Search Results for author: Filip Tronarp

Found 14 papers, 7 papers with code

Parallel-in-Time Probabilistic Numerical ODE Solvers

1 code implementation2 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.

The Rank-Reduced Kalman Filter: Approximate Dynamical-Low-Rank Filtering In High Dimensions

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.

Dimensionality Reduction

Probabilistic Exponential Integrators

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.

Uncertainty Quantification

Orthonormal Expansions for Translation-Invariant Kernels

no code implementations17 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 $\mathscr{L}_2(\mathbb{R})$.


Fenrir: Physics-Enhanced Regression for Initial Value Problems

1 code implementation2 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.

Numerical Integration regression

Pick-and-Mix Information Operators for Probabilistic ODE Solvers

2 code implementations20 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.

Bayesian Inference

A probabilistic Taylor expansion with Gaussian processes

no code implementations1 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.

Gaussian Processes regression

Calibrated Adaptive Probabilistic ODE Solvers

1 code implementation15 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.

Benchmarking Descriptive

Continuous-Discrete Filtering and Smoothing on Submanifolds of Euclidean Space

no code implementations17 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.

Bayesian ODE Solvers: The Maximum A Posteriori Estimate

no code implementations1 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.

Bayesian Inference

Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions

no code implementations29 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.

regression Uncertainty Quantification

Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective

1 code implementation8 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.

Gaussian process classification using posterior linearisation

no code implementations13 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).

Classification General Classification

Student-t Process Quadratures for Filtering of Non-Linear Systems with Heavy-Tailed Noise

no code implementations15 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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