Projects per year
Personal profile
Research interests
I am interested in stochastic numerics, differential equations and their applications to machine learning.
Since my time as a graduate student, I have particularly 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.
Alongside my interest in SDEs, I have worked on machine learning projects in collaboration with members of the Oxford-based DataSıg team (datasig.ac.uk). Here we introduced new differential equation models and algorithms, inspired by rough path theory, for tackling problems involving multivariate time series.
Education/Academic qualification
Mathematics, Doctor of Philosophy, Numerical approximations for stochastic differential equations, University of Oxford
Oct 2016 → Nov 2020
Award Date: 1 Oct 2021
Mathematics, Master of Mathematics, University of Oxford
Oct 2012 → Sept 2016
Award Date: 17 Sept 2016
External positions
Postdoctoral Research Associate, University of Oxford
May 2020 → Jul 2022
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Projects
- 1 Active
Research output
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An Asymptotic Radius of Convergence for the Loewner Equation and Simulation of SLE κ Traces via Splitting
Foster, J., Lyons, T. & Margarint, V., 30 Nov 2022, In: Journal of Statistical Physics. 189, 2, 18.Research output: Contribution to journal › Article › peer-review
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Brownian bridge expansions for Lévy area approximations and particular values of the Riemann zeta function
Foster, J. & Habermann, K., 3 Nov 2022, In: Combinatorics, Probability and Computing. 28 p.Research output: Contribution to journal › Article › peer-review
Open Access -
Efficient and Accurate Gradients for Neural SDEs
Kidger, P., Foster, J., Li, X. & Lyons, T., 31 Dec 2021, Advances in Neural Information Processing systems 34: NeurIPS 2021. NeurIPS ProceedingsResearch output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding
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Neural Rough Differential Equations for Long Time Series
Morrill, J., Salvi, C., Kidger, P. & Foster, J., 24 Jul 2021, Proceedings of the 38th International Conference on Machine Learning. PMLR, Vol. 38. p. 7829-7838 10 p. (Proceedings of Machine Learning Research).Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding
Open Access -
Neural SDEs as Infinite-Dimensional GANs
Kidger, P., Foster, J., Li, X., Oberhauser, H. & Lyons, T., 24 Jul 2021, Proceedings of the 38th International Conference on Machine Learning. PMLR, Vol. 38. p. 5453-5463 11 p. (Proceedings of Machine Learning Research).Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding