MS Applied Mathematics researcher at NED University of Engineering & Technology, Karachi, supervised by Dr. Fahim Raees. I develop physics-informed neural networks and neural operators for solving partial differential equations, with applications to interface-tracking problems in computational fluid dynamics and thermal analysis of building materials.
Seeking fully-funded PhD positions for Spring 2027
My research focuses on integrating deep learning with classical numerical methods for solving partial differential equations. Specifically, I study how physics-informed neural networks can be designed and trained to accurately capture evolving interfaces governed by the level-set advection equation—a problem central to computational fluid dynamics. I am interested in understanding and improving PINN training dynamics through architecture design, loss balancing, and regularization strategies, and I aim to extend these ideas to neural operator frameworks for broader PDE applications.
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.
Operator learning (DeepONet, FNO) for cross-domain PDE solving and surrogate modeling.
Numerical methods for PDEs, optimization, and gradient-based methods for scientific applications.
Physics-informed neural operators for thermal analysis of building materials in hot-dry climates, with applications to climate-resilient construction.
Machine Learning: Science and Technology, IOP Publishing, 2026 — doi:10.1088/2632-2153/ae8b74 — Published July 2026, Gold Open Access, CC BY 4.0
A 69-experiment ablation study of PINNs for the level-set advection equation across four benchmarks: linear translation, solid-body rotation, reversed vortex deformation, and the Zalesak rotating slotted disc. Key findings include an 82× error reduction via eikonal weight tuning, a novel RFF–eikonal joint design constraint, and state-of-the-art results on RV (T=8, 0.63%) and ZD (0.13%), outperforming PirateNet (Mullins et al., 2025) using a standard tanh network.
Scientific Reports, Springer Nature, 2026 — Under review; submitted July 2026
A two-stage framework combining a Crank–Nicolson FDM solver under diurnal solar forcing and a PINO/FNO surrogate for parametric thermal analysis of five indigenous Sindh wall materials across a nine-dimensional parameter space (1500 LHS samples). The trained PINO attains a 0.201 K MAE on peak inner-surface temperature while preserving the FDM material ranking exactly; trained on 150 samples it matches a data-only FNO trained on 300, and it reproduces the ISO 13786 time lag and decrement factor to 0.99 h and 0.010.
Zenodo, 2026 — doi:10.5281/zenodo.21860060
Extends the level-set PINN framework to three dimensions across four benchmarks (translating sphere, rotating sphere, Zalesak slotted sphere, reversed single vortex). An 18-run seed-swept eikonal weight study per benchmark shows 2D-derived optimal weights transfer to 3D benchmark-by-benchmark (3 of 4 unchanged). Introduces feature-restricted classification metrics (Ffill/Ferode) for thin-feature certification; baseline comparison against fifth-order WENO + TVD-RK3 FDM.
Zenodo, 2026 — doi:10.5281/zenodo.21862964
Extends the thermal surrogate (Paper 2) to a fully coupled Künzel HAM system with latent heat and dynamic moisture redistribution, using 30-day measured NASA POWER Sukkur (June 2025) boundary forcing and a 12-dimensional parameter space (2000 LHS samples). A data-only FNO achieves a 293× speed-up over FDM while preserving material ranking; Sobol analysis shows hygric parameters have statistically negligible total-effect indices on the ranking QoI.
NED University of Engineering & Technology, Karachi, Pakistan
Thesis: A Systematic Study of Physics-Informed Neural Networks for the Level-Set Interface Advection
Supervisor: Dr. Fahim Raees
Developed a PINN framework for the level-set advection equation and conducted a systematic 69-experiment study across four benchmark problems, identifying a novel RFF–eikonal joint design constraint that achieves an 82× error reduction.
I am actively seeking fully-funded PhD positions (Spring 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.