A quadratic decoder approach to nonintrusive reduced-order modeling of nonlinear dynamical systems

TL;DR

This paper introduces a quadratic decoder method for nonintrusive reduced-order modeling of nonlinear dynamical systems, balancing improved accuracy over linear methods with computational efficiency through tensorized algebra.

Contribution

It proposes a novel quadratic reduction scheme combined with an operator inference approach that efficiently models nonlinear dynamics on manifolds.

Findings

Quadratic reduction captures nonlinear dynamics effectively.

Tensorized linear algebra enables computationally efficient implementation.

Operator inference respects the underlying nonlinear manifold structure.

Abstract

Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated problems. Nonlinear approaches have shown to outperform linear methods in terms of dimension reduction versus accuracy but, typically, come with a large computational overhead. In this work, we consider a quadratic reduction scheme which induces nonlinear structures that are well accessible to tensorized linear algebra routines. We discuss that nonintrusive approaches can be used to simultaneously reduce the complexity in the equations and propose an operator inference formulation that respects dynamics on nonlinear manifolds.