Title of the talk: "Computational Modelling and Analysis under Uncertainty"

Date , Time & Venue: 11 Sept. 2025  at 05:00 PM, Seminar Hall, Dept. of Mathematics

Abstract:  Mathematical models governed by laws of Physics, along with recent advancements in data-driven modelling, have significantly advanced the field of computational modelling and analysis for science and engineering. However, model and parametric uncertainties are inherent in both traditional physics-based and modern data-driven deterministic models. Understanding how these uncertainties affect predictive outcomes is essential for gaining deeper insights and enabling more robust decision-making. Consequently, there is a growing need for numerical algorithms that can incorporate, quantify, and update uncertainty in a principled manner.

This talk will present a broad overview of probabilistic and statistical techniques for modelling tensor- valued uncertain properties in heterogeneous and anisotropic materials, employing a Lie algebra- based representation. These uncertainties are efficiently propagated using a sampling-based method known as the multilevel Monte Carlo (MLMC) technique, where the 'levels' correspond to a hierarchy of finite element models. Finally, the (latent) uncertain material parameters are inferred by integrating observational data with physics-based predictions within a Bayesian framework, where the posterior distribution is sampled using a multi-fidelity Metropolis-Hastings algorithm.

About the Speaker: Dr. Sharana Shivanand is a postdoctoral researcher in the Uncertainty Quantification (UQ) group at the Scientific Computing Centre, Karlsruhe Institute of Technology (KIT), Germany. Previously, he was a postdoc at The Alan Turing Institute, the UK's national institute for Data Science and AI. During this time, he was also a Visiting Research Fellow at the University of Cambridge. He received his Ph.D. in Applied Mathematics and M.Sc. in Computational Sciences in Engineering at the Technical University of Braunschweig, Germany.

His research focuses on development of statistical and probabilistic methods for physics-informed and data-driven numerical modelling. His research interests are at the intersection of uncertainty quantification, computational physics, and machine learning, addressing challenges in materials science, mechanics, and related science and engineering domains. He is currently developing multi-fidelity Bayesian inverse algorithms for the identification of parameters in compute-intensive simulations.