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Machine Learning and New Framework for Solving Partial Differential Equations

Organizer(s):
Name:	Affiliation:	Country:
Jingrun Chen	Suzhou Institute for Advanced Research, University of Science and Technology of China	Peoples Rep of China
Haijun Yu	Academy of Mathematics and Systems Science, Chinese Academy of Sciences	Peoples Rep of China
Shuo Zhang	Academy of Mathematics and Systems Science, Chinese Academy of Sciences	Peoples Rep of China

Introduction:

Recently, it has been a groundbreaking trend that synergistically combines the principles of partial differential equation (PDE) solvers and machine learning (ML) techniques to advance the solution of complex PDE systems. The new methodology may transcend traditional approaches in harnessing the predictive power of ML algorithms while preserving the mathematical rigor and interpretability inherent in PDE-based models. The interaction between PDE and ML may also introduce comprehensively new insights to the traditional approaches of PDE solution as well as the ML techniques. This mini-symposium proposes to gather experts in the fields of PDE solution and machine learning to communicated latest progress in the new framework of solving PDE particularly by/for machine learning. The framework is demonstrated through a series of case studies spanning diverse application domains. Moreover, the framework’s modular design allows for seamless integration into existing computational workflows and mathematical rigors, fostering broader adoption across scientific and engineering disciplines, and unlocking novel avenues for interdisciplinary research.

List of approved abstract
Name	Affiliation	Title
Wei Gong	Academy of Mathematics and Systems Science, Chinese Academy of Sciences	A novel shape optimization approach for source identification in elliptic equations
Xia Ji	Beijing institute of technology	A new method using C0IPG for the biharmonic eigenvalue problem
Tiexiang Li	Southeast University	Ball Mass-preserving Parameterizations with Applications on Brain Tumor Segmentations
Chunmei Su	Tsinghua University	Structure-preserving parametric finite element methods for curve diffusion
Haijun Yu	Academy of Mathematics and Systems Science, Chinese Academy of Science	Deep Neural Networks with Rectified Power Units: Efficient Training and Applications in Partial Differential Equations
Shuo Zhang	Academy of Mathematics and Systems Science, Chinese Academy of Sciences	Complex dualities and new solution frameworks
Chensong Zhang	Academy of Mathematics and Systems Science	A deep learning enabled massive parallel simulator for porous media flow
Xiang ZHOU	City University of Hong Kong	Weak Generative Sampler to Solve High - Dimensional PDEs for Stochastic Models: Efficiency and Adaptivity
Confirmed Speakers
Name:	Affiliation:	Country:
Maria Cameron	University of Maryland	USA
Wei Gong	Academy of Mathematics and Systems Science, Chinese Academy of Sciences	Peoples Rep of China
Xia Ji	Beijing Institute of Technology	Peoples Rep of China
Tiexiang Li	Southeast University / Nanjing Center for Applied Mathematics	Peoples Rep of China
Yuwen Li	Zhejiang University	Peoples Rep of China
Ting Lin	Peking University	Peoples Rep of China
Zuoqiang Shi	Tsinghua University	Peoples Rep of China
Natesan Srinivasan	Indian Institute of Technology Guwahati	India
Haiyan Su	Xinjiang University	Peoples Rep of China
Chunmei Su	Tsinghua University	Peoples Rep of China
Huiwen Wu	Zhejiang Lab	Peoples Rep of China
Haijun Yu	Academy of Mathematics and Systems Science, Chinese Academy of Sciences	Peoples Rep of China
Shuo Zhang	Academy of Mathematics and Systems Science, Chinese Academy of Sciences	Peoples Rep of China
Chensong Zhang	Academy of Mathematics and Systems Science, Chinese Academy of Sciences	Peoples Rep of China
Wenxiao Zhao	Academy of Mathematics and Systems Science, Chinese Academy of Sciences	Peoples Rep of China
Xiang Zhou	City University of Hong Kong	Peoples Rep of China