Search Results for author: Nathanael Bosch

Found 9 papers, 8 papers with code

Diffusion Tempering Improves Parameter Estimation with Probabilistic Integrators for Ordinary Differential Equations

1 code implementation19 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.

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.

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

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

Probabilistic ODE Solutions in Millions of Dimensions

no code implementations22 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.

Uncertainty Quantification

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

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

Planning from Images with Deep Latent Gaussian Process Dynamics

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.

Gaussian Processes Transfer Learning

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