Hybrid Temporal Differential Consistency Autoencoder for Efficient and Sustainable Anomaly Detection in Cyber-Physical Systems

Cyberattacks on critical infrastructure, particularly water distribution systems, have increased due to rapid digitalization and the integration of IoT devices and industrial control systems (ICS). These cyber-physical systems (CPS) introduce new vulnerabilities, requiring robust and automated intrusion detection systems (IDS) to mitigate potential threats. This study addresses key challenges in anomaly detection by leveraging time correlations in sensor data, integrating physical principles into machine learning models, and optimizing computational efficiency for edge applications. We build upon the concept of temporal differential consistency (TDC) loss to capture the dynamics of the system, ensuring meaningful relationships between dynamic states. Expanding on this foundation, we propose a hybrid autoencoder-based approach, referred to as hybrid TDC-AE, which extends TDC by incorporating both deterministic nodes and conventional statistical nodes. This hybrid structure enables the model to account for non-deterministic processes. Our approach achieves state-of-the-art classification performance while improving time to detect anomalies by 3%, outperforming the BATADAL challenge leader without requiring domain-specific knowledge, making it broadly applicable. Additionally, it maintains the computational efficiency of conventional autoencoders while reducing the number of fully connected layers, resulting in a more sustainable and efficient solution. The method demonstrates how leveraging physics-inspired consistency principles enhances anomaly detection and strengthens the resilience of cyber-physical systems.

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

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, extending 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 the C-MAPSS dataset, a benchmark for turbofan aeroengine degradation. TDC-AE outperforms LSTMs and Transformers while achieving a 200x 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, interpretable signal for anomaly detection.