BayesianROM

class BayesianROM(model, *, lifter=None, transformer=None, basis=None, ddt_estimator=None)

Probabilistic nonparametric reduced-order model.

This class connects classes from the various submodules to form a complete reduced-order modeling workflow for probabilistic models.

High-dimensional data \(\to\) transformed / preprocessed data \(\to\) compressed data \(\to\) low-dimensional probabilistic model.

Operator inference models are uniquely determined by operator matrices \(\Ohat\in\RR^{r\times d}\) that concatenate the entries of all operators in the model. For example, the time-continuous model

\[\ddt\qhat(t) = \chat + \Ahat\qhat(t) + \Hhat[\qhat(t)\otimes\qhat(t)]\]

is uniquely determined by the operator matrix

\[\Ohat = [~\chat~~\Ahat~~\Hhat~] \in \RR^{r \times d}.\]

Typical deterministic operator inference learns a single operator matrix \(\Ohat\) from state measurements, while probabilistic or Bayesian operator inference constructs a distribution of operator matrices, \(p(\Ohat)\). This class solves a Bayesian linear inference to define an OperatorPosterior and facilitates sampling from the posterior. See [GMW22].

Parameters:

modelopinf.models object

Nonparametric system model, an instance of one of the following:

• opinf.models.ContinuousModel

• opinf.models.DiscreteModel

The model must have a solver of one of the following types:

• opinf.lstsq.L2Solver

• opinf.lstsq.L2DecoupledSolver

• opinf.lstsq.TikhonovSolver

• opinf.lstsq.TikhonovDecoupledSolver

lifteropinf.lift object or None

Lifting transformation.

transformeropinf.pre object or None

Preprocesser.

basisopinf.basis object or None

Dimensionality reducer.

ddt_estimatoropinf.ddt object or None

Time derivative estimator. Ignored if model is not time continuous.

Notes

The operators attribute of the model represents a single draw from the operator distribution and is modified every time draw_operators() or predict() are called.

Properties:

basis

Dimensionality reducer.

ddt_estimator

Time derivative estimator.

lifter

Lifting transformation.

model

System model.

posterior

Posterior distribution for the operator matrices.

transformer

Preprocesser.

Methods:

decode	Map low-dimensional data to the original state space.
draw_operators	Set the model operators to a new random draw from the posterior operator distribution.
encode	Map high-dimensional data to its low-dimensional representation.
fit	Calibrate the model to training data.
fit_regselect_continuous	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.
fit_regselect_discrete	Calibrate the fully discrete model to training data, selecting the regularization hyperparameter(s) that minimize the sample mean training error while maintaining stability over the testing regime.
predict	Draw from the operator posterior and evaluate the resulting model.
project	Project a high-dimensional state vector to the subset of the high-dimensional space that can be represented by the basis.