Status:
Personal website:
Research groups:
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Research interests:
Neural differential equations (ODEs/CDEs/SDEs); deep learning; time series.
Further details:
A mathematician who enjoys martial arts, ice skating and scuba diving. My supervisor is Terry Lyons.
I am the maintainer for the Signatory project, and a core developer for the torchsde project.
See also my website.
Miscellaneous pieces of work:
- Seminar slides on neural differential equations
- Presentation on Neural Controlled Differential Equations
- Interpolating PDE solutions using feedforward neural networks (Numerical PDE super-resolution)
- Limits of Fisher–KPP equations, branching Brownian motion and a spatial lambda-Fleming–Viot model for population expansion (Stochastic analysis + PDE analysis for modelling population expansion.)
- Polynomial Approximation of Holomorphic Functions (My Master's Dissertation)
Teaching:
TA for C8.2 Stochastic Analysis and PDEs
(Hilary Term 2019)
TA for C4.1 Further Functional Analysis
(Michaelmas Term 2018)
Tutor for C8.2 Stochastic Analysis and PDEs
(Trinity Term 2018)
Major / recent publications:
Neural SDEs Made Easy: SDEs are Infinite-Dimensional GANs
Patrick Kidger, James Foster, Xuechen Li, Harald Oberhauser, Terry Lyons
Machine Learning and the Physical Sciences, NeurIPS (2020)
"Hey, that's not an ODE": Faster ODE Adjoints with 12 Lines of Code
Patrick Kidger, Ricky T. Q. Chen, Terry Lyons
Machine Learning and the Physical Sciences, NeurIPS (2020)
Neural CDEs for Long Time Series via the Log-ODE Method
James Morrill, Patrick Kidger, Cristopher Salvi, James Foster, Terry Lyons
Machine Learning and the Physical Sciences, NeurIPS (2020)
A Generalised Signature Method for Time Series
James Morrill, Adeline Fermanian, Patrick Kidger, Terry Lyons
arXiv:2006.00873
Generalised Interpretable Shapelets for Irregular Time Series
Patrick Kidger, James Morrill, Terry Lyons
arXiv:2005.13948
Neural Controlled Differential Equations for Irregular Time Series
Patrick Kidger, James Morrill, James Foster, Terry Lyons
Neural Information Processing Systems 2020 (Spotlight)
YouTube presentation
Universal Approximation with Deep Narrow Networks
Patrick Kidger, Terry Lyons
Conference on Learning Theory (2020)
50 second presentation
13 minute presentation
Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU
Patrick Kidger, Terry Lyons
arXiv:2001.00706
Deep Signature Transforms
Patrick Kidger, Patric Bonnier, Imanol Perez Arribas, Cristopher Salvi, Terry Lyons
Neural Information Processing Systems (2019)