Mathematical biology research, to be truly valuable, must be grounded in real biological mechanisms rather than esoteric math applied in a vacuum. — J. D. Murray’s rule of relevance

“All models are wrong, but some are useful.” — George E. P. Box

Portrait of Emmanuel Hackman

I am Emmanuel Hackman, a PhD student in Computational Science (Mathematics) at the University of Southern Mississippi.

My research sits at the intersection of mathematical biology, scientific computing and numerical analysis. I develop physics-informed neural networks (PINNs) and numerical methods for forward and inverse problems in partial differential equations, with a focus on neuroscience: estimating dopamine diffusion and uptake from sparse electrode recordings in Parkinson’s disease, and modelling glioblastoma (GBM). Next, I plan to extend this work to medical imaging, possibly in 3D.

Research · Publications · CV · Contact

Research interests

Mathematical biology Physics-informed neural networks Scientific computing Numerical analysis Scientific machine learning Parkinson’s disease Glioblastoma (GBM) Inverse problems Parameter identifiability and uncertainty quantification Mathematical neuroscience (dopamine transport)

What I am working on

My first paper — measurement-aware PINNs that estimate dopamine diffusion and uptake from sparse electrode recordings — is submitted and under review. I am now extending it to counterfactual inference (how would dopamine respond to an intervention such as transporter blockade?) and to nonlinear Michaelis–Menten uptake, and modelling glioblastoma (GBM). See Research for details.

Recent

  • 2026-10 — Paper on measurement-aware PINNs for dopamine diffusion and uptake submitted to Biomedical Signal Processing and Control (Elsevier); code and data archived on Zenodo.
  • 2026-10 — Third Place Poster Award at the 11th SIAM Central States Section Annual Meeting, Jackson State University, Jackson, MS (travel supported by an NSF Travel Award).
  • 2026-09 — Paper “Difference Equations and Limits in Geometry” (with Jiu Ding and Huijian Zhu) submitted to The American Mathematical Monthly.
  • 2026-07 — Poster at the Mississippi IDeA/EPSCoR Conference 2026 (MIEC26), Hattiesburg, MS.

Open to collaborations on inverse problems for neurotransmitter transport and electrochemical sensing, mathematical models of glioblastoma, and physics-informed methods for medical imaging. Get in touch.