张振 | A Neural Evolutionary Kernel Method for Solving Evolutionary PDEs

张振博士现任南方科技大学数学系长聘教授。他本科毕业于中国科学技术大学数学系，之后进入香港科技大学学习并于 2013 年获得应用数学博士学位，2013 年至 2015 年在新加坡国立大学从事计算数学的博士后研究，并在 2015 年加入了南方科技大学数学系。他主要从事应用数学方面的研究，目前在 M3AS、SISC、JFM、CMAME、JCP 等期刊发表 30 余篇论文。

We propose a Neural Evolutionary Kernel Method (NEKM), for solving a class of time-dependent partial differential equations (PDEs) via deep neural network (DNN)-based kernel representations. By integrating boundary integral techniques with operator learning, neural network architectures are designed to predict solutions of time-dependent partial differential equations (PDEs) at each time step, while embedding prior mathematical structure to enhance both computational efficiency and solution accuracy. Numerical experiments on the heat, wave, and Schr{o}dinger equations demonstrate that the Neural Evolutionary Kernel Method (NEKM) achieves high accuracy and favorable computational efficiency.