Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference
This work addresses the challenge of ensuring stability in data-driven model reduction for physical systems, which is incremental by building on existing operator inference methods.
The paper tackles the problem of learning stable reduced-order models from data for physical systems with quadratic nonlinearities by introducing a physics-informed regularizer and structure-preserving constraints in operator inference, resulting in models that remain accurate and stable even when standard regularization fails.
Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). This work focuses on the large class of physical systems that can be well described by models with quadratic nonlinear terms and proposes a regularizer for operator inference that induces a stability bias onto quadratic models. The proposed regularizer is physics informed in the sense that it penalizes quadratic terms with large norms and so explicitly leverages the quadratic model form that is given by the underlying physics. This means that the proposed approach judiciously learns from data and physical insights combined, rather than from either data or physics alone. Additionally, a formulation of operator inference is proposed that enforces model constraints for preserving structure such as symmetry and definiteness in the linear terms. Numerical results demonstrate that models learned with operator inference and the proposed regularizer and structure preservation are accurate and stable even in cases where using no regularization or Tikhonov regularization leads to models that are unstable.