Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms

• Published in: Computer methods in applied mechanics and engineering 2020-12, Vol.372 (C), p.113433, Article 113433
• Main Authors: Benner, Peter, Goyal, Pawan, Kramer, Boris, Peherstorfer, Benjamin, Willcox, Karen
• Format: Article
• Language: English
• Subjects: Chemical separation; Data-driven modeling; Dynamical systems; Least squares method; Mathematical analysis; Mathematical models; Model accuracy; Model reduction; Nonlinear dynamical systems; Nonlinear dynamics; Operator inference; Operators; Partial differential equations; Polynomials; Scientific machine learning
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2020.113433

This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art model reduction methods that are intrusive and thus require full knowledge of the governing equations and the operators of a full model of the discretized dynamical system, the proposed approach requires only the non-polynomial terms in analytic form and learns the rest of the dynamics from snapshots computed with a potentially black-box full-model solver. The proposed method learns operators for the linear and polynomially nonlinear dynamics via a least-squares problem, where the given non-polynomial terms are incorporated on the right-hand side. The least-squares problem is linear and thus can be solved efficiently in practice. The proposed method is demonstrated on three problems governed by partial differential equations, namely the diffusion–reaction Chafee–Infante model, a tubular reactor model for reactive flows, and a batch-chromatography model that describes a chemical separation process. The numerical results provide evidence that the proposed approach learns reduced models that achieve comparable accuracy as models constructed with state-of-the-art intrusive model reduction methods that require full knowledge of the governing equations. •Method learns low-dimensional models of dynamical systems with non-polynomial nonlinear terms.•Requires non-polynomial terms analytically; learns the other dynamics from snapshots.•Can achieve comparable accuracy as state-of-the-art intrusive model reduction methods on numerical examples.