The 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.

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Learnability of Models for Cyber-Physical Systems — A Review

  • Maximilian Schmidt,
  • Swantje Plambeck,
  • Goerschwin Fey

摘要

The 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.