优化大型ODE系统去卷积模型降阶的性能
Optimizing performance of the deconvolution model reduction for large ODE systems
AI总结：
本文通过截断奇异值分解（SVD）正则化方法，研究去卷积闭包在Irwing-Kirkwood-Noll过程中的数值性能，分析各参数对精度和效率的影响。
摘要：
我们研究了作者最近引入的正则化去卷积闭包的数值性能。该闭包的目的是为Irwing-Kirkwood-Noll过程提供本构方程，这是一种从粒子动力学牛顿方程推导连续介质平衡方程的著名方法。本文使用的该过程的一个版本依赖于Hardy以及独立地由Murdoch和Bedeaux发展的空间平均。应力的本构方程表示为作用于介观尺度平均密度和速度的几个算子项之和。每一项都是一个“卷积三明治”，包含去卷积算子、复合或乘积算子以及卷积（平均）算子。去卷积是利用不适定问题理论中的滤波正则化方法构建的。正则化的目的是确保数值稳定性。用于数值实验的特定技术是截断奇异值分解（SVD）。本构方程的精度取决于几个参数：平均窗函数的选择、介观尺度分辨率参数的值、尺度分离、奇异值截断水平以及平均值的谱滤波水平。我们进行数值实验以确定每个参数对方法精度和效率的影响。还获得了部分误差估计。
英文摘要：
We investigate the numerical performance of the regularized deconvolution closure introduced recently by the authors. The purpose of the closure is to furnish constitutive equations for Irwing-Kirkwood-Noll procedure, a well known method for deriving continuum balance equations from the Newton's equations of particle dynamics. A version of this procedure used in the paper relies on spatial averaging developed by Hardy, and independently by Murdoch and Bedeaux. The constitutive equations for the stress are given as a sum of several operator terms acting on the mesoscale average density and velocity. Each term is a "convolution sandwich" containing the deconvolution operator, a composition or a product operator, and the convolution (averaging) operator. Deconvolution is constructed using filtered regularization methods from the theory of ill-posed problems. The purpose of regularization is to ensure numerical stability. The particular technique used for numerical experiments is truncated singular value decomposition (SVD). The accuracy of the constitutive equations depends on several parameters: the choice of the averaging window function, the value of the mesoscale resolution parameter, scale separation, the level of truncation of singular values, and the level of spectral filtering of the averages. We conduct numerical experiments to determine the effect of each parameter on the accuracy and efficiency of the method. Partial error estimates are also obtained.
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