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Anomaly Detection in Complex Dynamical Systems: A Systematic Framework Using Embedding Theory and Physics-Inspired Consistency

Created by
  • Haebom

Author

Michael Somma, Thomas Gallien, Branka Stojanovic

Outline

This paper presents a systems-theoretic approach for anomaly detection in complex dynamic systems. Based on the Fractal Whitney Embedding Prevalence Theorem, which extends existing embedding techniques to complex system dynamics, we introduce state-derivative pairs as an embedding strategy to capture system evolution. To enhance temporal consistency, we develop a Temporal Differential Consistency Autoencoder (TDC-AE) that integrates TDC-Loss, which aligns approximated derivatives of latent variables with dynamic representations. Experimental results using the C-MAPSS turbofan engine dataset demonstrate that TDC-AE performs on par with LSTM and outperforms Transformer while reducing the number of MAC operations by approximately 100x, making it suitable for lightweight edge computing. Our results support the hypothesis that anomalies disrupt stable system dynamics.

Takeaways, Limitations

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Takeaways:
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An efficient and robust systems-theoretic approach for anomaly detection in complex dynamical systems is presented.
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Development of a TDC-AE model suitable for lightweight edge computing environments.
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Achieves superior performance and lower computational load compared to LSTM and Transformer.
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Suggesting the possibility of utilizing the breakdown of stable system dynamics as a key signal for anomaly detection.
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Limitations:
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Evaluation was conducted only on two subsets of the C-MAPSS dataset (FD001 and FD003). Generalization performance on a wider range of datasets and systems is needed.
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Lack of detailed description of parameter optimization of TDC-Loss.
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Further research is needed on applicability and scalability in real industrial environments.
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