Gradient optimized physics-informed neural network


  • 开始时间:2021-12-16 09:40
  • 活动地点:腾讯会议:187-850-699
  • 主讲人:李彪


<p>Recently, the physics-informed neural networks (PINNs) has received more and more attention because of it's ability to solve nonlinear partial differential equations (NPDEs) via only a small amount of data to quickly obtain data-driven solutions with high accuracy. However, despite their remarkabe promise in the early stage, their unbalanced back-propagation gradient calculation leads to drastic oscillations in the gradient value during model training, which is prone to unstable prediction accuracy. Based on this, we develop a gradient optimization algorithm, which proposes a new neural network structure and balances the interaction between different terms in the loss function during model training by means of gradient statistics, so that the newly proposed network architecture is more robust to gradient fluctuations. In this paper, we take the complex modified KdV equation as an example and use the gradient optimised PINNs (GOPINNs) deep learning method to obtain data-driven rational wave solution and soliton molecules solution. Numerical results show that the GOPINNs method effectively smooths the gradient fluctuations, and reproduces the dynamic behavior of these data-driven solutions better than the original PINNs method. In summary, our work provides new insights for optimi</p>


李彪,宁波大学数学与统计学院教授,浙江省151人才工程”(第三层次)、宁波市“4321” 人才工程(第二层次)。主要从事数学物理,Lie群及其在微分方程中的应用,数学机械化等领域的研究工作。已在SCI系统发表学术论文100余篇,发表论文已被SCI他引1000多次。主持完成国家自然科学基金3项,中国博士后基金1项,浙江省自然科学基金2项。参与完成国家自然科学基金和省、市自然科学基金多项。现参加国家自然科学基金重点项目一项,主持国家自然科学基金面上1项。