What can the equations of fluid motion teach us about the world — and the human brain?

Portrait of Emmanuel Hackman

I am Emmanuel Hackman, a PhD candidate in computational mathematics at the University of Southern Mississippi.

My research develops physics-informed neural networks for the 3D incompressible Navier–Stokes equations, with applications to fluid dynamics, material science, and cerebrospinal fluid flow in Parkinson’s disease.

Research · Publications · CV · Contact

Research interests

Physics-informed neural networks Navier–Stokes equations Computational fluid dynamics Numerical analysis Scientific machine learning Cerebrospinal fluid flow Parkinson’s disease imaging

What I am working on

I am building a reproducible research pipeline that benchmarks PINN-based solvers against classical numerical baselines — projection methods, spectral solvers, RK4 time integration — on canonical problems such as Taylor–Green, Kovasznay, and Beltrami flow, and then transfers the validated method to medical imaging data.

The headline near-term result is a 3D Navier–Stokes PINN validated against the analytic Beltrami benchmark, with side-by-side classical baselines on L^2 error, divergence, and wall-clock cost. See Research for details.

Recent

  • 2026-05 — First experiment runs (Kovasznay AD-vs-FV) completed; pressure metric fix landed.
  • 2026-05 — Dissertation research workspace scaffolded with full reproducibility checklist.
  • 2026 — Coursework and qualifying exam preparation at USM.

Open to collaborations on PINNs for incompressible flow, inverse problems in 4D-flow MRI, and physics-informed benchmarks. Get in touch.