155 citations · 517 across the 15 of their papers we have counts for
14 papers
Single-seed generation of Brownian paths and integrals for adaptive and high order SDE solvers
Andraž Jelinčič, James Foster, Patrick Kidger
Despite the success of adaptive time-stepping in ODE simulation, it has so far seen few applications for Stochastic Differential Equations (SDEs). To simulate SDEs adaptively, meth…
Optimistix: modular optimisation in JAX and Equinox
Jason Rader, Terry Lyons, Patrick Kidger
We introduce Optimistix: a nonlinear optimisation library built in JAX and Equinox. Optimistix introduces a novel, modular approach for its minimisers and least-squares solvers. Th…
Lineax: unified linear solves and linear least-squares in JAX and Equinox
Jason Rader, Terry Lyons, Patrick Kidger
We introduce Lineax, a library bringing linear solves and linear least-squares to the JAX+Equinox scientific computing ecosystem. Lineax uses general linear operators, and unifies…
On Neural Differential Equations
Patrick Kidger
The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and…
Efficient and Accurate Gradients for Neural SDEs
Patrick Kidger, James Foster, Xuechen Li +1
Neural SDEs combine many of the best qualities of both RNNs and SDEs: memory efficient training, high-capacity function approximation, and strong priors on model space. This makes…
Neural SDEs as Infinite-Dimensional GANs
Patrick Kidger, James Foster, Xuechen Li +2
Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal dynamics. However, a fundamental limitation has been that such models have typically bee…