Regression & Surrogates

Examples demonstrating surrogate model construction via linear regression, Bayesian compressive sensing, Gaussian processes, and dimensionality reduction.

ex_lreg.py

Polynomial chaos linear regression methods.

Compares various linear regression techniques (LSQ, ANL, OPT, MERR) for constructing polynomial chaos surrogates and evaluates their performance.

ex_lreg_basiseval.py

Polynomial chaos basis evaluation and regression.

Compares different regression methods (least squares, analytical, optimization) for polynomial chaos surrogate construction and evaluates basis function efficiency.

ex_lreg_merr.py

Linear regression with measurement error.

Performs polynomial chaos regression accounting for measurement errors in the data using the MERR (Measurement Error in Regression) method.

ex_bcs.py (demo)

Bayesian compressive sensing for sparse PC regression.

Uses BCS to construct a sparse polynomial chaos surrogate model with a specified multiindex and model data, comparing predictions with true function values.

ex_bcs_mindex_growth.py

Adaptive multiindex growth with BCS.

Iteratively grows a polynomial chaos surrogate using adaptive multiindex selection and BCS regression for sparse approximation.

ex_gp.py

Gaussian process regression.

Builds a Gaussian process surrogate model from training data, performs hyperparameter optimization, and evaluates prediction accuracy.

ex_kl.py

Karhunen–Loève expansion and SVD.

Builds KLE or SVD representations of model output data to capture variance with reduced dimensionality.

ex_klpc.py

KLE combined with polynomial chaos.

Uses Karhunen–Loève Expansion to reduce output dimensionality, then builds PC surrogates for the reduced modes to efficiently represent high-dimensional model outputs.