Constrained non-intrusive polynomial chaos expansion for physics-informed machine learning regression

Abstract

This work presents a constrained polynomial chaos expansion (PCE) as a physics-informed machine learning (ML) technique to supplement data with physical constraints in the regression framework. PCE is a popular metamodeling technique for uncertainty quantification of expensive computational models. PCE metamodels can also be trained on data in classical ML regression settings to yield pointwise predictions. However, standard PCE metamodel may yield predictions that can violate the underlying physical constraints on the model. In this work, we propose a constrained PCE approach that incorporates the constraints using virtual points in the input domain to solve a constrained least square optimization problem for the PCE coefficients. The resulting constrained PCE model provides an improved fit and leverage from the additional information on the physics of the model. The proposed approach is applied to datasets from 1D analytical functions to impose different types of physical constraints.