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

arXiv: https://arxiv.org/abs/2504.06320 · HTML: https://mlsanity.com/paper/2504.06320/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 32 references that are in the map.
- First posted on arXiv 8 Apr 2025.

## Builds on (most cited first, 5 of 5)

- [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)
- [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)
- [Anomaly Detection in Complex Dynamical Systems: A Systematic Framework Using Embedding Theory and Physics-Inspired Consistency](https://mlsanity.com/paper/2502.19307/) (2025)

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

- [LiDAR-BIND-T: Improved and Temporally Consistent Sensor Modality Translation and Fusion for Robotic Applications](https://mlsanity.com/paper/2509.05728/) (2025)

## Abstract (arXiv)

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.