Neural Network-Based Limiter with Transfer Learning  

作　　者：Rémi Abgrall Maria Han Veiga 

机构地区：[1]University of Zurich,Zurich,Switzerland [2]University of Michigan,Ann Arbor,USA

出　　处：《Communications on Applied Mathematics and Computation》2023年第2期532-572,共41页应用数学与计算数学学报（英文）

摘　　要：Recent works have shown that neural networks are promising parameter-free limiters for a variety of numerical schemes(Morgan et al.in A machine learning approach for detect-ing shocks with high-order hydrodynamic methods.et al.in J Comput Phys 367:166-191.,2018;Veiga et al.in European Conference on Computational Mechanics andⅦEuropean Conference on Computational Fluid Dynamics,vol.1,pp.2525-2550.ECCM.,2018).Following this trend,we train a neural network to serve as a shock-indicator function using simulation data from a Runge-Kutta discontinuous Galer-kin(RKDG)method and a modal high-order limiter(Krivodonova in J Comput Phys 226:879-896.,2007).With this methodology,we obtain one-and two-dimensional black-box shock-indicators which are then coupled to a standard limiter.Furthermore,we describe a strategy to transfer the shock-indicator to a residual distribution(RD)scheme without the need for a full training cycle and large data-set,by finding a mapping between the solution feature spaces from an RD scheme to an RKDG scheme,both in one-and two-dimensional problems,and on Cartesian and unstruc-tured meshes.We report on the quality of the numerical solutions when using the neural network shock-indicator coupled to a limiter,comparing its performance to traditional lim-iters,for both RKDG and RD schemes.

关 键 词：LIMITERS Neural networks Transfer learning Domain adaptation 

分 类 号：O24[理学—计算数学]