RESEARCH

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

                                          -George Box

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

APPLIED MATHEMATICS & FLUID DYNAMICS

• Fluid Dynamics: Investigating physical flow mechanisms, momentum transfer, and complex fluid behaviors across varying dynamic regimes.

• Fluid Flow Through Porous Media: Modeling immiscible and miscible multiphase flow, counter-current/co-current imbibition, and fingering instabilities in saturated and unsaturated porous matrices.

• Reservoir Simulation: Advanced modeling of enhanced oil recovery (EOR) processes, nanoparticle-based displacement, and secondary recovery dynamics.

• Heat and Mass Transfer: Analyzing energy transport, turbine cooling dynamics, reaction-diffusion processes, and exothermic reactions within porous systems.

• Groundwater Recharge: Analytical and numerical modeling of vertical groundwater recharge by spreading in partially saturated porous media.

• Differential Equations (Linear & Non-Linear): Formulating, analyzing, and solving highly non-linear partial differential equations governing physical phenomena.

METHODOLOGY & SCIENTIFIC MACHINE LEARNING

• Scientific Machine Learning (SciML): Integrating domain physics with deep learning to build scalable framework solvers for complex physical systems.

• Physics-Informed Neural Networks (PINNs) & Updated Variants: Developing locally adaptive, hard/soft Reynolds-parameterized, and other customized PINNs architectures to improve convergence, stability, and accuracy.

• Inverse PINNs & Parameter Estimation: Solving inverse problems, discovering hidden physics, and estimating system parameters directly from observational data.

• Artificial Neural Networks (ANNs): Designing neural network models to predict complex physical behaviors and multi-parameter transport phenomena.

• Semi-Analytical & Numerical Methods: Applying classic and modern analytical techniques, including Reduced Differential Transform Methods (RDTM) and similarity solutions, alongside numerical schemes.