24 citations · 54 across the 17 of their papers we have counts for
19 papers
Propagating Model Uncertainty through Filtering-based Probabilistic Numerical ODE Solvers
Dingling Yao, Filip Tronarp, Nathanael Bosch
Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs), also known as ODE filters, have been established as efficient methods for quantifying nu…
Probabilistic ODE Solvers for Integration Error-Aware Numerical Optimal Control
Amon Lahr, Filip Tronarp, Nathanael Bosch +3
Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if the discretization error…
Parallel-in-Time Probabilistic Numerical ODE Solvers
Nathanael Bosch, Adrien Corenflos, Fatemeh Yaghoobi +3
Probabilistic numerical solvers for ordinary differential equations (ODEs) treat the numerical simulation of dynamical systems as problems of Bayesian state estimation. Aside from…
The Rank-Reduced Kalman Filter: Approximate Dynamical-Low-Rank Filtering In High Dimensions
Jonathan Schmidt, Philipp Hennig, Jörg Nick +1
Inference and simulation in the context of high-dimensional dynamical systems remain computationally challenging problems. Some form of dimensionality reduction is required to make…
Probabilistic Exponential Integrators
Nathanael Bosch, Philipp Hennig, Filip Tronarp
Probabilistic solvers provide a flexible and efficient framework for simulation, uncertainty quantification, and inference in dynamical systems. However, like standard solvers, the…
Orthonormal Expansions for Translation-Invariant Kernels
Filip Tronarp, Toni Karvonen
We present a general Fourier analytic technique for constructing orthonormal basis expansions of translation-invariant kernels from orthonormal bases of …
Fenrir: Physics-Enhanced Regression for Initial Value Problems
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. Consequen…
Pick-and-Mix Information Operators for Probabilistic ODE Solvers
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. In this pa…
A probabilistic Taylor expansion with Gaussian processes
Toni Karvonen, Jon Cockayne, Filip Tronarp +1
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 consist of deri…
Calibrated Adaptive Probabilistic ODE Solvers
Nathanael Bosch, Philipp Hennig, Filip Tronarp
Probabilistic solvers for ordinary differential equations assign a posterior measure to the solution of an initial value problem. The joint covariance of this distribution provides…
Variable Splitting Methods for Constrained State Estimation in Partially Observed Markov Processes
Rui Gao, Filip Tronarp, Simo Särkkä
In this paper, we propose a class of efficient, accurate, and general methods for solving state-estimation problems with equality and inequality constraints. The methods are based…
Continuous-Discrete Filtering and Smoothing on Submanifolds of Euclidean Space
Filip Tronarp, Simo Särkkä
In this paper the issue of filtering and smoothing in continuous discrete time is studied when the state variable evolves in some submanifold of Euclidean space, which may not have…
Bayesian ODE Solvers: The Maximum A Posteriori Estimate
Filip Tronarp, Simo Sarkka, Philipp Hennig
It has recently been established that the numerical solution of ordinary differential equations can be posed as a nonlinear Bayesian inference problem, which can be approximately s…
Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions
Toni Karvonen, George Wynne, Filip Tronarp +2
Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically ne…
Iterated Extended Kalman Smoother-based Variable Splitting for -Regularized State Estimation
Rui Gao, Filip Tronarp, Simo Särkkä
In this paper, we propose a new framework for solving state estimation problems with an additional sparsity-promoting -regularizer term. We first formulate such problems as mi…
Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective
Filip Tronarp, Hans Kersting, Simo Särkkä +1
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measureme…
Gaussian process classification using posterior linearisation
Ángel F. García-Fernández, Filip Tronarp, Simo Särkkä
This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained…
Iterative Statistical Linear Regression for Gaussian Smoothing in Continuous-Time Non-linear Stochastic Dynamic Systems
Filip Tronarp, Simo Särkkä
This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stocha…
Student-t Process Quadratures for Filtering of Non-Linear Systems with Heavy-Tailed Noise
Jakub Prüher, Filip Tronarp, Toni Karvonen +2
The aim of this article is to design a moment transformation for Student- t distributed random variables, which is able to account for the error in the numerically computed mean. W…