报告题目 (Title)：Energetic variational discretizations and their applications (基于能量变分原理的数值离散方法及应用)

报告人 (Speaker)： Yiwei Wang 副研究员 (University of California)

报告时间 (Time)：2022年11月4日(周五) 09:00

报告地点 (Place)：腾讯会议（会议号：403-432-347 ，无密码）

邀请人(Inviter)：段成华

主办部门：理学院数学系

报告摘要：

Motivated by non-equilibrium thermodynamics, the framework of the energetic variational approach (EnVarA) provides a paradigm for building thermodynamically consistent variational models for many complicated systems in soft matter physics, material science, biology, and machine learning. In this talk, we'll present a numerical framework for developing structure-preserving variational discretizations for these variational models based on their energetic variational forms. The numerical approach starts with the energy-dissipation law, which describes all the physics and the assumptions in each system and can combine distinct types of spatial discretizations, including Eulerian, Lagrangian, particle, and neural-network-based discretizations. The resulting semi-discrete equation inherits the variational structures from the continuous energy-dissipation law. The numerical procedure guarantees the developed scheme is energy stable and preserves the intrinsic physical constraints, such as the conservation of mass and the maximum principle. We'll discuss several applications of this numerical approach, including variational Lagrangian schemes for phase-field models and generalized diffusions, and particle-based energetic variational inference for machine learning. The talk is mainly based on several joint works with Prof. Chun Liu (IIT) and Prof. Lulu Kang (IIT).