Benchmarking solution methods for parameter identification in dynamical systems

Abstract

AbstractAccurate models are crucial for simulating, optimizing, and controlling real‐world processes. Parameter identification—the task of estimating the unknown parameters of a dynamical system based on measurements—is challenging and there exist various methods to approach it. Integration‐based methods, such as shooting methods and full discretization, approximate the model output by numerically solving the dynamical system. Gradient matching methods, on the other hand, avoid solving the dynamical system and focus on minimizing the error between the measurement slope and the state derivatives instead. All approaches have advantages and disadvantages and a recipe for which method is best in a particular situation does not exist. In this paper, we present the results of a benchmark comparing single shooting, multiple shooting, full discretization, and gradient matching using a comprehensive database of test problems. We investigate if there is a notable difference in the performance of the various methods and if one approach is superior to the others. From the benchmark, we conclude that the integration‐based methods outperform gradient matching. While full discretization exhibits robustness, single and multiple shooting provide higher precision. Additionally, we observe that finding an optimal configuration of the methods across a diverse set of parameter identification problems remains challenging and often requires fine‐tuning.