[Séminaire] Prof. K. Bhattacharya (Caltech) ‘Multi-scale modeling and neural operators’ – Ouvert à tou·te·s

Résumé :

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.

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Kaushik Bhattacharya est professeur de mécanique et professeur de science des matériaux à la California Institute of Technology, où il occupe la chaire Howell N. Tyson, Sr. Il a obtenu son bachelor à la Indian Institute of Technology de Madras, en Inde, en 1986, son doctorat à l’Université du Minnesota en 1991 et a suivi une formation postdoctorale au Courant Institute for Mathematical Sciences entre 1991 et 1993. Il a rejoint le Caltech en 1993. Ses recherches portent sur le comportement mécanique des matériaux et utilisent spécifiquement la théorie pour guider le développement de nouveaux matériaux. Il a reçu la médaille von Kármán de la Society of Industrial and Applied Mathematics (2020), le Distinguished Alumni Award de l’Indian Institute of Technology de Madras (2019), le Outstanding Achievement Award de l’université du Minnesota (2018), la médaille Warner T. Koiter de l’American Society of Mechanical Engineering (2015) et le Graduate Student Council Teaching and Mentoring Award du Caltech (2013).