Upcoming Event: CSEM Student Forum

Numerical Challenges in Analyzing Chaotic Dynamical Systems

Arjit Seth, Graduate Student, Oden Institute

Abstract

Idealized chaotic systems are frequently employed as models for exploring the numerical and analytical behaviors underlying large-scale phenomena such as weather prediction. Beyond their illustrative role, such systems present intrinsic challenges in numerical analysis, algorithmic implementation, and data-driven inference, independent of large-scale computation. The chaotic behavior of such systems is characterized by the governing dynamics, the periodicity (or lack thereof) of their trajectories, and the pronounced sensitivity of these trajectories to parameters and initial or boundary conditions. This talk introduces the mathematical definitions of chaos and the principal analytical and numerical properties used to characterize chaotic dynamical systems. It offers a concise overview drawn from selected readings in the contemporary literature and informal sources. The presentation also includes numerical demonstrations in Julia illustrating parameter estimation and "scientific machine learning" approaches within the framework of chaotic dynamics.

Biography

Arjit is a graduate student in Aerospace Engineering and a member of the Computational Research in Ice–Ocean Systems (CRIOS) group led by Prof. Patrick Heimbach. His research focuses on the validation, verification, and parameter estimation of computational fluid dynamics models applied to ocean and sea-ice processes. He also has prior experience in aircraft design optimization and scientific machine learning.