MS Applied Mathematics researcher at NED University of Engineering & Technology, Karachi. I develop physics-informed neural networks for solving partial differential equations, with a focus on interface-tracking problems in computational fluid dynamics.
Currently seeking fully-funded PhD positions in scientific machine learning, neural operators, and data-driven PDE modeling.
Training strategies, loss balancing, causal weighting, and architectures (RFF, modified MLPs) for accurate PDE solutions.
Neural network approaches to interface tracking and advection in computational fluid dynamics.
Foundation models and operator learning (DeepONet, FNO) for cross-domain PDE solving and surrogate modeling.
Numerical methods for PDEs, optimization, and high-performance computing for scientific applications.
International Journal for Numerical Methods in Fluids (IJNMF), Wiley, 2026
A comprehensive study of PINNs for solving the level-set advection equation across four benchmark problems: translation, rigid-body rotation, Zalesak's disk, and the reversed single-vortex. 47 experiments systematically investigate network architecture (Tanh vs. RFF), training strategies (causal weighting, learning rate scheduling), eikonal regularization, and collocation sampling. The proposed PINN framework achieves results approximately 2× more accurate than the state-of-the-art classical numerical method on the reversed vortex benchmark.
NED University of Engineering & Technology, Karachi, Pakistan
Thesis: Physics-Informed Neural Networks for the Level-Set Equation
Supervisor: Dr. Fahim Raees
I am actively seeking fully-funded PhD positions (Fall 2026/2027) in scientific machine learning, with a focus on physics-informed methods and neural operators for PDE modeling. If you are interested in my work or have opportunities, I would be glad to hear from you.
Email: khan.pg4200844@cloud.neduet.edu.pk
ORCID: 0009-0001-7956-0080
GitHub: AkbarTheAnalyst