2 citations · 2 across the 1 of their papers we have counts for
5 papers
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…
The shifted ODE method for underdamped Langevin MCMC
James Foster, Terry Lyons, Harald Oberhauser
In this paper, we consider the underdamped Langevin diffusion (ULD) and propose a numerical approximation using its associated ordinary differential equation (ODE). When used as a…
Neural Controlled Differential Equations for Irregular Time Series
Patrick Kidger, James Morrill, James Foster +1
Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equat…
An optimal polynomial approximation of Brownian motion
James Foster, Terry Lyons, Harald Oberhauser
In this paper, we will present a strong (or pathwise) approximation of standard Brownian motion by a class of orthogonal polynomials. The coefficients that are obtained from the ex…