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Muhammed Ali Mehmood I am a final-year PhD student in Mathematics at Imperial College London, supervised by Prof. Ewelina Zatorska. My research lies at the intersection of the analysis of PDEs, machine learning, and scientific computation. I study nonlinear PDE systems arising from compressible fluid mechanics and congestion-driven flows (e.g. traffic, pedestrian dynamics, and multi-phase fluids).. Alongside rigorous analysis, I also develop and analyse machine learning methods for non-linear PDEs, including Physics-Informed Neural Networks (PINNs) and Randomised Neural Networks (RaNNs). I am particularly interested in designing neural network architectures that overcome most of the practical issues with NNs for non-linear PDEs, such as long training times, poor scalability and expressivity. Prior to my PhD, I completed an MSc in Pure Mathematics at Imperial College London and a BSc in Mathematics at King’s College London. You can view my MSc thesis here. Beyond academia, I am strongly interested in machine learning research and applied ML roles, where mathematical structure, modelling insight, and data-driven methods intersect. I maintain a portfolio of ML projects, including a NLP-based classification system for A-level math questions (used to launch m6ths.com) and scientific ML neural network solvers; these can be found on my GitHub. |
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