Multiscale Modelling and Simulation for Anomalous and Nonergodic Dynamics: From Statistics to Mathematics

Date: 

Friday, 18 October, 2024 - 15:00 to 16:00

Speaker : Weihua Deng, School of Mathematics and Statistics and State Key Laboratory of Natural Product Chemistry , Lanzhou University 

Time : 15:00 - 16:00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

Zoom A link will appear here

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: Multiscale Modelling, Anomalous Dynamics, Deep Learning 

Abstract:  In recent decades, anomalous and nonergodic dynamics are topical issues in almost all disciplines. In 2004, the phrase ``anomalous is normal" was used in a title of a PRL paper, which reveals that the diffusion of classical particles on a solid surface has rich anomalous behavior controlled by the friction coefficient, meaning that anomalous dynamics phenomena are ubiquitous in the natural world. This talk first introduces the dynamics from a physical and atomistic way, by considering the random walk of the diffusing particles, then derives the partial differential equations with integral-differential operators governing the PDFs of the various statistical observables. Finally, we discuss the (traditional and deep learning based) numerical methods for the newly build PDEs. 

Biography: Dr Deng is a professor of  School of Mathematics and Statistics and State Key Laboratory of Natural Product Chemistry, Lanzhou University. His reseaech interests include multiscale modelling, scientific computation, deep learning, and their applications in chemistry and biology. 

Bibliography

[1]  Tian Zhou; Heng Wang; Weihua Deng, Feynman–Kac equation for Brownian non-Gaussian polymer diffusion,  Journal of Physics A: Mathematical and Theoretical, 57, 285001, 2024.

[2] Heng Wang, Weihua Deng, Solving bivariate kinetic equations for polymer diffusion using deep learning, Journal of Machine Learning, 3, 2, 215-244, 2024.

[3]  Weihua Deng, Anomalous and nonergodic multiscale modeling, analyses, and algorithms, Science China Mathematics, 53, 8, 1039-1066, 2023.

[4]  Weihua Deng, Buyang Li, Wenyi Tian, Pingwen Zhang, Boundary problems for the fractional and tempered fractional operators. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal  16, 1, 125-149, 2018

Category: