Digital Twin-based Anomaly Detection with Curriculum Learning in Cyber-physical Systems
Open accessAbstract
Anomaly detection is critical to ensure the security of cyber-physical systems (CPS) . However, due to the increasing complexity of attacks and CPS themselves, anomaly detection in CPS is becoming more and more challenging. In our previous work, we proposed a digital twin-based anomaly detection method, called ATTAIN, which takes advantage of both historical and real-time data of CPS. However, such data vary significantly in terms of difficulty. Therefore, similar to human learning processes, deep learning models (e.g., ATTAIN) can benefit from an easy-to-difficult curriculum. To this end, in this paper, we present a novel approach, named digitaL twin-based Anomaly deTecTion wIth Curriculum lEarning ( LATTICE ) , which extends ATTAIN by introducing curriculum learning to optimize its learning paradigm. LATTICE attributes each sample with a difficulty score, before being fed into a training scheduler. The training scheduler samples batches of training data based on these difficulty scores such that learning from easy to difficult data can be performed. To evaluate LATTICE, we use five publicly available datasets collected from five real-world CPS testbeds. We compare LATTICE with ATTAIN and two other state-of-the-art anomaly detectors. Evaluation results show that LATTICE outperforms the three baselines and ATTAIN by 0.906%-2.367% in terms of the F1 score. LATTICE also, on average, reduces the training time of ATTAIN by 4.2% on the five datasets and is on par with the baselines in terms of detection delay time.
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Training data for ML-based attack detection typically includes process variables, network traffic features, and historical failure/attack traces from benchmark datasets such as SWaT, WADI, or CICIDS.
“The training data typically includes a mix of process variables (e.g., pressure, temperature, vibration), network traffic features (packet size, frequency, latency), and historical failure/attack traces from benchmark datasets such as SWaT, WADI, or CICIDS [29, 32].”
From Towards enhanced cybersecurity in industrial control systems: a systematic review of context-based modeling, digital twins, and machine learning approaches (2025) · cites this paper as [32]
Digital twins have been employed to simulate cyber-attacks by reproducing both normal and abnormal system behaviors.
“In the literature, digital twins have also been employed to simulate cyber-attacks by reproducing both normal and abnormal system behaviors [28, 32].”
From Towards enhanced cybersecurity in industrial control systems: a systematic review of context-based modeling, digital twins, and machine learning approaches (2025) · cites this paper as [32]
Historical data was also used in the articles examined.
“Historical data was also used in the articles examined[28, 32, 33].”
From Towards enhanced cybersecurity in industrial control systems: a systematic review of context-based modeling, digital twins, and machine learning approaches (2025) · cites this paper as [32]
Cites
Bengio, Y., Louradour, J., Collobert, R., & Weston, J. (2009) · Proceedings of the 26th Annual International Conference on Machine Learning · doi:10.1145/1553374.1553380 · Cited by 5,366 · cited 8× · see citing works
“This work later inspires many researchers to explore CL for various tasks such as grammar learning [30, 30, 45] and language learning [6].”
BackgroundInfluentialBattle of the Attack Detection Algorithms: Disclosing Cyber Attacks on Water Distribution Networks
Taormina, R., Galelli, S., Tippenhauer, N. O., Salomons, E., Ostfeld, A., Eliades, D. G., Aghashahi, M., Sundararajan, R., Pourahmadi, M., Banks, M. K., et al. (2018) · Journal of Water Resources Planning and Management · doi:10.1061/(asce)wr.1943-5452.0000969 · Cited by 277 · cited 2× · see citing works
“We evaluate LATTICE with five CPS datasets, namely Secure Water Treatment (SWaT) [39], Water Distribution (WADI) [1], Battle Of The Attack Detection Algorithms (BATADAL) [52], PHM challenge 2015 dataset [25], and Gas Pipeline Dataset [40].”
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KDDT: Knowledge Distillation-Empowered Digital Twin for Anomaly Detection
Xu, Q., Ali, S., Yue, T., Nedim, Z., & Singh, I. (2023) · Proceedings of the 31st ACM Joint European Software Engineering Conference and Symposium on the Foundations of Software Engineering · doi:10.1145/3611643.3613879 · Cited by 11 · see citing works
Self-citationAbraham, D., Erceylan, G., Gkioulos, V., & Houmb, S. H. (2025) · International Journal of Information Security · doi:10.1007/s10207-025-01158-1 · Cited by 10 · see citing works
- Authors
- Xu, Q., Ali, S., & Yue, T.
- Affiliations
- University of Oslo (NO)
- Simula Research Laboratory (NO)
- Venue
- ACM Transactions on Software Engineering and Methodology
- Published
- 2023-07-22
- Volume
- 32
- Issue
- 5
- Pages
- 1-32
- ISSN
- 1049-331X (ISSN-L)
- 1557-7392
- OpenAlex
- W4319037055
- Cited by
- 49
- References
- 2
- Citations by year
- 2026: 10 · 2025: 21 · 2024: 13 · 2023: 5
- FWCI
- 5.45
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- ACM Transactions on Software Engineering and Methodology (publishedVersion)
- arXiv (Cornell University) (submittedVersion, cc-by)
- arXiv (Cornell University) (cc-by)
- Funders
- Research Council of Norway (270053)
- Norwegian Ministry of Education and Research
- European Commission (871319)
- Topics
- Physical Sciences › Computer Science › Computer Networks and Communications › Network Security and Intrusion Detection
- Physical Sciences › Computer Science › Artificial Intelligence › Anomaly Detection Techniques and Applications
- Physical Sciences › Computer Science › Computer Networks and Communications › Software System Performance and Reliability
- Keywords
- anomaly detection, cyber-physical systems, digital twin, curriculum learning, lattices, cyber-physical security, attack detection, training time reduction
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