5 citations · 12 across the 15 of their papers we have counts for
16 papers
Euclidean Fourier Neural Operators
Nathanael Bosch, Niklas Frederik Schmitz, Michael F. Herbst
Fourier neural operators (FNOs) provide an efficient framework for learning mappings between function spaces as they are, by construction, independent of the grid resolution at whi…
Stable and Scalable Probabilistic Numerical Solvers for Stiff and High-Dimensional ODEs
Nathanael Bosch
Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs) have been established as a flexible and efficient simulation framework with built-in nume…
Multi-layer Stack Ensembles for Time Series Forecasting
Nathanael Bosch, Oleksandr Shchur, Nick Erickson +2
Ensembling is a powerful technique for improving the accuracy of machine learning models, with methods like stacking achieving strong results in tabular tasks. In time series forec…
AlgoTune: Can Language Models Speed Up General-Purpose Numerical Programs?
Ori Press, Brandon Amos, Haoyu Zhao +21
Despite progress in language model (LM) capabilities, evaluations have thus far focused on models' performance on tasks that humans have previously solved, including in programming…
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…
Low-Rank Filtering and Smoothing for Sequential Deep Learning
Joanna Sliwa, Frank Schneider, Nathanael Bosch +2
Learning multiple tasks sequentially requires neural networks to balance retaining knowledge, yet being flexible enough to adapt to new tasks. Regularizing network parameters is a…
Diffusion Tempering Improves Parameter Estimation with Probabilistic Integrators for Ordinary Differential Equations
Jonas Beck, Nathanael Bosch, Michael Deistler +4
Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. I…
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…
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…
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…
ProbNum: Probabilistic Numerics in Python
Jonathan Wenger, Nicholas Krämer, Marvin Pförtner +9
Probabilistic numerical methods (PNMs) solve numerical problems via probabilistic inference. They have been developed for linear algebra, optimization, integration and differential…
Probabilistic ODE Solutions in Millions of Dimensions
Nicholas Krämer, Nathanael Bosch, Jonathan Schmidt +1
Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this w…
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…
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…
Planning from Images with Deep Latent Gaussian Process Dynamics
Nathanael Bosch, Jan Achterhold, Laura Leal-Taixé +1
Planning is a powerful approach to control problems with known environment dynamics. In unknown environments the agent needs to learn a model of the system dynamics to make plannin…