1 code implementation • 19 Feb 2024 • Jonas Beck, Nathanael Bosch, Michael Deistler, Kyra L. Kadhim, Jakob H. Macke, Philipp Hennig, Philipp Berens
Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging.
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.
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.
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.
1 code implementation • 3 Dec 2021 • Jonathan Wenger, Nicholas Krämer, Marvin Pförtner, Jonathan Schmidt, Nathanael Bosch, Nina Effenberger, Johannes Zenn, Alexandra Gessner, Toni Karvonen, François-Xavier Briol, Maren Mahsereci, Philipp Hennig
Probabilistic numerical methods (PNMs) solve numerical problems via probabilistic inference.
no code implementations • 22 Oct 2021 • Nicholas Krämer, Nathanael Bosch, Jonathan Schmidt, Philipp Hennig
Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems.
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.
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.
1 code implementation • L4DC 2020 • Nathanael Bosch, Jan Achterhold, Laura Leal-Taixé, Jörg Stückler
We propose to learn a deep latent Gaussian process dynamics (DLGPD) model that learns low-dimensional system dynamics from environment interactions with visual observations.