Model Error Embedding with Orthogonal Gaussian Processes

TL;DR

This paper introduces an orthogonal Gaussian process embedding framework for modeling and correcting errors in complex physical system models, enabling better separation of model and error parameters and improved predictive accuracy.

Contribution

It extends orthogonal GP methods to embedded model-error modeling, incorporating spatiotemporal correlations and addressing high dimensionality with likelihood-informed subspaces.

Findings

Effectively corrects model predictions to match data trends

Enables meaningful stand-alone model predictions

Recovers prior predictive distribution beyond training data

Abstract

Computational models of complex physical systems often rely on simplifying assumptions which inevitably introduce model error, with consequent predictive errors. Given data on model observables, the estimation of parameterized model-error representations, along with other model parameters, would be ideally done while separating the contributions of each of the two sets of parameters, in order to ensure meaningful stand-alone model predictions. This work builds an embedded model error framework using a weight-space representation of Gaussian processes (GPs) to flexibly capture model-error spatiotemporal correlations and enable inference with GP-embedding in non-linear models. To disambiguate model and model-error/bias parameters, we extend an existing orthogonal GP method to the embedded model-error setting and derive appropriate orthogonality constraints. To address the increased dimensionality introduced by the GP representation, we employ the likelihood-informed subspace method. The construction is demonstrated on linear and non-linear examples, where it effectively corrects model predictions to match data trends. Extrapolation beyond the training data recovers the prior predictive distribution, and the orthogonality constraints lead to meaningful stand-alone model predictions and nearly uncorrelated posteriors between model and model-error parameters.