctrl_dim) – Control applied at time t

Returns:

state – Predicted model state at time t+1

Return type:

Numpy array of size self.state_dim

pred_batch(state, ctrl)

Run batch model predictions. Depending on the model, this can be much faster than repeatedly calling pred.

Parameters:

• state (Numpy array of size (N, self.state_dim)) – N model input states

• ctrl (Numpy array of size (N, self.system.ctrl_dim)) – N controls

Returns:

state – N predicted states

Return type:

Numpy array of size (N, self.state_dim)

pred_diff(state, ctrl)

Use code from https://gist.github.com/sbarratt/37356c46ad1350d4c30aefbd488a4faa .

def get_batch_jacobian(net, x, to):

# noutputs: total output dim (e.g. net(x).shape(b,1,4,4) noutputs=1*4*4 # b: batch # i: in_dim # o: out_dim # ti: total input dim # to: total output dim x_batch = x.shape[0] x_shape = x.shape[1:] x = x.unsqueeze(1) # b, 1 ,i x = x.repeat(1, to, *(1,)*len(x.shape[2:])) # b * to,i copy to o dim x.requires_grad_(True) tmp_shape = x.shape y = net(x.reshape(-1, *tmp_shape[2:])) # x.shape = b*to,i y.shape = b*to,to y_shape = y.shape[1:] # y.shape = b*to,to y = y.reshape(x_batch, to, to) # y.shape = b,to,to input_val = torch.eye(to).reshape(1, to, to).repeat(x_batch, 1, 1) # input_val.shape = b,to,to value is (eye) y.backward(input_val) # y.shape = b,to,to return x.grad.reshape(x_batch, *y_shape, *x_shape).data # x.shape = b,o,i

pred_diff_batch(state, ctrl)

Prediction, but with gradient information

get_parameters()

Returns a dict containing trained model parameters.

Only implemented for trainable models.

set_parameters(params)

Sets trainable model parameters from dict.

Only implemented for trainable parameters.

class autompc.sysid.sindy.FourthOrderFiniteDifference

Bases: BaseDifferentiation

class autompc.sysid.sindy.SINDyFactory(*args, **kwargs)

Bases: ModelFactory

Sparse Identification of Nonlinear Dynamics (SINDy) is an system identification approach that works as follows. Using a library of \(k\) pre-selected functions (e.g. \(f \in \mathbb{R}^k\)), it computes numerically the derivatives of the system states (e.g. \(\dot{x} \in \mathbb{R}^n\)) iteratively solves a least-squares optimization to identify the weights \(K \in \mathbb{R}^{n \times k}\) that best fit the data: e.g. \(\|\dot{x} - Kf(x) \|^2\). In every iteration, functions whose weights are below a user-specified threshold \(\lambda\) are discarded. For more information, the reader is referred to https://arxiv.org/pdf/2004.08424.pdf

Hyperparameters:

• time_mode (Type str, Choices: [“discrete”, “continuous”]): Whether to learn dynamics equations as discrete-time or continous-time.

• method (Type str, Choices: [“lstsq, lasso”], Default: “lstsq”): Method for selecting model coefficients.

• lasso_alpha (Type: str, Low: 10^-5, High: 10^2, Default: 1): α parameter for lasso regression. (Conditioned on method=”lasso”)

• poly_basis (Type: bool): Whether to use polynomial basis functions

• poly_degree (Type: int, Low: 2, High: 8, Default: 3): Maximum degree of polynomial terms. (Conditioned on poly_basis=”true”)

• poly_cross_terms (Type: bool): Whether to include polynomial cross-terms. (Conditioned on poly_basis=”true”)

• trig_basis (Type: bool): Whether to include trigonometric basis terms.

• trig_freq (Type: int, Low: 1, High: 8, Default: 1): Maximum trig function frequency to include. (Conditioned on trig_basis=”true”)

• trig_interaction (Type: bool): Whether to include cross-multiplication terms between trig functions and other state variables.

get_configuration_space()

Returns the model configuration space.

class autompc.sysid.sindy.SINDy(system, method, lasso_alpha=None, threshold=0.01, poly_basis=False, poly_degree=1, poly_cross_terms=False, trig_basis=False, trig_freq=1, trig_interaction=False, time_mode='discrete')

Bases: Model

traj_to_state(traj)

Parameters:

traj (Trajectory) – State and control history up to present time

Returns:

state – Corresponding model state

Return type:

numpy array of size self.state_dim

update_state(state, new_ctrl, new_obs)

Parameters:

• state (numpy array of size self.state_dim) – Current model state

• new_ctrl (numpy array of size self.system.ctrl_dim) – New control input

• new_obs (numpy array of size self.system.obs_dim) – New observation

Returns:

state – Model state after observation and control

Return type:

numpy array of size self.state_dim

property state_dim

Returns the size of the model state

train(trajs, xdot=None, silent=False)

Parameters:

• trajs (List of pairs (xs, us)) – Training set of trajectories

• silent (bool) – Silence progress bar output

Only implemented for trainable models.

pred(state, ctrl)

Run model prediction.

Parameters:

• state (Numpy array of size self.state_dim) – Model state at time t

• ctrl (Numpy array of size self.system.ctrl_dim) – Control applied at time t

Returns:

state – Predicted model state at time t+1

Return type:

Numpy array of size self.state_dim

pred_batch(states, ctrls)

Run batch model predictions. Depending on the model, this can be much faster than repeatedly calling pred.

Parameters:

• state (Numpy array of size (N, self.state_dim)) – N model input states

• ctrl (Numpy array of size (N, self.system.ctrl_dim)) – N controls

Returns:

state – N predicted states

Return type:

Numpy array of size (N, self.state_dim)

pred_diff(state, ctrl)

Run model prediction and compute gradients.

Parameters:

• state (Numpy array of size self.state_dim) – Model state at time t

• ctrl (Numpy array of size self.system.ctrl_dim) – Control at time t

Returns:

• state (Numpy array of size self.state_dim) – Predicted model state at time t+1

• state_jac (Numpy array of shape (self.state_dim,) – self.state_dim) Gradient of predicted model state wrt to state

• ctrl_jac (Numpy array of shape (self.state_dim,) – self.ctrl_dim) Gradient of predicted model state wrt to ctrl

compute_gradient(states, ctrls, basis, coeff, feat_names)

pred_diff_batch(states, ctrls)

Run model prediction and compute gradients in batch.

Parameters:

• state (Numpy array of shape (N, self.state_dim)) – N input model states

• ctrl (Numpy array of size (N, self.system.ctrl_dim)) – N input controls

Returns:

• state (Numpy array of size (N, self.state_dim)) – N predicted model states

• state_jac (Numpy array of shape (N, self.state_dim,) – self.state_dim) Gradient of predicted model states wrt to state

• ctrl_jac (Numpy array of shape (N, self.state_dim,) – self.ctrl_dim) Gradient of predicted model states wrt to ctrl

get_parameters()

Returns a dict containing trained model parameters.

Only implemented for trainable models.

set_parameters(params)

Sets trainable model parameters from dict.

Only implemented for trainable parameters.

Module contents