深圳技术大学大数据与互联网学院数学系学术报告（十四）

    报告标题：Residual-Quantile Adjustment for Adaptive Training of Physics-informed Neural Network

报 告 人：周翔

报告时间：2023年2月22日（星期三）10:00-11:00

报告地点：大数据与互联网学院513会议室

邀 请 人：谷淑婷

摘  要：

Adaptive training methods for Physics-informed neural network (PINN) require dedicated constructions of the distribution of weights assigned at each training sample. To efficiently seek such an optimal weight distribution is not a simple task and most existing methods choose the adaptive weights based on approximating the full distribution or the maximum of residuals. In this paper, we show that the bottleneck in the adaptive choice of samples for training efficiency is the behavior of the tail distribution of the numerical residual. Thus, we propose the Residual-Quantile Adjustment (RQA) method for a better weight choice for each training sample. After initially setting the weights proportional to the p-th power of the residual, our RQA method reassign all weights above q-quantile (90% for example) to the median value, so that the weight follows a quantile-adjusted distribution derived from the residuals. This iterative reweighting technique, on the other hand, is also very easy to implement. Experiment results show that the proposed method can outperform several adaptive methods on various partial differential equation (PDE) problems

报告人简介：

周翔教授本科毕业于北京大学数学科学学院，博士毕业于普林斯顿大学。曾先后在普林斯顿大学和布朗大学做过研究助理（RA），于2012年入职香港城市大学数学系，他主要的研究领域包括稀有事件，随机模型中的计算方法的研究以及机器学习算法。主要研究兴趣包括：非线性随机动力学体系中的transition，随机模拟，鞍点的计算以及高维的非凸能量景观的探索等等。