Data-driven augmentation of first-principles models under constraint-free well-posedness and stability guarantees

TL;DR

This paper proposes a data-driven approach to augment first-principles models with learning components, ensuring well-posedness and stability without constraints, and enabling automatic model order selection.

Contribution

It introduces a constraint-free parametrization guaranteeing well-posedness and stability, and an efficient identification pipeline for non-smooth regularization, advancing model augmentation techniques.

Findings

Guarantees well-posedness of augmented models

Ensures stability via contraction-based parametrization

Handles non-smooth regularization for automatic model selection

Abstract

The integration of first-principles models with learning-based components, i.e., model augmentation, has gained increasing attention, as it offers higher model accuracy and faster convergence properties compared to black-box approaches, while generating physically interpretable models. Recently, a unified formulation has been proposed that generalizes existing model augmentation structures, utilizing linear fractional representations (LFRs). However, several potential benefits of the approach remain underexplored. In this work, we address three key limitations. First, the added flexibility of LFRs also introduces possible algebraic loops, i.e., a problem of well-posedness. To address this challenge, we propose a constraint-free direct parametrization of the model structure with a well-posedness guarantee. Second, we introduce a constraint-free parametrization that ensures stability of the overall model augmentation structure via contraction. Third, we adopt an efficient identification pipeline capable of handling non-smooth cost functions, such as group-lasso regularization, which facilitates automatic model order selection and discovery of the required augmentation configuration. These contributions are demonstrated on various simulation and benchmark identification examples.