214 citations · 1.8k across the 88 of their papers we have counts for
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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…
Linear-Time Probabilistic Solutions of Boundary Value Problems
Nicholas Krämer, Philipp Hennig
We propose a fast algorithm for the probabilistic solution of boundary value problems (BVPs), which are ordinary differential equations subject to boundary conditions. In contrast…
A Probabilistic State Space Model for Joint Inference from Differential Equations and Data
Jonathan Schmidt, Nicholas Krämer, Philipp Hennig
Mechanistic models with differential equations are a key component of scientific applications of machine learning. Inference in such models is usually computationally demanding, be…