On October 7, 2025 from 10:30 To 12:30
Kaushik Bhattacharya is Professor of Mechanics and Professor of Materials Science at the California Institute of Technology, where he holds the Howell N. Tyson Chair. His research focuses on the mechanical behaviour of materials and specifically uses theory to guide the development of new materials. His presentation will focus on the theme: “Multi-scale modelling and neural operators”. Abstract: The behavior of materials involve physics at multiple length and time scales: electronic, atomistic, domains, defects etc. The engineering properties that we observe and exploit in application are a sum total of all these interactions. Multiscale modeling seeks to understand this complexity with a divide and conquer approach. It introduces an ordered hierarchy of scales, and postulates that the interaction is pairwise within this hierarchy. The coarser-scale controls the finer-scale and filters the details of the finer scale. Still, the practical implementation of this approach is computationally challenging. This talk introduces the notion of neural operators as controlled approximations of operators mapping one function space to another and explains how they can be used for multiscale modeling. We demonstrate the ideas with examples, and highlight the open mathematical issues.
