報 告 人：李彪 教授

報告題目：Gradient-optimized physics-informed neural networks (GOPINNs): a deep learning method for solving the complex modified KdV equation

報告時間：2023年12月3日（周日）上午11：30-12：30

報告地點：靜遠樓1506學術報告廳

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

       李彪，寧波大學數學與統計學院教授，博導。主要從事非線性數學物理，可積系統及應用，深度學習等方面的研究。主持完成國家自然科學基金4項、省部級項目3項； 參與完成國家自然科學基金重點項目2項；現主持國家自然科學基金面上項目1項和參加國家自然科學基金重點項目1項。發表論文SCI論文100余篇，他引3千多次。

報告摘要：

       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.