报 告 人：李彪 教授

报告题目：Gradient-optimized physics-informed neural networks (GOPINNs): a deep learning method for solving the complex modified KdV equation

报告时间：2023年12月3日（周日）上午11：30-12：30

报告地点：静远楼1506学术报告厅

主办单位：bat365中文官方网站、数学研究院、科学技术研究院

报告人简介：

       李彪，宁波大学bat365中文官方网站教授， 博导。主要从事非线性数学物理，可积系统及应用，深度学习等方面的研究。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项和参加国家自然科学基金重点项目1项。发表论文SCI论文100余篇，他引3千多次。

报告摘要：

       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-optimized 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.