no code implementations • 22 May 2023 • Katharina Ott, Michael Tiemann, Philipp Hennig, François-Xavier Briol
Bayesian probabilistic numerical methods for numerical integration offer significant advantages over their non-Bayesian counterparts: they can encode prior information about the integrand, and can quantify uncertainty over estimates of an integral.
no code implementations • 22 May 2023 • Katharina Ott, Michael Tiemann, Philipp Hennig
As a first contribution, we show that basic and lightweight Bayesian deep learning techniques like the Laplace approximation can be applied to neural ODEs to yield structured and meaningful uncertainty quantification.
no code implementations • 27 Feb 2023 • Katharina Ensinger, Sebastian Ziesche, Barbara Rakitsch, Michael Tiemann, Sebastian Trimpe
This filtering technique combines two signals by applying a high-pass filter to one signal, and low-pass filtering the other.
no code implementations • 2 Feb 2021 • Katharina Ensinger, Friedrich Solowjow, Sebastian Ziesche, Michael Tiemann, Sebastian Trimpe
On the other hand, classical numerical integrators are specifically designed to preserve these crucial properties through time.
no code implementations • ICLR 2021 • Katharina Ott, Prateek Katiyar, Philipp Hennig, Michael Tiemann
If the trained model is supposed to be a flow generated from an ODE, it should be possible to choose another numerical solver with equal or smaller numerical error without loss of performance.
no code implementations • 30 Jul 2020 • Katharina Ott, Prateek Katiyar, Philipp Hennig, Michael Tiemann
If the trained model is supposed to be a flow generated from an ODE, it should be possible to choose another numerical solver with equal or smaller numerical error without loss of performance.
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.