Physics-Informed Variational State-Space Gaussian Processes
This addresses computational bottlenecks for researchers and practitioners using physics-informed Gaussian processes in scientific and engineering applications, representing a strong incremental improvement.
The authors tackled the problem of inefficient computational scaling and limited applicability of physics-informed Gaussian process models by introducing a variational spatio-temporal state-space GP that handles physical constraints while achieving linear-in-time computation costs. They demonstrated superior predictive and computational performance compared to state-of-the-art methods in synthetic and real-world settings.
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.