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.
Machine Learning: Science and Technology, IOP Publishing, 2026. Under review; submitted August 2026 (MLST-105968)
Identifies a fundamental failure mode in standard gradient-norm loss balancing for PINN eikonal regularisation: the eikonal residual of the correct solution is nonzero wherever the level-set departs from a signed-distance function, so driving it to zero corrupts the solution. Introduces SDF-Aware Weighting (SAW), which combines a residual-quantile gate with a gradient-norm ratio to exclude points with legitimate SDF departure before scaling the surviving term. Across four 3D benchmarks a single SAW configuration selects an eikonal weight within an order of magnitude of an 18-run manual sweep spanning four decades (10−1 to 10−5); on the Zalesak slotted sphere SAW attains lower error than any weight in that sweep. Introduces feature-restricted classification metrics (Ffill/Ferode) to certify thin-feature preservation independently of global error.
Machine Learning: Science and Technology, IOP Publishing, 2026. Under review; submitted September 2026 (MLST-106107)
Tests whether a neural operator reproduces the decision a solver would make, using coupled heat and moisture transport through five indigenous earthen wall materials over a 30-day hot-dry summer. A verified finite-volume solver generates 2000 solutions over a 13-dimensional parameter space, and the FNO predicts temperature and moisture fields to relative L2 errors of 8.7×10−4 and 8.1×10−3. For the scalar ranking quantity a Gaussian process is five times more accurate, yet both surrogates reproduce every solver ranking. Hygric parameters have negligible influence, so the ranking is governed by thermal properties.
arXiv, 2026. arXiv:2609.38195
A spacetime Fourier neural operator that maps an initial interface to the full level-set trajectory, trained only on the transport residual and an eikonal constraint, with the initial condition imposed by construction and no reference solutions at any point. On a reversed single vortex it reaches 1.61% relative L2 error against 0.37% for a supervised baseline with the same architecture. Where the eikonal constraint holds, it conserves enclosed area 2.7× better than the supervised operator, and a hybrid using eight reference solutions beats a supervised operator using sixteen.
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.
International Islamic University Islamabad, Pakistan
CGPA: 3.37/4.00 · HEC Need-Based Scholarship (Higher Education Commission)
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.