1 code implementation • 2 Oct 2023 • Nathanael Bosch, Adrien Corenflos, Fatemeh Yaghoobi, Filip Tronarp, Philipp Hennig, Simo Särkkä

Probabilistic numerical solvers for ordinary differential equations (ODEs) treat the numerical simulation of dynamical systems as problems of Bayesian state estimation.

2 code implementations • NeurIPS 2023 • Jonathan Schmidt, Philipp Hennig, Jörg Nick, Filip Tronarp

In this paper, we propose a novel approximate Gaussian filtering and smoothing method which propagates low-rank approximations of the covariance matrices.

1 code implementation • NeurIPS 2023 • Nathanael Bosch, Philipp Hennig, Filip Tronarp

However, like standard solvers, they suffer performance penalties for certain stiff systems, where small steps are required not for reasons of numerical accuracy but for the sake of stability.

no code implementations • 17 Jun 2022 • Filip Tronarp, Toni Karvonen

We present a general Fourier analytic technique for constructing orthonormal basis expansions of translation-invariant kernels from orthonormal bases of $\mathscr{L}_2(\mathbb{R})$.

1 code implementation • 2 Feb 2022 • Filip Tronarp, Nathanael Bosch, Philipp Hennig

We show how probabilistic numerics can be used to convert an initial value problem into a Gauss--Markov process parametrised by the dynamics of the initial value problem.

2 code implementations • 20 Oct 2021 • Nathanael Bosch, Filip Tronarp, Philipp Hennig

Probabilistic numerical solvers for ordinary differential equations compute posterior distributions over the solution of an initial value problem via Bayesian inference.

no code implementations • 1 Feb 2021 • Toni Karvonen, Jon Cockayne, Filip Tronarp, Simo Särkkä

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.

1 code implementation • 15 Dec 2020 • Nathanael Bosch, Philipp Hennig, Filip Tronarp

The contraction rate of this error estimate as a function of the solver's step size identifies it as a well-calibrated worst-case error, but its explicit numerical value for a certain step size is not automatically a good estimate of the explicit error.

no code implementations • 17 Apr 2020 • Filip Tronarp, Simo Särkkä

For approximate filtering and smoothing the projection approach is taken, where it turns out that the prediction and smoothing equations are the same as in the case when the state variable evolves in Euclidean space.

no code implementations • 1 Apr 2020 • Filip Tronarp, Simo Sarkka, Philipp Hennig

The remaining three classes are termed explicit, semi-implicit, and implicit, which are in similarity with the classical notions corresponding to conditions on the vector field, under which the filter update produces a local maximum a posteriori estimate.

no code implementations • 29 Jan 2020 • Toni Karvonen, George Wynne, Filip Tronarp, Chris. J. Oates, Simo Särkkä

We show that the maximum likelihood estimation of the scale parameter alone provides significant adaptation against misspecification of the Gaussian process model in the sense that the model can become "slowly" overconfident at worst, regardless of the difference between the smoothness of the data-generating function and that expected by the model.

1 code implementation • 8 Oct 2018 • Filip Tronarp, Hans Kersting, Simo Särkkä, Philipp Hennig

We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions.

no code implementations • 13 Sep 2018 • Ángel F. García-Fernández, Filip Tronarp, Simo Särkkä

This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL).

no code implementations • 15 Mar 2017 • Jakub Prüher, Filip Tronarp, Toni Karvonen, Simo Särkkä, Ondřej Straka

Advantage of the Student- t process quadrature over the traditional Gaussian process quadrature, is that the integral variance depends also on the function values, allowing for a more robust modelling of the integration error.

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