Dr Maciej Buze
Lecturer in Mathematics and AIResearch Overview
I work at the intersection of applied and computational mathematics and mathematical analysis, on problems inspired by materials science, physics, data science and AI. Most are variational: an energy, its minimisers and critical points, and how these change with a parameter. My current themes are: energy landscapes of atomistic systems, where I develop numerical continuation and deflation methods that scale to large simulations with machine-learned interatomic potentials; rigorous discrete-to-continuum analysis of cracks, dislocations and plasticity; learning compact geometric models of the microstructure of metals such as steel from image data, using optimal transport and GPU computing, in collaboration with Tata Steel; and the theory and algorithms of unbalanced optimal transport, a tool for comparing distributions that is central to modern machine learning. I aim for results that are rigorous where possible and computable at scale, and release them as open-source software. See https://mbuze.github.io for details.
PhD Supervision Interests
I am happy to supervise PhD projects in any of my research themes: the mathematics of materials (atomistic energy landscapes, defects and plasticity, microstructure modelling), optimal transport, and their interfaces with machine learning and AI, from the mathematics behind learning methods to machine learning for science. Projects can lean towards rigorous analysis, towards numerical methods and GPU computing, or combine both, and many involve collaborators in materials science and industry. Rather than advertising fixed projects, I shape each project around the student's background and interests: see my website for details, and get in touch to discuss a tailored project.
Data-Driven Modelling of Metallic Materials Across Scales
Participation in conference - Academic
Polynomial diagrams for microstructure modelling
Invited talk
PyAPD: A Python library for working with minimisation diagrams with GPU acceleration
Invited talk
Barycenters in unbalanced optimal transport
Invited talk
CoMPASs: Computational materials science and mathematics at the particle and atomistic scales
Participation in conference - Academic
Barycenters in unbalanced optimal transport (for ensemble aggregation?)
Invited talk
Barycenters in Unbalanced Optimal Transport
Invited talk
Upscaling an atomistic model of anti-plane near-crack-tip plasticity
Invited talk
Upscaling an atomistic model of anti-plane near-crack-tip plasticit
Invited talk
Multiscale Modeling and Simulation (Journal)
Publication peer-review
Mathematical Models and Methods in Applied Sciences (Journal)
Publication peer-review
Edinburgh Mathematical Society
Election to learned society
Visiting Assistant Professor
Appointment
MARS: Mathematics for AI in Real-world Systems
MARS: Mathematics for AI in Real-world Systems
- MARS: Mathematics for AI in Real-world Systems