Cyber-Resilient Digital Twins: Discriminating Attacks for Safe Critical Infrastructure Control
Authors: Mohammadhossein Homaei, Iman Khazrak, Rubén Molano, Andrés Caro, Mar Ávila
Organizations: Departamento de Ingeniería de Sistemas Informáticos y Telemáticos, Universidad de Extremadura, Av. Universidad S/N, Escuela Politécnica, Cáceres, 10003, Extremadura, Spain · Department of Computer Science, Bowling Green State University, Bowling Green, 43403, OH, USA
Industrial Cyber-Physical Systems (ICPS) face growing threats from cyber-attacks that exploit sensor and control vulnerabilities. Digital Twin (DT) technology can detect anomalies via predictive modelling, but current methods cannot distinguish attack types and often rely on costly full-system shutdowns. This paper presents i-SDT (intelligent Self-Defending DT), combining hydraulically-regularized predictive modelling, multi-class attack discrimination, and adaptive resilient control. Temporal Convolutional Networks (TCNs) with differentiable conservation constraints capture nominal dynamics and improve robustness to adversarial manipulations. A recurrent residual encoder with Maximum Mean Discrepancy (MMD) separates normal operation from single- and multi-stage attacks in latent space. When attacks are confirmed, Model Predictive Control (MPC) uses uncertainty-aware DT predictions to keep operations safe without shutdown. Evaluation on SWaT and WADI datasets shows major gains in detection accuracy, 44.1% fewer false alarms, and 56.3% lower operational costs in simulation-in-the-loop evaluation. with sub-second inference latency confirming real-time feasibility on plant-level workstations, i-SDT advances autonomous cyber-physical defense while maintaining operational resilience.
Figures & tables
Approach
Physics Informed
Attack Taxonomy
Uncertainty Aware
Resilient Control
TranAD (2022) ( Tuli et al., 2022 )
✗
✗
✗
✗
LGAT (2025) ( Wen et al., 2025 )
✗
✗
✗
✗
CDT (2026) ( Homaei et al., 2026 )
✓
✗
✗
✗
DT-MPC (2025) ( Zhang et al., 2025 )
✗
✗
✗
✓
Secure RMPC (2025) ( Xie et al., 2025 )
✗
✗
✗
✓
i-SDT (Proposed)
✓ †
✓
✓
✓
Table 1: Comparison of i-SDT with State-of-the-Art Approaches
Table 3: Multi-class attack detection on SWaT (36 scenarios). All baselines evaluated via Linear Probing on frozen latent representations; this protocol structurally favours i-SDT whose encoder is natively regularised for taxonomy separation via MMD, and the reported gains should be interpreted accordingly. Bold = best, † = significant ( p<0.05 , paired bootstrap, 104 resamples). Evaluated on NVIDIA RTX 4070 (12 GB).
Method
Normal ( N )
Single-Stage ( AS )
Multi-Stage ( AM )
Overall
MTTD (s)
Prec.
Rec.
F1
Prec.
Rec.
F1
Prec.
Rec.
F1
FAR
F1A
OmniAnomaly ( Su et al., 2019 )
0.881
0.928
0.904
0.717
0.669
0.692
0.694
0.631
0.661
0.119
0.677
112.7
USAD ( Audibert et al., 2020 )
0.897
0.939
0.918
0.749
0.703
0.725
0.718
0.662
0.689
0.098
0.707
95.3
MTAD-GAT ( Zhao et al., 2020 )
0.916
0.954
0.935
0.803
0.774
0.788
0.771
0.738
0.754
0.081
0.771
81.6
TranAD ( Tuli et al., 2022 )
0.924
0.958
0.941
0.814
0.786
0.800
0.783
0.749
0.766
0.074
0.783
76.9
i-SDT ( γ=0.80 , Proposed)
0.958 †
0.976 †
0.967 †
0.887 †
0.864 †
0.875 †
0.871 †
0.842 †
0.856 †
0.042 †
0.866 †
51.4 †
Table 4: Multi-class attack detection on WADI (15 scenarios). Same Linear Probing evaluation protocol as Table 3 ; the same structural caveat applies. Results for γ=0.80 . Bold = best, † = significant ( p<0.05 ). Evaluated on NVIDIA RTX 4070 (12 GB).
Method
SWaT
WADI
MMD 2
Sil. Coeff.
MMD 2
Sil. Coeff.
OmniAnomaly ( Su et al., 2019 )
0.038
0.297
0.034
0.274
USAD ( Audibert et al., 2020 )
0.051
0.348
0.046
0.321
MTAD-GAT ( Zhao et al., 2020 )
0.069
0.433
0.063
0.411
TranAD ( Tuli et al., 2022 )
0.078
0.468
0.071
0.439
i-SDT (Proposed)
0.142 †
0.673 †
0.131 †
0.641 †
Table 5: ADE embedding separation of single- vs. multi-stage attacks (higher MMD = better).
Mitigation Strategy
SWaT (36 Attacks)
WADI (15 Attacks)
Drel
Safety Viol.
Trecovery (s)
Act. Sat.
Drel
Safety Viol.
Trecovery (s)
Act. Sat.
Immediate Shutdown
1.000
0%
3847
0%
1.000
0%
4231
0%
DT-MPC ( Zhang et al., 2025 )
0.614
6.9%
378
9.8%
0.639
8.1%
401
11.3%
i-SDT w/o Robust Margin
0.563
8.3%
412
12.5%
0.591
9.7%
438
14.2%
i-SDT (Full Robust MPC)
0.437 †
2.1% †
267 †
3.8% †
0.461 †
2.9% †
284 †
4.6% †
Target Objective
≤0.50
≤5%
<300
–
≤0.50
≤5%
<300
–
Table 6: Disruption mitigation and resilience (simulation-in-the-loop evaluation; see Section 3.1 ). Drel : normalized cost; Trecovery : recovery time.
Metric
Value
Notes
Training (Offline):
DT training time
2.8 hrs
SWaT, E=200 , early-stop
ADE training time
1.4 hrs
SWaT, E=150 , early-stop
Fine-tuning (10%)
0.5 hrs
New-plant adaptation
Inference (Online, per 1 Hz cycle):
DT inference (TCN + NMC=50 )
16.1 ms
50 stochastic fwd. passes
Table 7: Computational Performance on Evaluation Platform (Intel Core i9-14900K, NVIDIA RTX 4070 12 GB, 64 GB RAM, PyTorch 2.0, CUDA 11.8). All inference timings averaged over 103 consecutive cycles on the SWaT test set ( d=51 ). Edge deployment is reserved as future work (Section 6 ).
Table 9: Performance under random sensor dropout. p : fraction of sensors unavailable per step.
Configuration
F1A
FAR
No Transfer (Train on WADI)
0.866
0.042
Direct Transfer (Zero-shot)
0.647
0.183
Fine-tune 10% WADI Normal
0.782
0.089
Fine-tune 50% WADI Normal
0.831
0.061
Gap (10% Fine-tune)
-9.7%
+111.9%
Table 10: Cross-Domain Transfer (SWaT → WADI). Note: 9.7% gap indicates domain-specific tuning remains necessary despite physics priors; transfer learning reduces labeling burden by 90% but cannot eliminate it entirely.
Configuration
F1A
FAR
Drel
Safety Viol.
MTTD (s)
Notes
i-SDT (Full)
0.894
0.033
0.437
2.1%
43.7
Baseline
Physics Weight Ablation:
α0=0 (no mass balance)
0.853
0.067
0.512
3.8%
62.3
−4.6%
λp=0 (no pipe physics)
0.864
0.058
0.491
3.2%
58.1
−3.3%
α0=0.01
0.871
0.051
0.478
2.9%
53.1
−2.6%
α0=0.10
0.882
0.041
0.461
2.5%
48.2
−1.3%
Table 11: Comprehensive Ablation Study on SWaT
Method
Precision
Recall
F1
OmniAnomaly (2019) ( Su et al., 2019 ) ∗
0.938
0.821
0.876
USAD (2020) ( Audibert et al., 2020 ) ∗
0.946
0.837
0.888
MTAD-GAT (2020) ( Zhao et al., 2020 ) ∗
0.951
0.862
0.904
TranAD (2022) ( Tuli et al., 2022 ) ∗
0.957
0.874
0.914
LGAT (2025) ( Wen et al., 2025 ) ∗
0.961
0.891
0.925
i-SDT (Proposed)
0.967
0.918
0.942
Table 12: Comparison with recent SOTA on SWaT (binary detection, for contextual reference only ∗ ).
Digital Twins (DTs) are increasingly used to monitor and analyze Cyber Physical Systems (CPS). However, in adversarial environments, the fidelity of a DT cannot be assumed. Communication delays, data manipulation, sensor degradation, or partial information loss may cause the DT state to diverge from the physical process it represents. Such divergence creates temporal inconsistencies that may reveal cyber physical attacks. This paper proposes a detection framework that monitors temporal consistency between the physical system and a potentially degraded DT view. A DT predictor is trained exclusively on normal system behavior to model short-term system dynamics. During operation, discrepancies between predicted and observed states are transformed into multi-horizon temporal features capturing the magnitude, persistence, and evolution of prediction residuals. An unsupervised density model characterizes normal consistency patterns, while a sequential change detection mechanism identifies sustained deviations indicative of attacks. The approach is evaluated on three widely used Industrial Control System (ICS) datasets, SWaT, HAI, and BATADAL, under multiple DT degradation scenarios, including time desynchronization and partial observability loss. Results show that temporal inconsistency patterns enable reliable event-level attack detection with bounded false alarm rates and low detection latency. The proposed method achieves up to 98% detection reliability on SWaT and false alarm rates below 2%. Unlike conventional anomaly detection methods, the proposed framework does not require attack signatures or labeled attack data and remains effective even when the DT view is degraded. These results suggest that DT degradation, often treated as a limitation, can instead serve as a useful signal for cyber physical security monitoring.
Konstantinos E. Kampourakis, Vasileios Gkioulos, Sokratis Katsikas
Norwegian University of Science and Technology (NTNU), 2802 Gjøvik, Norway
Anomaly-based intrusion detection systems in industrial control systems (ICS) and operational technology (OT) environments are increasingly required to meet formal resilience criteria: absorbed adversarial disturbances, graceful degradation under sustained attack, and certified system-level guarantees. Existing resilience frameworks for cyber-physical systems define absorb-recover-adapt trajectories at the architectural level but do not treat machine learning anomaly detectors as first-class components, leaving a gap between component-level robustness evaluation and system-level resilience certification. In this paper, we establish that adversarial robustness in ICS anomaly detection is a specific instantiation of system resilience, and formalise this connection by mapping four resilience constructs, i.e. disturbance class, absorption capacity, recovery trajectory, and degradation function, onto the adversarial machine learning setting. We derive a compositional resilience bound for heterogeneous ICS detection networks, showing that the binding constraint on system-level resilience is the coupling-adjusted absorption capacity of each node along the attack path, not the per-node capacity -- so the binding node need not be the weakest one. Empirical validation on the BATADAL water distribution system benchmark demonstrates that the resulting metrics surface operationally significant phenomena invisible to standard benchmarks: the absorption-degradation divergence under adversarial training, and the paradox that hardening the binding node in isolation reduces system-level resilience. Implications for ICS architecture design and certification standards are discussed.
Branka Stojanović, Andreas Flatscher, Michael Somma
1JOANNEUM RESEARCH Forschungsgesellschaft mbH, Austria · 2TU Graz, Institute for Technical Informatics, Austria
Anomaly detection in Industrial Internet of Things (IIoT) environments is essential to protect the Industrial Control Systems (ICS) and Cyber-Physical Systems (CPS) from occuring run time false data injection and other malicious attacks. The increasing complexity of sensor networks and interconnected control loops makes it difficult to identify anomalous behavior hidden within high-dimensional and time-dependent signals. To address these challenges, this article introduces Adaptive Spatio-Temporal Reinforcement Optimization ASTRO (ASTRO), a novel anomaly detection framework that pioneers the use of reinforcement learning for dynamic threshold optimization. By integrating a Deep Q-Network (DQN) with Graph Neural Networks (GNNs), temporal modelling and a Multi-Head Attention mechanism, ASTRO continuously adapts its decision boundaries to improve detection accuracy. The GNN component models the spatial relations among sensors, Temporal model captures time series dependencies and the attention layer highlights most informative time steps. The model generates continuous anomaly scores, which are transformed into binary decisions using an adaptive threshold, optimized via a Deep Q-Network (DQN). The ASTRO approach is evaluated on two real world industrial benchmarks: the Secure Water Treatment (SWaT) and Water Distribution (WADI) datasets. The proposed model achieves an exceptional performance on the SWaT with F1 score of 0.990. Moreover, on highly complex 127 end devices WADI dataset, it secures F1 score of 0.788, outperforming state-of-the-art baselines by nearly 14%. Results across multiple runs confirm consistent generalization and stability. These experiments demonstrate that the ASTRO framework is highly practical and scalable method for strengthening the large scale cyber physical infrastructures
Rai Ali Yar, Umaisa Lail, Anwar Shah
Department of Computer Science, FAST NUCES, Development Sector, Faisalabad, Pakistan · Department of Information Technology, Riphah International University, Faisalabad, Pakistan