We propose a new hyper-reduction method for a recently introduced nonlinear model reduction framework based on dynamically transformed basis functions and especially well-suited for advection-dominated systems. Furthermore, we discuss applying this new method to a wildland fire model whose dynamics feature traveling combustion waves and local ignition and is thus challenging for classical model reduction schemes based on linear subspaces. The new hyper-reduction framework allows us to construct parameter-dependent reduced-order models (ROMs) with efficient offline/online decomposition. The numerical experiments demonstrate that the ROMs obtained by the novel method outperform those obtained by a classical approach using the proper orthogonal decomposition and the discrete empirical interpolation method in terms of run time and accuracy.
翻译:我们为最近推出的非线性模式削减框架提出了一个新的超增量削减方法,其基础是动态转变的基础功能,特别是适合于平流主导系统的功能。此外,我们讨论将这一新方法应用到一个野地火灾模型,其动态特征是流动燃烧波和局部点火,因此对基于线性子空间的典型模式削减计划具有挑战性。新的超减量框架允许我们用高效离线/线上分解来构建依赖参数的减量模型(ROMs)。数字实验表明,通过新颖方法获得的ROM在运行时间和准确性方面优于通过使用正常或图解分解法和独立实验性内插法获得的经典方法获得的。