Zoom link https://kaust.zoom.us/j/98528956129

Committee members

• Prof. Hong G. Im – Ph.D. Advisor
• Prof. Sanjay Rastogi – Committee Chair
• Prof. Michael E. Mueller – External examiner
• Prof. Peter J. Schmid – Committee member from ME program)

Abstract

This thesis presents a data-driven reduced-order modeling (ROM) approach to accelerate the time integration of stiff, chemically reacting systems by alleviating their inherent multi-timescale stiffness. The methodology follows an encode–forecast–decode strategy: a nonlinear autoencoder (AE) performs dimensionality reduction (encoding and decoding), and a neural ordinary differential equation (NODE) models the system dynamics in the resulting low-dimensional latent space. The ROM serves as a non-stiff surrogate for the time evolution of the thermochemical state (temperature and species concentrations) during highly stiff ignition processes. Timescale analysis of the dynamical Jacobians shows that the AE’s projection inherently filters out fast, unnecessary modes, effectively identifying a slow invariant manifold more efficiently than classical eigenvalue-based approaches.

Furthermore, an information-theoretic analysis explains the effectiveness of the learned latent representation: monitoring mutual information during training reveals distinct learning phases in the encoder and decoder, corresponding to the discovery of a smooth, low-dimensional manifold of the system’s dynamics. The AE’s nonlinear mapping redistributes the state’s probability density, transforming events that are rare in the original physical space into more probable, well-mixed events in the latent space. This density redistribution and “better mixing” make the stiff system’s behavior more uniform and tractable after projection.

Finally, a stretching-based diagnostic grounded in Riemannian geometry is employed to analyze a range of dynamical systems, including the Rober kinetics, Brusselator, and Lorenz systems. In this framework, the geodesic deviation-quantified through orthogonal and tangential stretching rates-serves as an effective geometric indicator for detecting invariant manifolds. This methodology is further extended to identify the location of slow invariant manifolds (SIMs) directly within the physical composition space. Importantly, this analysis offers critical insight into how latent-space transformations can mitigate stiffness by isolating and preserving the essential slow dynamics that govern system evolution.

Biography

Vijayamanikandan Vijayarangan earned his Bachelor’s degree in Aeronautical Engineering from Rajalakshmi Engineering College (Anna University), India, in 2017, followed by a Master’s degree in Aerospace Engineering with a specialization in Propulsion and Combustion from the Indian Institute of Technology Kanpur, India, in 2020. He is currently pursuing Ph.D. in Mechanical Engineering within the Physical Science and Engineering Division at King Abdullah University of Science and Technology (KAUST), Saudi Arabia. His research centers on the integration of deep learning with computational physics.