Maciej Buze

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.

An illustration: a clamped, pre-buckled sheet of atoms, pushed at its centre. Continuation traces a symmetric family of equilibria, and deflation finds two further, asymmetric families (the shadows). drag to turn · click a shadow

Overview

Equilibrium configurations of an atomistic system are critical points of its potential energy. Processes such as crack propagation, dislocation nucleation and plastic avalanches are governed by how these critical points, stable and unstable, depend on a loading parameter. Energy minimisation and molecular dynamics probe this landscape locally, at fixed load and near a chosen configuration; rare transitions are reached only at unrealistic rates, and saddle points only when the end states are known in advance.

Numerical continuation follows branches of critical points through folds and bifurcations, and deflation finds further solutions by excluding known ones. Both are established tools of bifurcation theory, but remain underused at the atomistic scale, where systems have millions of degrees of freedom, the Hessian is too costly to assemble, and the energy comes from an interatomic potential rather than a formula.

We are building these tools into a general methodology for large-scale atomistic modelling:

  • Continuation at scale. Matrix-free predictor–corrector schemes with adaptive step control and reparameterisation, so that paths of equilibria can be followed through instabilities in realistic systems.
  • Deflation for atoms. Deflation operators that respect locality and the symmetries of the lattice, turning branch-following into a systematic search for distinct equilibria.
  • Software. Implementations that work with standard atomistic codes such as LAMMPS and with machine-learned interatomic potentials, with benchmarks and documentation.
  • Applications. Structural avalanches and plasticity in amorphous solids, dislocation nucleation at surface steps, void formation and migration in metals, and lattice trapping in fracture.

Publications

  • F. Birks, I. Ghanem, L. Pastewka, J. Kermode, and M. Buze. 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}, }
  • J. Braun and M. Buze. 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}, }
  • S. Bagchi, I. Baghishov, M. Buze, et al. New Mathematics for the Exascale: Applications to Materials Science. White paper, Institute for Pure and Applied Mathematics, UCLA (2023).
    bibtex@techreport{bagchi2023exascale, title = {New Mathematics for the Exascale: Applications to Materials Science}, author = {S. Bagchi and I. Baghishov and M. Buze and others}, institution = {Institute for Pure and Applied Mathematics, UCLA}, type = {White paper}, year = {2023}, }
  • M. Buze and J. R. Kermode. Numerical-continuation-enhanced flexible boundary condition scheme applied to mode-I and mode-III fracture. Physical Review E 103(3), 033002 (2021). arXivdoicode
    bibtex@article{buze2021ncflex, title = {Numerical-continuation-enhanced flexible boundary condition scheme applied to mode-I and mode-III fracture}, author = {M. Buze and J. R. Kermode}, journal = {Physical Review E}, volume = {103}, number = {3}, pages = {033002}, year = {2021}, doi = {10.1103/PhysRevE.103.033002}, eprint = {2008.12822}, archivePrefix = {arXiv}, }
  • M. Buze, T. Hudson, and C. Ortner. Analysis of cell size effects in atomistic crack propagation. ESAIM: Mathematical Modelling and Numerical Analysis 54(6), 1821–1847 (2020). arXivdoi
    bibtex@article{buze2020cellsize, title = {Analysis of cell size effects in atomistic crack propagation}, author = {M. Buze and T. Hudson and C. Ortner}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis}, volume = {54}, number = {6}, pages = {1821--1847}, year = {2020}, doi = {10.1051/m2an/2020005}, eprint = {1905.13328}, archivePrefix = {arXiv}, }

Collaborators

  • James Kermode University of Warwick
  • Lars Pastewka University of Freiburg
  • Julian Braun Heriot-Watt University
  • Thomas Hudson University of Warwick
  • Christoph Ortner University of British Columbia
  • Fraser Birks University of Warwick (PhD student)
  • Ibrahim Ghanem University of Freiburg (PhD student)
  • Inayat Ullah Lancaster University (PhD student)
  • Lev Truskinovsky CNRS, ESPCI Paris
  • Subrahmanyam Pattamatta University of Hong Kong
  • Marcus Noack Lawrence Berkeley National Laboratory
  • Soumendu Bagchi Oak Ridge National Laboratory

Software

  • LACT numerical continuation for LAMMPS
  • NCFlex.jl numerical-continuation-enhanced flexible boundary conditions for fracture

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