Our research is in computational applied mathematics, including numerical analysis, mathematical modelling and software. We are interested in taking challenging science or engineering problems and identifying efficient computational strategies to address them. We work with domain specialists, as well as computer scientists, high performance computing specialists, and with industry. We use methods from analysis (especially numerical analysis), geometry, probability, and statistics in our work. We also incorporate and rely on many concepts from statistical physics and theoretical chemistry. We develop our own industrial-strength software for various applications, an increasingly demanding part of our work.

News and Updates

June 2023

Further work on Langevin convergence with Peter Whalley and Daniel Paulin. Building on our previous results on Wasserstein convergence rates, we have extended the results to even more schemes, including Brunger-Brooks-Karplus and stochastic position/velocity Verlet. We've also explored the incorporation of stochastic gradients, and examined the bias and convergence performance in sampling for Bayesian logistic regression. Preprint on the ArXiv here.

May 2023

Working with Gabriel Stoltz (ENPC), Ben and Katerina developed a flexible new optimization scheme which incorporates generalized kinetic energy control for additional stability. Numerical methods and Lyapunov functions are provided in the preprint .

March 2023

Our new work on Langevin convergence rates provides tight estimates for Wasserstein convergence for Langevin splitting schemes, see the arxiv preprint .

January 2023

Oberwolfach meeting planned for 2024 on Constraints, stochastic numerics and mathematical modelling, jointly organised with Rachel Ward, Richard Tsai and Gilles Vilmart.

May 2022

Paper on multirate training accepted for ICML 2022. This paper provides a substantial efficiency improvement for transfer learning applications.

May 2021

New paper on constraint-based regularization accepted for ICML 2021!

May 2021

Dominic Philips to join the group in Autumn 2021. Dominic will be working on AI driven sampling of the shapes of biomolecules in a project jointly supervised with Antonia Mey (Chemistry) and Flaviu Cipcigan (IBM Research).

May 2021

Several new MAC-MIGS students join the group. Peter Whalley will be working in statistical methods, jointly supervised with Daniel Paulin; Donald Hobson is working on causal graphs and analysis of neural computational models, jointly supervised by Michal Branicki.

June 2021

We organized a special 1-day meeting on June 3 on Mathematical Topics in Machine Learning, with talks by Arnulf Jentzen, Gabriel Stoltz, Amos Storkey, and Eric Vanden-Eijnden. The videos of the talks are available here