Discovering Model Structure of Dynamical Systems with Combinatorial Bayesian Optimization

Lucas Rath, Alexander von Rohr, Andreas Schultze, Sebastian Trimpe, Burkhard Corves

Abstract: Deciding on a model structure is a fundamental problem in machine learning. In this paper we consider the problem of building a data-based model for dynamical systems from a library of discrete components. In addition to optimizing performance, we consider crash and inequality constraints that arise from additional requirements, such as real-time capability and model complexity. We address this task of model structure selection with a focus on dynamical systems and propose to search over potential model structures efficiently using a constrained combinatorial Bayesian Optimization (BO) algorithm. We propose expressive surrogate models suited for combinatorial domains and an acquisition function that can handle inequality and crash constraints. We provide simulated benchmark problems within the domain of equation discovery of nonlinear dynamical systems. Our method outperforms the state-of-the-art in constrained combinatorial optimization of black-box functions and has a favorable computational overhead compared to other BO methods. As a real-world application example, we apply our method to optimize the configuration of an electric vehicle's digital twin while ensuring its real-time capability for the use in one of the world's largest driving simulators.

Submission Length: Long submission (more than 12 pages of main content)

Changes Since Last Submission: Minor formatting changes.

Code: https://github.com/lucasrm25/Model-Structure-Selection-CBOSS

Assigned Action Editor: ~Roman_Garnett1

License: Creative Commons Attribution 4.0 International (CC BY 4.0)

Submission Number: 1777