Learning ODE Models with Qualitative Structure Using Gaussian Processes
This work addresses data efficiency in modeling dynamical systems for scientific and engineering applications, offering an incremental improvement by integrating prior domain knowledge.
The authors tackled the problem of learning dynamical systems from limited data by incorporating qualitative structural information, such as Lie Group symmetries and fixed points, into sparse Gaussian Process models, resulting in significant improvements in extrapolation performance and long-term behavior while reducing computational costs.
Recent advances in learning techniques have enabled the modelling of dynamical systems for scientific and engineering applications directly from data. However, in many contexts explicit data collection is expensive and learning algorithms must be data-efficient to be feasible. This suggests using additional qualitative information about the system, which is often available from prior experiments or domain knowledge. We propose an approach to learning a vector field of differential equations using sparse Gaussian Processes that allows us to combine data and additional structural information, like Lie Group symmetries and fixed points. We show that this combination improves extrapolation performance and long-term behaviour significantly, while also reducing the computational cost.