Title of the talk: Research seminar by Dr Abhishek Kumar Singh on Feb 23, 2026

Date & Time: February 23, 2026 at 5 PM on Seminar Room, Dept. of Mathematics

Abstract: Physics-informed neural networks (PINNs) have recently emerged as a powerful data-driven framework for solving forward and inverse problems governed by differential equations. However, automatic differentiation, which forms the core of PINNs, is not directly applicable to differential equations involving non-local operators. In this research seminar, I will present my work on non-local physics-informed neural networks (NL-PINNs), where standard approximation techniques are employed to treat non-local operators, while automatic differentiation is retained for local terms. In the inverse setting, this framework enables the accurate estimation of unknown model parameters directly from observed data. In addition, I will discuss parameter estimation in M ̈untz–Legendre polynomials, where the fractional parameter defining the polynomial space is optimized using differential evolution to achieve the best possible accuracy in solving differential equations containing non-local operators.

About the speaker: Dr. Abhishek Kumar Singh is a Postdoctoral Fellow at the Institute of Mathematics and Computer Science, University of Greifswald, Germany (since November 2023). Prior to this, he worked as an Early-Doc Fellow at IIT Delhi (August–October 2023). He received his PhD in Mathematics from IIT Delhi in August 2023, an M.Tech in Industrial Mathematics and Scientific Computing from IIT Madras in 2017, and an MSc in Mathematics from Banaras Hindu University in 2014. His research focuses on numerical methods and data-driven approaches for stochastic and deterministic fractional differential equations.