A Probabilistic Taylor Expansion with Applications in Filtering and Differential Equations

02/01/2021
by   Toni Karvonen, et al.
0

We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consists of derivative evaluations at the expansion point and the prior covariance kernel belongs to the class of Taylor kernels, which can be written in a certain power series form. This permits statistical modelling of the uncertainty in a variety of algorithms that exploit first and second order Taylor expansions. To demonstrate the utility of this Gaussian process model we introduce new probabilistic versions of the classical extended Kalman filter for non-linear state estimation and the Euler method for solving ordinary differential equations.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/16/2021

A Feynman-Kac Type Theorem for ODEs: Solutions of Second Order ODEs as Modes of Diffusions

In this article, we prove a Feynman-Kac type result for a broad class of...
research
08/26/2022

Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations

Data in many applications follows systems of Ordinary Differential Equat...
research
09/21/2022

Chaotic Hedging with Iterated Integrals and Neural Networks

In this paper, we extend the Wiener-Ito chaos decomposition to the class...
research
02/09/2022

Adjoint-aided inference of Gaussian process driven differential equations

Linear systems occur throughout engineering and the sciences, most notab...
research
11/24/2021

State-space deep Gaussian processes with applications

This thesis is mainly concerned with state-space approaches for solving ...
research
08/18/2023

Explicit Runge-Kutta algorithm to solve non-local equations with memory effects: case of the Maxey-Riley-Gatignol equation

A standard approach to solve ordinary differential equations, when they ...
research
07/25/2018

Convergence Rates of Gaussian ODE Filters

A recently-introduced class of probabilistic (uncertainty-aware) solvers...

Please sign up or login with your details

Forgot password? Click here to reset