Research Projects

I aim to investigate the onset and development of chaos and instability in magneto-fluid systems using a combination of high-fidelity numerical simulations and modern artificial intelligence techniques. My primary motivation stems from the deep theoretical and practical importance of understanding chaotic magneto-fluid dynamics, which are prevalent in astrophysical plasmas, planetary cores, fusion reactors, and magnetically influenced fluidic systems. Through this project, I seek to explore how small perturbations in such systems grow and lead to unpredictable, chaotic states - highlighting the sensitive dependence on initial conditions that characterises these systems. The central objectives of my research are fourfold: To examine the role of different instabilities in initiating and evolving complex fluid structures that ultimately exhibit chaotic behaviour. To apply generalized perturbation techniques to Lorenz-type dynamical systems and study their impact on nonlinear transport processes, such as heat and mass transfer, within chaotic regimes. To develop and utilize a dual computational framework that includes both spectral solvers (using the Dedalus platform) and Physics-Informed Neural Networks (PINNs), facilitating robust detection, characterization, and prediction of chaotic patterns. To contextualize and validate these findings through application to astrophysical and plasma-related systems, focusing on phenomena such as magneto-fluid instabilities, shock waves, and multidiffusive convection. In my methodology, I plan to use Dedalus - a flexible, open-source spectral solver - for direct numerical simulations of the governing partial differential equations. This method will allow for the precise resolution of spatiotemporal instabilities across two- and three-dimensional domains. In parallel, I will implement Physics-Informed Neural Networks as a mesh-free modeling tool capable of learning from the system’s governing equations. This approach is especially advantageous in scenarios where experimental data are limited or noisy, offering a powerful means for parameter estimation and surrogate modelling. The synergy between Dedalus and PINNs will enable both detailed, high-resolution modelling and rapid, generalised prediction - paving the way for efficient analysis, early detection of chaotic transitions, and improved control strategies in engineering and natural systems. Ultimately, this research will contribute to a deeper understanding of nonlinear fluid dynamics under magnetic influences and help address critical challenges in modeling turbulent, multiscale systems. It also aligns strongly with my postdoctoral aspirations to advance computational physics and explore the frontiers of fluid dynamical systems through interdisciplinary tools.