This website requires JavaScript.

Operator inference for non-intrusive model reduction with nonlinear manifolds

Rudy GeelenStephen WrightKaren Willcox
May 2022
摘要
This paper proposes a novel approach for learning a data-driven quadraticmanifold from high-dimensional data, then employing the quadratic manifold toderive efficient physics-based reduced-order models. The key ingredient of theapproach is a polynomial mapping between high-dimensional states and alow-dimensional embedding. This mapping comprises two parts: a representationin a linear subspace (computed in this work using the proper orthogonaldecomposition) and a quadratic component. The approach can be viewed as a formof data-driven closure modeling, since the quadratic component introducesdirections into the approximation that lie in the orthogonal complement of thelinear subspace, but without introducing any additional degrees of freedom tothe low-dimensional representation. Combining the quadratic manifoldapproximation with the operator inference method for projection-based modelreduction leads to a scalable non-intrusive approach for learning reduced-ordermodels of dynamical systems. Applying the new approach to transport-dominatedsystems of partial differential equations illustrates the gains in efficiencythat can be achieved over approximation in a linear subspace.
展开全部
图表提取

暂无人提供速读十问回答

论文十问由沈向洋博士提出,鼓励大家带着这十个问题去阅读论文,用有用的信息构建认知模型。写出自己的十问回答,还有机会在当前页面展示哦。

Q1论文试图解决什么问题?
Q2这是否是一个新的问题?
Q3这篇文章要验证一个什么科学假设?
0
被引用
笔记
问答