no code implementations • 2 Aug 2022 • Emilia Magnani, Nicholas Krämer, Runa Eschenhagen, Lorenzo Rosasco, Philipp Hennig
Neural operators are a type of deep architecture that learns to solve (i. e. learns the nonlinear solution operator of) partial differential equations (PDEs).
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 • NeurIPS 2021 • 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.
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 • 22 Oct 2021 • Nicholas Krämer, Jonathan Schmidt, Philipp Hennig
Thereby, we extend the toolbox of probabilistic programs for differential equation simulation to PDEs.
no code implementations • 14 Jun 2021 • 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.
1 code implementation • NeurIPS 2021 • Jonathan Schmidt, Nicholas Krämer, Philipp Hennig
Mechanistic models with differential equations are a key component of scientific applications of machine learning.
no code implementations • 18 Dec 2020 • Nicholas Krämer, Philipp Hennig
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems.
no code implementations • ICML 2020 • Hans Kersting, Nicholas Krämer, Martin Schiegg, Christian Daniel, Michael Tiemann, Philipp Hennig
To address this shortcoming, we employ Gaussian ODE filtering (a probabilistic numerical method for ODEs) to construct a local Gaussian approximation to the likelihood.