Fast Gaussian Process Based Gradient Matching for Parameter Identification in Systems of Nonlinear ODEs
By Philippe Wenk, Alkis Gotovos, Stefan Bauer, Nico S. Gorbach, Andreas Krause, Joachim M. Buhmann. 2018
52 citations recorded by the source corpus.
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a dynamical system without explicitly solving it. While the benefits in computational cost are well established, a rigorous mathematical framework has been missing. We offer a novel interpretation which leads to a better understanding and improvements in state-of-the-art performance in terms of accuracy for nonlinear dynamical systems.
Subfields: Artificial Intelligence, Control and Systems Engineering
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Bernhard Schölkopf
- Stefan Bauer
- Jan Peters
- Niklas Pfister
- Yoshua Bengio
- Sergey Levine
- Andreas Krause
- Dominik Janzing
In Control and Systems Engineering
- Jan Peters
- Bernhard Schölkopf
- Niklas Pfister
- Andreas Krause
- Stefan Bauer
- Michael A. Osborne
- Gabriele Abbati
- Sergey Levine
Citations in the corpus
- Causal Models for Dynamical Systems (2020, methodology): “…of goodness-of-fit of the integrated system, nonlinear least squares methods or gradient matching [Bard, 1974, Benson, 1979, Calderhead et al., 2009, Varah, 1982, Ramsay et al., 2007, Macdonald and Husmeier, 2015, Dattner and Klaassen, 2015, Raue et al., 2015, Oates et al., 2014, Wenk et al., 2019].”
- AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs (2019, background): “As shown e.g. in the appendix of Wenk et al. (2018), the prior defined in equation (11) automatically induces a GP prior on the conditional derivatives of z .”