论文标题
非线性动力学系统的非感知降低订购建模的二次解码器方法
A quadratic decoder approach to nonintrusive reduced-order modeling of nonlinear dynamical systems
论文作者
论文摘要
线性投影方案之类的正交分解等线性投影方案可以有效地降低动力学系统的维度，但自然受到限制，例如，对于对流为主的问题。非线性方法已显示出优于降低与准确性的线性方法的表现，但通常具有较大的计算开销。在这项工作中，我们考虑了一种二次还原方案，该方案诱导了张力线性代数例程可访问的非线性结构。我们讨论，非感知方法可用于同时降低方程式中的复杂性，并提出尊重非线性歧管动态的操作推理表述。
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.
