应兰州大学数学与统计学院邀请，美国阿拉巴马大学赵山教授将于2026年6月13日举办线下学术报告。欢迎广大师生参加。

题目：FFT-accelerated high order finite difference methods and their hybridization with neural networks for elliptic interface problems

时间：2026年6月13日9:30—10：30

地点：理工楼518会议室

摘要：In this talk, we will introduce an augmented matched interface and boundary (AMIB) method for solving elliptic interface problems. By effectively generating fictitious values needed in fourth order central difference approximations, the AMIB method is able to not only treat various jump conditions and boundary conditions, but also handle complicated geometries, including corner treatments. By using fictitious values to reconstruct Cartesian derivative jumps as auxiliary variables in an augmented formulation, the fast Fourier transform (FFT) algorithm will not sense the solution discontinuities, so that the discrete Laplacian can be efficiently inverted in the fourth order AMIB method. Recently, we have developed a hybrid method that integrates machine learning techniques into fast Poisson solvers for solving a simple elliptic interface problem. A neural network, trained on jump conditions, is constructed to directly predict Cartesian derivative jumps for correcting finite difference approximations. This hybrid approach extends the capabilities of AMIB methods by efficiently addressing interfaces with geometric singularities through its mesh-free neural network framework. The resulted finite difference method is not only easy to implement but also achieves fourth-order accuracy and FFT efficiency.

报告人简介

赵山，美国阿拉巴马大学数学系教授。研究方向为计算生物物理学、生物数学、计算电磁学等交叉学科的数学建模、数值分析与算法创新。赵山教授长期致力于偏微分方程数值解、快速算法及其在分子生物科学与生物物理中的应用研究。他曾在SIAM计算科学与工程大会、SIAM生命科学大会等国际顶级会议上多次作报告，深入探讨界面问题数值方法、复杂生物系统建模及大分子结构相互作用计算等前沿课题。赵山教授迄今已发表90余篇SCI论文，论文被引用逾3500次，其中一篇于2020年荣获世界华人数学家联盟（ICCM）最佳论文若琳奖。他曾主持美国国家科学基金会（NSF）多项科研项目，已指导15名博士研究生和3名博士后完成研究工作。

甘肃省计算数学基础学科研究中心

数学与统计学院

萃英学院

2026年6月9日