Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms
Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms
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DOI：
10.1016/j.cma.2020.113433
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发表时间：
2020-12-01
影响因子：
7.2
通讯作者：
Willcox, Karen
中科院分区：
文献类型：
--
作者：
Benner, Peter;Goyal, Pawan;Willcox, Karen
这项工作提出了一种非侵入式的模型降阶方法来学习动力系统的低维模型与非多项式的非线性项是空间局部的，并给出了解析形式。与最先进的模型简化方法相比，该方法是侵入性的，因此需要完全了解离散动态系统的完整模型的控制方程和算子，所提出的方法只需要解析形式的非多项式项，并从用潜在的黑盒全模型求解器计算的快照中学习其余的动态。所提出的方法通过最小二乘问题学习线性和多项式非线性动力学的算子，其中给定的非多项式项被合并在右侧。最小二乘问题是线性的，因此在实践中可以有效地解决。所提出的方法证明了三个问题所支配的偏微分方程，即扩散反应Chafee-Infante模型，管式反应器模型的反应流，和一个间歇色谱模型，描述了化学分离过程。数值结果提供的证据表明，所提出的方法学习减少模型，达到相当的精度与国家的最先进的侵入式模型简化方法，需要充分了解的控制方程的模型。(C)2020爱思唯尔B. V.保留所有权利。
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. (C) 2020 Elsevier B.V. All rights reserved.