fit_regselect_continuous()

BayesianROM.fit_regselect_continuous(candidates: list, train_time_domains: list, states: list, ddts: list = None, input_functions: list = None, fit_transformer: bool = True, fit_basis: bool = True, regularizer_factory=None, gridsearch_only: bool = False, test_time_length: float = 0, stability_margin: float = 5, num_posterior_draws: int = 20, test_cases: list = None, verbose: bool = False, **predict_options: dict)

Calibrate the time-continuous model to training data, selecting the regularization hyperparameter(s) that minimize the sample mean training error while maintaining stability over the testing regime.

This method requires the model to be time-continuous; use fit_regselect_discrete() for discrete models. The model.solver.regularizer is repeatedly adjusted, and the operator posterior is recalibrated, until a best regularization is selected. Training error is measured by comparing training data to the sample mean of num_posterior_draws model predictions. Stability is required for each of the individual model predictions. See [GMW22, MHW21].

Parameters:

candidateslist of regularization hyperparameters

Regularization hyperparameters to check before carrying out a derivative-free optimization.

train_time_domainslist of s (k_i,) ndarrays

Time domain corresponding to the training states.

stateslist of s (n, k_i) ndarrays

State snapshots in the original state space. Each array states[i] is data corresponding to a different trajectory; each column states[i][:, j] is one snapshot.

ddtslist of s (n, k_i) ndarrays or None

Snapshot time derivative data. Each array ddts[i] are the time derivatives of states[i]; each column ddts[i][:, j] corresponds to the snapshot states[i][:, j]. If None (default), these are estimated using ddt_estimator.

input_functionslist of s callables or None

Input functions mapping time to input vectors. Only required if the model takes external inputs. Each input_functions[i] is the function corresponding to states[i], and input_functions[i](train_time_domains[i][j]) is the input vector corresponding to the snapshot states[i][:, j].

fit_transformerbool

If True (default), calibrate the preprocessing transformation using the states. If False, assume the transformer is already calibrated.

fit_basisbool

If True (default), calibrate the high-to-low dimensional mapping using the states. If False, assume the basis is already calibrated.

regularizer_factorycallable or None

Function mapping regularization hyperparameters to the full regularizer. Specifically, regularizer_factory(candidates[i]) will be assigned to model.solver.regularizer for each i. If None (default), set regularizer_factory() to the identity function.

gridsearch_onlybool

If True, stop after checking all regularization candidates and do not follow up with optimization.

test_time_lengthfloat or None

Amount of time after the training regime in which to require model stability.

stability_marginfloat

Factor by which the predicted reduced states may deviate from the range of the training reduced states without the trajectory being classified as unstable.

num_posterior_drawsint

Number of draws from the operator posterior for stability checks and for estimating the sample mean of model predictions.

test_caseslist of ContinuousRegTest objects

Additional test cases for which the model is required to be stable. See opinf.utils.ContinuousRegTest.

verbosebool

If True, print information during the regularization selection.

predict_optionsdict or None

Extra arguments for opinf.models.ContinuousModel.predict().

Notes

If there is only one trajectory of training data (s = 1), states may be provided as an (n, k) ndarray. In this case, it is assumed that ddts (if provided) is an (n, k) ndarray.

The train_time_domains may be a single one-dimensional array, in which case it is assumed that each trajectory states[i] corresponds to the same time domain. Similarly, if input_functions is a single callable, it is assumed to be the input function for each trajectory.