Maciej Buze
Assistant Professor (Lecturer) in Mathematics and AI
About
MARS: Mathematics for AI in Real-world Systems
School of Mathematical Sciences, Lancaster University
My research spans a wide range of topics at the intersection of applied and computational mathematics and mathematical analysis, and is primarily inspired by applications in materials science, physics and data science.
I use and develop tools in calculus of variations, bifurcation theory, numerical analysis, optimal transport, uncertainty quantification, approximation theory, scientific GPU computing, data analysis and machine learning. My current research themes are listed below.
m.buze@lancaster.ac.uk · Google Scholar · GitHub · ORCID · CV
Research
Energy landscapes of atomistic systems
Mapping the energy landscapes of large atomistic simulations, with continuation and deflation methods that scale to machine-learned interatomic potentials and reveal how defects nucleate, move and cascade.
numerical continuation, deflation, machine-learned interatomic potentials, defect nucleation, structural avalanches
Modelling microstructure
Microstructures as optimal clusterings, with anisotropic power and polynomial diagrams computed by semi-discrete optimal transport on the GPU that capture the grains of real metals and their crystallographic structure, in collaboration with Tata Steel.
anisotropic power diagrams, polynomial diagrams, semi-discrete optimal transport, clustering, crystallography, EBSD, PyAPD
Optimal transport: theory and algorithms
Moving mass optimally when it can also be created or destroyed: barycentres in the Hellinger–Kantorovich distance, their multi-marginal formulations, and entropic regularisation of unbalanced problems.
unbalanced optimal transport, Hellinger–Kantorovich distance, barycentres, multi-marginal optimal transport, entropic regularisation, Sinkhorn algorithm
Defects and plasticity across scales
Rigorous bottom-up models of cracks and dislocations, from the discrete lattice to mesoscale plasticity.
fracture, near-crack-tip plasticity, dislocations, lattice Green’s functions, flexible boundary conditions, discrete-to-continuum
News
- Two co-supervised PhD students in Chemistry start this month: Menna Shirras, on machine learning for the quantum description of uranyl chemistry, and Catherine Needham, on the same for lanthanide and minor actinide chemistry (tentative titles). The studentships come from our successful bid to the Faculty of Science and Technology PhD in Natural Sciences competition, and from a Nuclear Decommissioning Authority PhD bursary with matched funding from the SATURN CDT.
- Our new undergraduate programme, the BSc in Mathematics, Artificial Intelligence and Real-world Systems, which I helped develop, welcomes its first students. I am teaching MATH4120: Mathematical Modelling and Programming, a new first-year module designed for it.
- Co-organised the inaugural MARS Annual Symposium in Lancaster, 9–11 September, on computational mathematics and probabilistic machine learning.
- New preprint with D. P. Bourne, T. Gallouët and Q. Mérigot: Polynomial diagrams for microstructure modelling.
- Our paper with F. Birks, I. Ghanem, L. Pastewka and J. Kermode, Resolving structural avalanches in amorphous carbon with arclength continuation, is out in Physical Review Letters.
- Organised the workshop Data-driven modelling of metallic materials across scales at Lancaster Castle, 6–8 May, funded by DSAIL and MARS.
Selected publications
-
Polynomial diagrams for microstructure modelling.
arXiv preprint (2026). under review
arXiv
bibtex
@misc{bourne2026polynomial, title = {Polynomial diagrams for microstructure modelling}, author = {D. P. Bourne and M. Buze and T. Gallouët and Q. Mérigot}, year = {2026}, eprint = {2605.20816}, archivePrefix = {arXiv}, } -
Resolving structural avalanches in amorphous carbon with arclength continuation.
Physical Review Letters 136, 206101 (2026).
arXivdoi
bibtex
@article{birks2026avalanches, title = {Resolving structural avalanches in amorphous carbon with arclength continuation}, author = {F. Birks and I. Ghanem and L. Pastewka and J. Kermode and M. Buze}, journal = {Physical Review Letters}, volume = {136}, pages = {206101}, year = {2026}, doi = {10.1103/6n5m-rxc1}, eprint = {2601.22933}, archivePrefix = {arXiv}, } -
Incompleteness of Sinclair-type continuum flexible boundary conditions for atomistic fracture simulations.
Multiscale Modeling & Simulation 23(2), 711–752 (2025).
arXivdoi
bibtex
@article{braun2025incompleteness, title = {Incompleteness of Sinclair-type continuum flexible boundary conditions for atomistic fracture simulations}, author = {J. Braun and M. Buze}, journal = {Multiscale Modeling & Simulation}, volume = {23}, number = {2}, pages = {711--752}, year = {2025}, doi = {10.1137/24M1661078}, eprint = {2403.05462}, archivePrefix = {arXiv}, } -
Constrained Hellinger–Kantorovich barycenters: least-cost soft and conic multimarginal formulations.
SIAM Journal on Mathematical Analysis 57(1), 495–519 (2025).
arXivdoicode
bibtex
@article{buze2025chk, title = {Constrained Hellinger–Kantorovich barycenters: least-cost soft and conic multimarginal formulations}, author = {M. Buze}, journal = {SIAM Journal on Mathematical Analysis}, volume = {57}, number = {1}, pages = {495--519}, year = {2025}, doi = {10.1137/24M1639804}, eprint = {2402.11268}, archivePrefix = {arXiv}, } -
Anisotropic power diagrams for polycrystal modelling: efficient generation of curved grains via optimal transport.
Computational Materials Science 245, 113317 (2024).
arXivdoicode
bibtex
@article{buze2024apd, title = {Anisotropic power diagrams for polycrystal modelling: efficient generation of curved grains via optimal transport}, author = {M. Buze and J. Feydy and S. M. Roper and K. Sedighiani and D. P. Bourne}, journal = {Computational Materials Science}, volume = {245}, pages = {113317}, year = {2024}, doi = {10.1016/j.commatsci.2024.113317}, eprint = {2403.03571}, archivePrefix = {arXiv}, } -
Atomistic modelling of near-crack-tip plasticity.
Nonlinearity 34(7), 4503–4542 (2021).
arXivdoi
bibtex
@article{buze2021plasticity, title = {Atomistic modelling of near-crack-tip plasticity}, author = {M. Buze}, journal = {Nonlinearity}, volume = {34}, number = {7}, pages = {4503--4542}, year = {2021}, doi = {10.1088/1361-6544/abf33c}, eprint = {2007.02408}, archivePrefix = {arXiv}, }
PhD students
- Menna Shirras Machine learning for the quantum description of uranyl chemistry (tentative title).
- Catherine Needham Machine learning for the quantum description of lanthanide and minor actinide chemistry (tentative title).
- Dawid Lipinski Optimal transport techniques in natural sciences and machine learning.
- Inayat Ullah Homotopy continuation methods in atomistic modelling of matter.
- Fraser Birks How amorphous carbon breaks — atomistic models and machine learning.
I am always happy to hear from prospective PhD students and postdocs interested in the mathematics of materials, optimal transport or scientific machine learning. Get in touch: m.buze@lancaster.ac.uk