报告题目：可积深度学习(Integrable Deep Learning )---PINN based on Miura transformations and discovery of new localized wave solutions
报 告 人：陈勇（华东师范大学 教授）
会议时间：2023年3月30日 8:30-9:30
会议地点：腾讯会议，会议号： 429-410-857
报告摘要：We put forth two physics-informed neural network (PINN) schemes based on Miura transformations. The novelty of this research is the incorporation of Miura transformation constraints into neural networks to solve nonlinear PDEs, which is an implementation method of unsupervised learning. The most noteworthy advantage of our method is that we can simply exploit the initial-boundary data of a solution of a certain nonlinear equation to obtain the data-driven solution of another evolution equation with the aid of Miura transformations and PINNs. In the process, the Miura transformation plays an indispensable role of a bridge between solutions of two separate equations. It is tailored to the inverse process of the Miura transformation and can overcome the difficulties in solving solutions based on the implicit expression. Moreover, two schemes are applied to perform abundant computational experiments to effectively reproduce dynamic behaviors of solutions for the well-known KdV equation and mKdV equation. Significantly, new data-driven solutions are successfully simulated and one of the most important results is the discovery of a new localized wave solution: kink-bell type solution of the defocusing mKdV equation and it has not been previously observed and reported to our knowledge. It provides a possibility for new types of numerical solutions by fully leveraging the many-to-one relationship between solutions before and after Miura transformations. Performance comparisons in different cases as well as advantages and disadvantages analysis of two schemes are also discussed. On the basis of the performance of two schemes and no free lunch theorem, they both have their own merits and thus more appropriate one should be chosen according to specific cases.
报告人简介：陈勇，华东师范大学数学科学学院教授、博士生导师，计算机理论所所长，上海市闵行区拔尖人才。从事可积系统、计算机代数及程序开发、可积深度学习算法的研究。提出了可积深度学习理论框架，发展了李群理论，开发了一系列可机械化实现的可积系统的研究程序。已在SCI收录的国际学术期刊上发表论文300余篇，引用7000余篇次。主持和参加了国家自然科学基金重点项目、973项目、国家自然科学基金面上项目，长江创新团队项目等。
