Bayesian Inference and Learning in Nonlinear Dynamical Systems: A Framework for Incorporating Explicit and Implicit Prior Knowledge
This provides a consistent tool for system identification that can incorporate explicit and implicit prior knowledge, addressing a bottleneck in fields like control or robotics, though it appears incremental as it builds on existing Bayesian methods.
The paper tackles the challenge of fusing diverse prior knowledge with data for learning nonlinear dynamical systems, particularly when functions are nested within known equations, by introducing a general-purpose Bayesian framework that enables both online and offline inference and learning without requiring user-tailored transformations.
Accuracy and generalization capabilities are key objectives when learning dynamical system models. To obtain such models from limited data, current works exploit prior knowledge and assumptions about the system. However, the fusion of diverse prior knowledge, e. g. partially known system equations and smoothness assumptions about unknown model parts, with information contained in the data remains a challenging problem, especially in input-output settings with latent system state. In particular, learning functions that are nested inside known system equations can be a laborious and error-prone expert task. This paper considers inference of latent states and learning of unknown model parts for fusion of data information with different sources of prior knowledge. The main contribution is a general-purpose system identification tool that, for the first time, provides a consistent solution for both, online and offline Bayesian inference and learning while allowing to incorporate explicit and implicit prior system knowledge. We propose a novel interface for combining known dynamics functions with a learning-based approximation of unknown system parts. Based on the proposed model structure, closed-form densities for efficient parameter marginalization are derived. No user-tailored coordinate transformations or model inversions are needed, making the presented framework a general-purpose tool for inference and learning. The broad applicability of the devised framework is illustrated in three distinct case studies, including an experimental data set.