报告题目：Sum-of-Gaussians Based Machine Learning Force Field and Tensor Neural Networks for High-Dimensional Equations

报告时间：2025年12月10日15:00—17:00

报告地点：数学楼2-2

报告摘要：This talk includes two topics by using sum-of-Gaussians for constructing neural networks. The first topic is machine-learning interatomic potentials which have emerged as a revolutionary class of force-field models in molecular simulations, delivering quantum-mechanical accuracy at a fraction of the computational cost and enabling the simulation of large-scale systems over extended timescales. We propose a Sum-of-Gaussians Neural Network (SOG-Net), a lightweight and versatile framework for integrating long-range interactions into machine learning force field. By learning sum-of-Gaussians multipliers across different convolution layers, the SOG-Net adaptively captures diverse long-range decay behaviors while maintaining close-to-linear computational complexity during training and simulation via non-uniform fast Fourier transforms. In the second topic, we introduce an accurate, efficient, and low-memory sum-of-Gaussians tensor neural network (SOG-TNN) algorithm for solving the high-dimensional Schrödinger equation. The SOG-TNN utilizes a low-rank tensor product representation of the solution to overcome the curse of dimensionality associated with high-dimensional integration. The Coulomb interaction is handled by an SOG decomposition such that it is dimensionally separable, leading to a tensor representation with rapid convergence. We further develop a range-splitting scheme that partitions the Gaussian terms into short-, long-, and mid-range components such that they can be approximated accurately. Numerical results demonstrate the outstanding performance of the new method, revealing that the SOG-TNN is a promising way for tackling large and complex quantum systems.

报告人简介：徐振礼，上海交通大学教授。中国科学技术大学本硕博，曾任美国北卡罗莱纳大学夏洛特分校博士后、德国斯图加特大学洪堡学者。2010年任职上海交通大学，2019-2021年任绿帽小说 副院长，2021-2025年任教务处副处长。2010年入选新世纪优秀人才计划，2012年中组部青年拔尖人才计划，2023年获国家自然科学基金杰出青年基金。担任AAMM、CMS和MCA等杂志编委。兼任上海市数学会副理事长、上海交通大学ESG研究院副院长等职。曾获上海市和国家级教学成果奖，上海市自然科学奖一等奖、上海交通大学十大科技进展等。研究方向为高性能计算、分子动力学算法、机器学习方法和偏微分方程的数值方法等，发表100多篇研究论文。