報(bào) 告 人：李彪 教授

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

報(bào)告時(shí)間：2023年12月3日（周日）上午11：30-12：30

報(bào)告地點(diǎn)：靜遠(yuǎn)樓1506學(xué)術(shù)報(bào)告廳

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

       李彪，寧波大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院教授，博導(dǎo)。主要從事非線性數(shù)學(xué)物理，可積系統(tǒng)及應(yīng)用，深度學(xué)習(xí)等方面的研究。主持完成國(guó)家自然科學(xué)基金4項(xiàng)、省部級(jí)項(xiàng)目3項(xiàng)； 參與完成國(guó)家自然科學(xué)基金重點(diǎn)項(xiàng)目2項(xiàng)；現(xiàn)主持國(guó)家自然科學(xué)基金面上項(xiàng)目1項(xiàng)和參加國(guó)家自然科學(xué)基金重點(diǎn)項(xiàng)目1項(xiàng)。發(fā)表論文SCI論文100余篇，他引3千多次。

報(bào)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.