论文标题
二次歧管的非侵入模型降低的操作员推断
Operator inference for non-intrusive model reduction with quadratic manifolds
论文作者
论文摘要
本文提出了一种从高维数据中学习数据驱动的二次歧管的新方法，然后采用此二次歧管来得出有效的基于物理学的降低模型。该方法的关键成分是高维状态和低维嵌入之间的多项式映射。该映射包括两个部分：线性子空间中的表示形式（使用适当的正交分解在本工作中计算）和二次组件。该方法可以看作是数据驱动的闭合建模的一种形式，因为二次组件将方向引入了线性子空间的正交补体中的近似值，但没有引入任何额外的自由度以降低低维表示。将二次歧管近似与基于投影的模型还原的操作推理方法相结合会导致一种可扩展的非侵入性方法，用于学习动态系统的减少阶数模型。将新方法应用于偏微分方程的运输主导系统说明了在线性子空间中近似值可以实现的效率的提高。
This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach is a polynomial mapping between high-dimensional states and a low-dimensional embedding. This mapping consists of two parts: a representation in a linear subspace (computed in this work using the proper orthogonal decomposition) and a quadratic component. The approach can be viewed as a form of data-driven closure modeling, since the quadratic component introduces directions into the approximation that lie in the orthogonal complement of the linear subspace, but without introducing any additional degrees of freedom to the low-dimensional representation. Combining the quadratic manifold approximation with the operator inference method for projection-based model reduction leads to a scalable non-intrusive approach for learning reduced-order models of dynamical systems. Applying the new approach to transport-dominated systems of partial differential equations illustrates the gains in efficiency that can be achieved over approximation in a linear subspace.
