James Foster
Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
G-Research PhD Prize (2020, first place)
STEM for Britain 2021 (finalist in the mathematical sciences category)
NeurIPS 2021 Outstanding Reviewer Award (given to the top 8% of reviewers)
I have now moved to the University of Bath, and have PhD positions available (1 & 2).
I am interested in stochastic numerics, differential equations and their applications to machine learning.
Since my time as a graduate student, I have especially enjoyed the numerical analysis of Brownian motion and Stochastic Differential Equations (SDEs). This research has focused on developing numerical methods and applying them to prominent SDEs in data science, such as Langevin dynamics and Neural SDEs.
In particular, the main result of my DPhil thesis provides an interesting connection between Brownian motion and random polynomials. This idea was illustrated in a poster and Matlab example:
https://www.chebfun.org/examples/stats/RandomPolynomials.html
(courtesy of Prof. Nick Trefethen)
Graduate lecturer at Worcester College, tutoring Linear Algebra and Analysis (2017-2018)
TT 2019, 2022: Tutor (Consultation Sessions) - B8.4 Information Theory
MT 2018, HT 2021, 2022: Tutor - B8.4 Information Theory
TT 2017, 2018: Tutor (Consultation Sessions) - B8.4 Communication Theory
MT 2016, 2017: Teaching Assistant - B8.4 Communication Theory
HT 2017: Teaching Assistant - B8.3 Mathematical Models of Financial Derivatives
High order splitting methods for SDEs satisfying a commutativity condition
James Foster, Gonçalo dos Reis and Calum Strange
arXiv:2210.17543 (2022)
Brownian bridge expansions for Lévy area approximations and particular values of the Riemann zeta function
James Foster and Karen Habermann
Combinatorics, Probability and Computing 2022
An asymptotic radius of convergence for the Loewner equation and simulation of SLE traces via splitting
James Foster, Terry Lyons and Vlad Margarint
Journal of Statistical Physics (2022)
Efficient and Accurate Gradients for Neural SDEs
Patrick Kidger, James Foster, Xuechen Li and Terry Lyons
Neural Information Processing Systems 2021
The Signature Kernel is the solution of a Goursat PDE
Cristopher Salvi, Thomas Cass, James Foster, Terry Lyons and Weixin Yang
SIAM Journal on Mathematics of Data Science (2021)
Neural SDEs as Infinite-Dimensional GANs
Patrick Kidger, James Foster, Xuechen Li, Harald Oberhauser and Terry Lyons
International Conference on Machine Learning 2021
Neural Rough Differential Equations for Long Time Series
James Morrill, Cristopher Salvi, Patrick Kidger, James Foster and Terry Lyons
International Conference on Machine Learning 2021
The shifted ODE method for underdamped Langevin MCMC
James Foster, Terry Lyons and Harald Oberhauser
arXiv:2101.03446
Neural Controlled Differential Equations for Irregular Time Series
Patrick Kidger, James Morrill, James Foster and Terry Lyons
Neural Information Processing Systems 2020 (Spotlight)
An optimal polynomial approximation of Brownian motion
James Foster, Terry Lyons and Harald Oberhauser
SIAM Journal on Numerical Analysis (2020)