Publications
My main focus is on neural differential equations (ODEs, CDEs, SDEs).
The single thing I’m proudest of is my doctoral thesis, which is essentially the textbook for neural differential equations. If you’re new to the topic you may also like my seminar slides Neural Differential Equations in Machine Learning, which gives an introduction. (Briefly: you can tackle problems in physics, finance, time series, generative models.)
2022
On Neural Differential Equations
Patrick Kidger
Doctoral Thesis, Mathematical Institute, University of Oxford
2021
Equinox: neural networks in JAX via callable PyTrees and filtered transformations
Patrick Kidger, Cristian Garcia
Differentiable Programming workshop at Neural Information Processing Systems (NeurIPS) 2021
Efficient and Accurate Gradients for Neural SDEs
Patrick Kidger, James Foster, Xuechen Li, Terry Lyons
Neural Information Processing Systems (NeurIPS) 2021
Neural Controlled Differential Equations for Online Prediction Tasks
James Morrill, Patrick Kidger, Lingyi Yang, Terry Lyons
Preprint
Neural SDEs as Infinite-Dimensional GANs
Patrick Kidger, James Foster, Xuechen Li, Harald Oberhauser, Terry Lyons
International Conference on Machine Learning (ICML) 2021
"Hey, that's not an ODE": Faster ODE Adjoints via Seminorms
Patrick Kidger, Ricky T. Q. Chen, Terry Lyons
International Conference on Machine Learning (ICML) 2021
Neural Rough Differential Equations for Long Time Series
James Morrill, Cristopher Salvi, Patrick Kidger, James Foster, Terry Lyons
International Conference on Machine Learning (ICML) 2021
Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU
Patrick Kidger, Terry Lyons
International Conference on Learning Representations (ICLR) 2021
2020
Neural Controlled Differential Equations for Irregular Time Series
Patrick Kidger, James Morrill, James Foster, Terry Lyons
Neural Information Processing Systems (NeurIPS) 2020 – Spotlight
A Generalised Signature Method for Time Series
James Morrill, Adeline Fermanian, Patrick Kidger, Terry Lyons
Preprint
Generalised Interpretable Shapelets for Irregular Time Series
Patrick Kidger, James Morrill, Terry Lyons
Preprint
Universal Approximation with Deep Narrow Networks
Patrick Kidger, Terry Lyons
Conference on Learning Theory 2020
2019
Deep Signature Transforms
Patrick Kidger, Patric Bonnier, Imanol Perez Arribas, Cristopher Salvi, Terry Lyons
Neural Information Processing Systems 2019
Miscellaneous Notes
Neural Differential Equations in Machine Learning
(Seminar slides)
Interpolating PDE solutions using feedforward neural networks
(Numerical PDE super-resolution)
Limits of Fisher–KPP equations, branching Brownian motion and a spatial Λ-Fleming–Viot model for population expansion
(Stochastic analysis + PDEs for modelling population expansion)
Polynomial Approximation of Holomorphic Functions
(My Master’s dissertation)