题目：Gradient optimized physics-informed neural networks (GOPINNs): A deep learning method for solving the complex modified KdV equation
时间：2022年4月29日，18:00-19:00
地点：腾讯会议（会议号：605-368-951）
主讲人: 李彪教授（宁波大学）
摘要：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 remarkable 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 optimizing the learning performance of neural networks and improves the prediction accuracy by a factor of 10 to 30 when solving the complex modified KdV equation.
主讲人简介：李彪，宁波大学数学与统计学院教授，博导。主要研究方向为非线性数学物理，孤子与可积系统。主持完成国家自然科学基金4项、省部级项目3项；参与完成国家自然科学基金重点项目2项；现主持国家自然科学基金面上项目1项。发表论文SCI论文100余篇，他引2千多次。
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