Variational Schemes to Generalized Diffusions, Gradient flows and Beyond: An Discrete Energetic Variational Approach

Abstract: In this talk, we present a systematic framework of deriving variational schemes for generalized diffusions and gradient flows, by a discrete energetic variational approach, which performs an energetic variational approach (EnVarA) at a semi-discrete level. In particular, we apply such an approach to construct variational Lagrangian schemes and particle methods for porous medium type generalized diffusion and Allen-Cahn type equations. Numerical examples show the advantages of our schemes in capturing singularities, thin diffuse interfaces, and free boundaries. Our approach also has a potential connection application in Variational Inference problems in the field of machine learning. This is joint work with Professor Chun Liu (IIT).

numerical analysis

Audience: researchers in the topic

( paper )

Comments: Zoom meeting ended

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Global Seminar on Mathematical Modeling and Applications

Series comments: Description: Occasional seminar on mathematical modeling and related topics

In light of the worldwide cancellations of meetings workshops and conferences many of us are forced to switch to online mode of communication. Thus following the example of many other initiatives we decided to organize a Global Seminar on Mathematical Modeling and Applications.

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