ODIN: ODE-Informed Regression for Parameter and State Inference in Time-Continuous Dynamical Systems
This addresses the problem of efficient and accurate inference in dynamical systems for applied sciences and engineering, with incremental improvements in computational efficiency.
The paper tackles parameter and state inference in time-continuous dynamical systems, particularly in data-scarce settings, by introducing a generative modeling approach based on constrained Gaussian processes, resulting in outperforming state-of-the-art methods in accuracy and computational cost in experiments.
Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on constrained Gaussian processes and leverage it to build a computationally and data efficient algorithm for state and parameter inference. In an extensive set of experiments, our approach outperforms the current state of the art for parameter inference both in terms of accuracy and computational cost. It also shows promising results for the much more challenging problem of model selection.