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

arXiv: https://arxiv.org/abs/2502.19307 · HTML: https://mlsanity.com/paper/2502.19307/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 35 references that are in the map.
- First posted on arXiv 26 Feb 2025.

## Builds on (most cited first, 6 of 6)

- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Numerical differentiation of noisy data: A unifying multi-objective optimization framework](https://mlsanity.com/paper/2009.01911/) (2020)
- [LSTM-Autoencoder based Anomaly Detection for Indoor Air Quality Time Series Data](https://mlsanity.com/paper/2204.06701/) (2022)
- [Recurrent Neural Networks: An Embedded Computing Perspective](https://mlsanity.com/paper/1908.07062/) (2019)

## Built on by (most cited first, 1 of 1)

- [Hybrid Temporal Differential Consistency Autoencoder for Efficient and Sustainable Anomaly Detection in Cyber-Physical Systems](https://mlsanity.com/paper/2504.06320/) (2025)

## Abstract (arXiv)

Anomaly detection in complex dynamical systems is essential for ensuring reliability, safety, and efficiency in industrial and cyber-physical infrastructures. Predictive maintenance helps prevent costly failures, while cybersecurity monitoring has become critical as digitized systems face growing threats. Many of these systems exhibit oscillatory behaviors and bounded motion, requiring anomaly detection methods that capture structured temporal dependencies while adhering to physical consistency principles. In this work, we propose a system-theoretic approach to anomaly detection, grounded in classical embedding theory and physics-inspired consistency principles. We build upon the Fractal Whitney Embedding Prevalence Theorem that extends traditional embedding techniques to complex system dynamics. Additionally, we introduce state-derivative pairs as an embedding strategy to capture system evolution. To enforce temporal coherence, we develop a Temporal Differential Consistency Autoencoder (TDC-AE), incorporating a TDC-Loss that aligns the approximated derivatives of latent variables with their dynamic representations. We evaluate our method on two subsets (FD001, FD003) of the C-MAPSS dataset, a benchmark for turbofan engine degradation. TDC-AE machtes LSTMs and outperforms Transformers while achieving a nearly 100x reduction in MAC operations, making it particularly suited for lightweight edge computing. Our findings support the hypothesis that anomalies disrupt stable system dynamics, providing a robust signal for anomaly detection.