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Item type:Publication, Access status: without files , Learnability of models for cyber-physical systems — a reviewThe complexity of Cyber-Physical Systems (CPS) emerges from a tight integration of numerous digital and physical components. Recent powerful machine learning algorithms are increasingly applied to learn models of CPS from data. However, theoretical limitations of such a pragmatic approach are often left aside. In this paper, we review the learnability of such data-driven models for CPS. Learnability is a key aspect in all parts of the model learning process which seeks for guarantees and preconditions for formal properties of a learned model such as accuracy, robustness, and interpretability. We review the state-of-the-art in model learning for CPS that focuses on these learnability aspects. We arrange and discuss this state-of-the-art alongside the steps of the model learning process, being (1) data quality assurance, (2) model learning, (3) model evaluation, and (4) model refinement. Additionally, we analyze the involvement of prior knowledge and its influence on model learnability. Finally, we discuss the implications of our findings for the development of models for CPS and identify directions for future research, e.g., incorporating prior knowledge more deeply into the model learning process.Publicationtype: Book Part14 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Identification of hybrid systems with dynamics-based modeling through symbolic regression(Elsevier, 2026-01); ; ; ; Hybrid systems combine both continuous and discrete behavior. These systems serve as models in many fields, including control systems, robotics, and industrial processes. However, due to their complexity, finding an accurate model is a challenge. This paper presents a holistic approach to learning models of hybrid systems using symbolic regression. Our method leverages symbolic regression to automatically discover accurate and interpretable mathematical models in the form of hybrid systems from observed data. An advantage of our algorithm is that it detects transitions between different behavioral modes of a system based on the inherent dynamics. From learned expressions for the dynamical behavior of a system, we form a hybrid system by combining the learned expressions with a decision tree determining the current behavioral mode from data. This hybrid decision tree serves regression, prediction, and further related tasks. Our results demonstrate that symbolic regression can effectively identify the underlying dynamics of a real hybrid system and predict output signals on new input data with high accuracy.Publicationtype: Journal Article14 41 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , One-shot learning in hybrid system identification: a new modular paradigm(2025-10-11); ; ; Identification of hybrid systems requires learning models that capture both discrete transitions and continuous dynamics from observational data. Traditional approaches follow a stepwise process, separating trace segmentation and mode-specific regression, which often leads to inconsistencies due to unmodeled interdependencies. In this paper, we propose a new iterative learning paradigm that jointly optimizes segmentation and flow function identification. The method incrementally constructs a hybrid model by evaluating and expanding candidate flow functions over observed traces, introducing new modes only when existing ones fail to explain the data. The approach is modular and agnostic to the choice of the regression technique, allowing the identification of hybrid systems with varying levels of complexity. Empirical results on benchmark examples demonstrate that the proposed method produces more compact models compared to traditional techniques, while supporting flexible integration of different regression methods. By favoring fewer, more generalizable modes, the resulting models are not only likely to reduce complexity but also simplify diagnostic reasoning, improve fault isolation, and enhance robustness by avoiding overfitting to spurious mode changes.Publicationtype: Conference Paper33 11 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Dynamics-based identification of hybrid systems using symbolic regression(IEEE, 2024-08); ; ; ; Travé-Massuyès, LouiseSymbolic regression has shown potential in the identification of physical systems. Hybrid systems, which combine both continuous and discrete behavior, are a relevant extension of purely physical systems, used in many fields, including robotics, biological systems, and control systems. However, due to their complexity, finding an accurate model is a challenge. This paper presents a novel approach to learning models of hybrid systems using symbolic regression. Our method leverages the power of genetic programming to automatically discover accurate and interpretable mathematical models in the form of hybrid systems from observed data. Symbolic regression detects transitions between different continuous behavior of a system directly based on the dynamics, instead of pure distances of observed trajectories. Furthermore, models generated by symbolic regression can be used to predict future system behavior, detect anomalies, and identify the underlying dynamics of the system while providing a human-readable representation. Our results demonstrate that symbolic regression can effectively identify the underlying dynamics of a real system represented in a hybrid model, providing a valuable tool for system identification and diagnosis.Publicationtype: Conference Paper21