Scientific ML · PDE Solving · Neural Operators
I work with MS and PhD researchers who need PINNs, Fourier Neural Operators, or level-set methods implemented and understood — not just handed off. Active researcher, not a formatting shop.
Services
PINNs for custom PDEs
Architecture design, loss formulation, causal weighting, and ablation strategy for your specific equation and domain.
∂u/∂t + N[u] = fFNO / Neural Operator surrogates
Fourier Neural Operator training pipelines — data generation, autoregressive rollout, and operator-learning best practices.
𝒢: a(x) → u(x)Level-set & interface tracking
Interface advection benchmarks (translation, rotation, Zalesak's disk), level-set reinitialisation, and mass conservation analysis.
∂φ/∂t + v·∇φ = 0Thermal & transport PDEs
FDM baselines (Crank-Nicolson, Robin BCs), MMS verification, PINO surrogates for parametric thermal problems.
ρc∂T/∂t = ∇·(k∇T)Code implementation
Python/PyTorch notebooks — clean, reproducible, Colab-ready. From data pipelines to training loops to figures for publication.
loss.backward()Manuscript & thesis support
Consistency audits, metric definitions, result tables, and LaTeX editing for papers targeting journals like CMAME or Heat and Mass Transfer.
‖u − û‖₂ / ‖u‖₂About
I am an MS Applied Mathematics student at NED University of Engineering and Technology, Karachi, supervised by Dr. Fahim Raees. My thesis focuses on Physics-Informed Neural Networks and neural operators for interface advection and thermal PDE problems.
I also serve as a Research Assistant under HEC Sindh Project 321 and as a Mathematics lecturer at PN Cadet College Ormara. My published and submitted work includes benchmarks on level-set advection where my PINN results beat the current state of the art on Zalesak's disk and reversed vortex problems.
I take on consulting work because I find that many researchers — especially those new to scientific ML — need someone who understands both the mathematics and the implementation, not just one or the other.
Research
Under review — CMAME
A Systematic Study of Physics-Informed Neural Networks for the Level-Set Interface Advection
Ablation study across translation, rotation, reversed vortex, and Zalesak's disk benchmarks. 0.13% relative L2 on Zalesak's disk — below current SoTA.
Submitted — Heat and Mass Transfer (Springer Nature)
A Physics-Informed Neural Operator for Thermal Ranking of Low-Cost Wall Materials in Hot-Dry Climates
Two-stage FDM (Crank-Nicolson) + PINO framework applied to five indigenous Sindh wall materials over a 10-dimensional parametric sweep.
Contact
If you have a PDE problem, a stalled PINN experiment, or a paper that needs a second pair of eyes from someone who has been through the same process — reach out. I respond to every serious inquiry.