I'm a PhD student in Mathematics at the University of Bath, working with James Foster.
I am interested in the combination of differential equations and machine learning. This has included efficient backpropagation algorithms for neural differential equations and extending flow map methods to SDEs.
Flow and diffusion models generate high-quality samples in many modalities; however, many network evaluations are required during inference due to numerical integration of an underlying differential equation. This work introduces Strong Stochastic Flow Maps as a framework for learning the strong solution map of SDEs, directly generalizing deterministic flow maps to the stochastic setting.
Training Neural ODEs requires backpropagating through an ODE solve. The state-of-the-art backpropagation method is recursive checkpointing that balances recomputation with memory cost. This work introduces a class of algebraically reversible ODE solvers that significantly improve upon both the time and memory cost of recursive checkpointing.
