@inproceedings{
hamelijnck2024physicsinformed,
title={Physics-Informed Variational State-Space Gaussian Processes},
author={Oliver Hamelijnck and Arno Solin and Theodoros Damoulas},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=tCf7S75xFa}
}
Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models. Gaussian processes (GPs) are particularly suited to this task as they can model complex, non-linear phenomena whilst incorporating prior knowledge and quantifying uncertainty. Current approaches have found some success but are limited as they either achieve poor computational scalings or focus only on the temporal setting. This work addresses these issues by introducing a variational spatio-temporal state-space GP that handles linear and non-linear physical constraints while achieving efficient linear-in-time computation costs. We demonstrate our methods in a range of synthetic and real-world settings and outperform the current state-of-the-art in both predictive and computational performance.
Physics-Informed Variational State-Space Gaussian Processes
Oliver Hamelijnck Arno Solin Theodoros Damoulas