报告题目：可积深度学习

报 告 人：陈勇 教授 (华东师范大学)

报告摘要 ：介绍非线性科学与计算机发展关系-可积系统，探讨我们提出的可积深度学习的理论架构和发展方向。介绍我们有关可积深度学习的研究工作：基于PINN算法并对其改进，研究可积方程中的多孤子，高阶呼吸子，高阶怪波，周期背景下的高阶怪波，向量多孤子，孤子分子及其动力学行为；提出了高维可积系统PINN算法；提出了基于守恒律的两阶段PINN算法的提出。

报告人简介：陈勇，华东师范大学，博士生导师， 计算机理论所所长，上海市闵行区拔尖人才. 长期从事非线性数学物理、可积系统、计算机代数及程序开发、可积深度学习算法，混沌理论、大气和海洋动力学等领域的研究工作. 提出了一系列可以机械化实现非线性方程求解的方法，发展了李群理论并成功应用于大气海洋物理模型的研究，可积深度学习算法的研究开发出一系列可机械化实现的非线性发展方程的研究程序。已在SCI收录的国际学术期刊上发表论文280篇. 发表论文的SCI 引用4000余篇次，其中ESI热点论文2篇、高被引论文10篇。SCI一区、二区文章90余篇。主持国家自然科学基金面上项目4项，国家自然科学基金重点项目2项(第一参加人和项目负责人)、973项目1项(骨干科学家)、国家自然科学基金长江创新团队项目2项(PI)。

报告题目：Nonlinear wave equations and deep learning

报告人：闫振亚 教授

报告摘要：We mainly introduce the deep learning methods and applications in the forward and inverse problems relates to solitons equations 。

报告人简介：中国科学院数学与系统科学研究院, 研究员，博士生导师、国家杰出青年基金获得者、“数学与量子物理效应创新交叉团队”入选中科院2017年度创新交叉团队项目。主要研究数学物理、非线性波与可积系统、Riemann-Hilbert方法、反散射理论、怪波、PT-对称及其在非线性光学、量子物理、BEC等中的应用。

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

报告人：李彪 教授

报告摘要：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.

报告人简介： 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。

报告题目：基于DeepOnet神经网络的船舶横摇极短期运动预报

报告人：赵勇，副教授

报告摘要：船舶姿态极短期运动预报对舰载机起降安全性能具有十分重要的影响，其中横摇运动影响更为明显。采用深度算子神经网络（Deep Operator Networks）建立预测模型，基于DTMB 5512船模实验数据，进行了单工况和多工况预报。实验结果显示，不论是在单工况预报，还是多工况预报，DeepOnet模型的预报均方误差量级都小于10-4，能够有效预报船舶横摇极端期运动，且不同输入步数下预报误差在同一量级。与经典模型长短时间记忆（LSTM）神经网络相比，DeepOnet模型预报精度更好。

报告人简介：赵勇，博士，硕士生导师，大连海事大学船舶与海洋工程学院副教授。长期从事船舶与海洋工程流体力学教学和科研工作。研究方向包括船舶水动力分析、CFD数值方法、机器学习在船舶与海洋工程中应用等，发表学术论文40余篇，主持国家自然科学基金项目2项。

报告题目：Physics Informed Neural Networks (PINNs) for Fluid Flow and Heat Transfer Problems.

报告人：王志成 副教授

报告摘要：Tomographic background oriented Schlieren (Tomo-BOS) imaging measures density or temperature fields in three dimensions using multiple camera BOS projections, and is particularly useful for instantaneous flow visualizations of complex fluid dynamics problems. We propose a new method based on physics-informed neural networks (PINNs) to infer the full continuous three-dimensional (3-D) velocity and pressure fields from snapshots of 3-D temperature fields obtained by Tomo-BOS imaging. The PINNs seamlessly integrate the underlying physics of the observed fluid flow and the visualization data, hence enabling the inference of latent quantities using limited experimental data. In this hidden fluid mechanics paradigm, we train the neural network by minimizing a loss function composed of a data mismatch term and residual terms associated with the coupled Navier–Stokes and heat transfer equations. We first quantify the accuracy of the proposed method based on a two-dimensional synthetic data set for buoyancy-driven flow, and subsequently apply it to the Tomo-BOS data set, where we are able to infer the instantaneous velocity and pressure fields of the flow over an espresso cup based only on the temperature field provided by the Tomo-BOS imaging. Moreover, we conduct an independent PIV experiment to validate the PINN inference for the unsteady velocity field at a centre plane. To explain the observed flow physics, we also perform systematic PINN simulations at different Reynolds and Richardson numbers and quantify the variations in velocity and pressure fields. The results in this paper indicate that the proposed deep learning technique can become a promising direction in experimental fluid mechanics.

报告人简介：王志成，博士 2007 年获得北京交通大学热能与动力工程学士学位，2013 年在唐大伟研究员的指导下获得中国科学院工程热物理研究所博士学位并留所工作，2016 年至2021年先后在美国麻省理工学院机械工程系和布朗大学应用数学系从事博士后研究，与 M.T. Triantafyllou, G.E. Karniadakis 等教授合作，2021年5月进入大连理工能源与动力学院任副教授。成果发表在 J. Fluid Mechanics, J. Computational Physics, PNAS, CMAME 等期刊。王博士的主要研究兴趣包括湍流和两相流数值计算，谱元法，机器学习等。

                                                                                             大连理工大学数学科学学院

                                                                                                                           2021年12月14日