We propose a new technique for obtaining reduced order models for nonlinear
dynamical systems. Specifically, we advocate the use of the recently developed
Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the
nonlinear term. DMD is a spatio-temporal matrix decomposition of a data matrix
that correlates spatial features while simultaneously associating the activity
with periodic temporal behavior. With this decomposition, one can obtain a
fully reduced dimensional surrogate model and avoid the evaluation of the
nonlinear term in the online stage. This allows for an impressive speed up of
the computational cost, and, at the same time, accurate approximations of the
problem. We present a suite of numerical tests to illustrate our approach and
to show the effectiveness of the method in comparison to existing approaches.

本文提出了一种新的技术来获取非线性动力系统的降阶模型，并且通过最近开发的动态模式分解 (DMD) 来近似非线性项，从而获得完全降阶的替代模型。通过该技术所得，可以在不影响问题精度的同时，实现计算成本的大幅度降低。作者通过一系列数字测试证明了该方法的实用性和有效性，并与现有的方法进行了比较。