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

报告人：徐振礼 教授（上海交通大学）

地点：致远楼103室

时间：2025年12月22日 星期一 10：00-11：00

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. We propose a Sum-of-Gaussians Neural Network (SOG-Net) 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 Coulomb interaction is handled by an SOG decomposition such that it is dimensionally separable, leading to a tensor representation with rapid convergence. Range-splitting scheme is develop to partition 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 methods.

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