“All models are wrong, but some models are useful.” 

                                                                                                                                                                   -George Box 

My research interest lies at the intersection of the following two disciplines: 

Scientific Machine Learning & AI 

• Scientific Machine Learning (SciML): Developing robust frameworks for solving differential equations using deep learning.

• Physics-Aware Neural Networks: Investigating different variants of neural network architectures to enhance solution accuracy and convergence.

• Physics-Based Deep Learning: Techniques for learning from sparse data by enforcing physical laws (conservation of mass/momentum).

• Optimization of Neural Networks: Enhancing convergence rates and stability in training deep neural networks for scientific problems.

Scientific Computation & Applied Mathematics (Fluid Mechanics)

• Computational Fluid Dynamics (CFD): Modeling complex fluid behaviors and flow instabilities.

• Porous Media Flow: Simulation of multiphase flows, secondary and enhanced oil recovery processes, and instability phenomena (e.g., viscous fingering) in porous media.

• Reaction-Diffusion Systems: Numerical study of non-linear PDEs like Fisher-KPP and similar equations.

• Inverse Problems: Parameter estimation and discovering hidden physics from observational data.

• Mathematical Modelling: Analysis of highly non-linear partial differential equations.