Counterfactual Enabled Neuro-Symbolic Digital Twins for Intelligent Industrial Maintenance

1  Introduction

Accidental equipment breakdowns cost manufacturing businesses as much as 50 billion dollars each year and even single failures at high-throughput manufacturing facilities cost up to 260,000 dollars per hour [1,2]. The proliferation of Industrial Internet of Things (IIoT) sensors and edge computing makes it possible to engage in continuous monitoring [3–5], but converting such sensor streams to sound and actionable maintenance decisions is a consequential and open issue.

The process of degradation is nonlinear, and includes thermal stress, fatigue crack propagation, bearing wear, and lubrication failure, which cannot be fully represented by purely data-driven models without domain knowledge [6,7]. In addition to the quality of prediction, maintenance decisions are multi-objective in nature: unplanned failures will cost resources in terms of repair, loss of production, and safety risk, and overly conservative preventive maintenance will waste resources; the optimum trade-off depends on the type of machine, the mode of operation, the load history, and the business environment [4,8,9].

The existing predictive maintenance methods do not sufficiently complement each other. Models based on physics, inspired by Paris-law crack growth or Arrhenius thermal aging [7] give interpretable predictions, but need accurate parameters and controlled conditions, which are hard to achieve. Random forests [10], gradient boosting [11], recurrent networks [12], and convolutional architectures [13], are good at making predictions, yet are black-box and cannot provide physically grounded counterfactuals, and extrapolate poorly. With hybrid approaches, physics is usually assumed to be a fixed part that is not trained together with the other parts [6,14–16]. Another one is decision optimization for competing objectives.

Digital twin technology [17–19] offers a platform by developing synchronized virtual copies that allow real-time monitoring, simulation, optimization. The Cognitive Digital Twin (CDT) [17] extends this with symbolic reasoning. Neuro-symbolic systems [20,21] combine deep learning with logical constraints. Grounded in causal inference theory, counterfactual reasoning enables predictive systems to answer hypothetical queries [21,22], e.g., estimating Remaining Useful Life (RUL) under alternative actions via conditional variational autoencoders (CVAE) [23,24]. Reinforcement learning (RL) [25,26] enables policy optimization without real-world trials.

This work addresses four gaps through an integrated system: constructing multi-task temporal prognostics to predict RUL, failure probability, and repair cost from multivariate sensor history; embedding symbolic constraints; using CVAE-based counterfactuals; and training a Q-learning agent on simulated transitions.

The main contributions are the following:

•   An end-to-end hybrid neuro-symbolic predictive maintenance framework with jointly trained physics constraints.

•   A conditional variational autoencoder enabling counterfactual cost-risk analysis and decision support.

•   A unified data-to-action pipeline linking sensor data to maintenance decisions.

•   A multi-objective Q-learning framework achieving a 51.7% failure reduction without real equipment interaction.

•   Real-time deployment at 23.1 ms latency on dual Tesla T4 GPUs with 1.6 GB memory.

2  Related Work

In the era of Industry 4.0, digital twin (DT) technology is one of the most appealing technologies for enabling predictive maintenance (PdM) [27,28] by combining multi-source data, physics-based models, and the use of artificial intelligence for continuous health checks. There are three types of modelling paradigms that are commonly used in DT-based PdM: physics-based models based on first principles degradation laws, and data-driven models that learn patterns from data, and hybrid models that combine both [27,29,30].

Studies in various sectors such as Electrical Machines [29], Power Generation [31], Space Nuclear Systems [32] and Marine Propulsion [33] have shown that DTs can greatly decrease the amount of unplanned downtime in these areas when compared to traditional corrective maintenance. The same improvements are observed in industrial applications like CNC, hydraulic and rotational systems with DT frameworks integrated into IoT [30,34].

Although significant progress has been made, the field is still disjointed and has no common architectures and explainability [35,36]. Requirements-driven roadmaps highlight the importance of explicit asset modeling, failure taxonomies, maintenance logic and decision traceability, which are not always present in existing implementations [35]. Furthermore, safety-critical applications require transparency, which is not encouraged by black-box ML [36,37]. To overcome this challenge the Cognitive Digital Twin (CDT) introduces semantic technologies, ontologies and reasoning approaches to establish links between data-centric and symbolic representations [38], but only limited use of deep learning and counterfactual reasoning to date.

With the improvements of deep learning, the modeling of temporal degradation degradation improved in the field of PdM. LSTM networks [12,39] are able to learn sequential patterns, CNNs [13] are able to learn local patterns, and gradient boosting [11] is very effective for tabular data. But these techniques are generally local physics, and therefore predict inconsistently globally. A physics-informed neural network (PINNs) instead overcomes this by incorporating physical laws into learning [14]. Hybrid methods also show great potential: Zhang et al. [32] attain less than 0.6% state-tracking error in space nuclear systems with physics-based models and Transformer architectures, while Liu et al. [33] obtain less than 0.9% error in marine engine degradation with adaptive DT frameworks. Zero-shot fault generalization is also promising for knowledge–data fusion methods [40]. Predictive maintenance advances have become a blend of physics-based modeling, data-driven learning and a hybrid of the two. Event-triggered neural learning has been used for constrained industrial systems and hybrid signal-processing and CNN methods are used to enhance elevator fault diagnosis [41,42]. Sectorspecific solutions are emphasized in multi-sensor optimization frameworks like ParallelGraphNet [43] and particle filtering RUL in pumps [44]. Physics-informed neural networks, such as SA-PINN [44] and temporal models such as TCN-BiLSTM [45] complement transformer backbones for improving fatigue life prediction. In the end, causal inference frameworks [46] are very similar to counterfactual reasoning which allows for an interpretable diagnostic in complex systems.

Reinforcement learning has been used in the context of maintenance scheduling [25] and counterfactual reasoning offers a causal structure for decision making [21,22]. Moreover, Yang et al. [47] showcase hybrid modeling, where the attention based LSTM, GANs and MLPs are used for RUL estimation of lithium-ion batteries.

None of the existing methods, integrate DT-based prognostics with physics-based learning, counterfactual reasoning, and RL-based multi-objective optimization. The proposed framework is the first to integrate these components into a single DT architecture suitable for real-time industrial deployment.

3  Methodology

Fig. 1 shows the framework in four stages. Stage 1 converts raw sensor streams and produces sequences (L = 10 timesteps). Stage 2 uses a temporal transformer with a physics loss module to predict RUL, failure probability, and cost. Stage 3 trains a CVAE on observed states and uses generated counterfactual next states as simulated transitions for Q-learning, without RL feedback to the CVAE. Stage 4 provides practical maintenance suggestions (maintain, reduce load, or a combination). Table 1 provides the complete architecture specifications for all three learned components: the temporal transformer, the CVAE, and the Q-learning agent.

Figure 1: Hybrid neuro-symbolic framework with (1) data ingestion, (2) transformer-based hybrid modeling with physics losses, (3) CVAE-generated counterfactual states passed unidirectionally to a Q-learning agent, and (4) optimal maintenance action output. The RL agent provides no feedback to the CVAE.

Fig. 2 shows the proposed digital twin for industrial maintenance. A physical machine streams IIoT sensor data (vibration, temperature, RPM, pressure, current). These readings update a software replica, where a hybrid neuro-symbolic model estimates Remaining Useful Life, failure probability, and repair cost. A CVAE generates counterfactual projections of machine states under candidate interventions, and a Q-learning policy selects the optimal action for the maintenance operator. This closed loop of observation, virtual update, counterfactual projection, and decision feedback defines the digital twin. Predictive and decision components are validated on a 14-day synthetic dataset, with real-time synchronization planned for deployment.

Figure 2: Digital twin for predictive maintenance. IIoT sensor data update a virtual replica, which estimates health state, generates counterfactuals, and issues optimal actions. Validated components: Hybrid neuro-symbolic model and CVAE+Q-learning; real-time synchronization is planned.

3.1 Dataset Description

The industrial machine predictive maintenance dataset [48] is a synthetic collection of 24,042 timestamped records spanning a 14-day window (1 January to 14 January 2024). The dataset comprises 20 individual machine units distributed across four machine types: 5 CNC units (IDs 1–5), 5 Pump units (IDs 6–10), 5 Compressor units (IDs 11–15), and 5 Robotic Arm units (IDs 16–20). The 20-unit figure refers to unique physical machine identities, not to the number of machine types. Each unit is sampled at an average interval of approximately 3 min, though intervals are irregular (ranging from 3 to 24 min) due to the stochastic generation process; Table 2 demonstrates this with five consecutive records from machine ID 1 (CNC). The data was created in Python to simulate realistic behavior of industrial degradation including physically realistic sensor ranges, time-dependent degradation behavior, and correlated failure behavior; it is not based on actual industrial deployments. This provenance ought to be noted when determining the generalizability of findings. Each record contains all 15 original dataset columns, which are listed in Table 3 with explicit separation of inputs and outputs. The nine input features comprise six continuous sensor measurements (vibration RMS, motor temperature, phase current, pressure level, RPM, and ambient temperature), two operational descriptors (machine type and operating mode), and one maintenance history field (hours since last maintenance, hm). The four supervised outputs are: RUL in hours (regression), failure within 24 h (binary classification), failure type (multi-class classification), and estimated repair cost (regression). Estimated repair cost is used only as a regression prediction target and is never used as a model input.

3.2 Exploratory Data Analysis

Prior to modeling, a set of targeted analyses was conducted to better understand the dataset. Fig. 3a shows that RUL follows a right-skewed distribution, with a mean of 87.2 h (std. 52.3). This indicates that most machines operate comfortably within a healthy range, while a smaller portion approaches critical end-of-life conditions.

Figure 3: (a) RUL distribution across 24,042 samples. Mean 87.2 h (std 52.3 h); right-skewed with a minority of machines near end of life. (b) sensor-target correlation structure used to inform modeling and physics constraints.

Fig. 3b presents the sensor correlation matrix: RUL correlates strongly with vibration (r=−0.81), motor temperature (r=−0.74), and current (r=−0.68), while RPM shows positive correlation (r=+0.62), consistent with degraded machines running at reduced speeds. These correlations directly motivated the physics interaction features.

Fig. 4 traces sensor degradation over time for a representative machine: vibration and temperature rise progressively toward failure events while RPM declines, and RUL decreases monotonically, validating the monotonicity constraint included in the physics loss module.

Figure 4: Sensor degradation trends for a representative machine. Dashed lines mark failure events; vibration and temperature rise monotonically while RPM declines, validating the monotonicity constraint.

3.3 Feature Engineering

Rolling window statistics (w=5) capture short-term degradation drift per machine:

v¯t(w)=1w∑i=t−w+1tvi,σv,t(w)=1w∑i(vi−v¯t(w))2(1)

Applied to vibration, temperature, and current, these add six features. Physics-motivated interaction terms capture mechanically and thermodynamically coupled sensor pairs:

fvib-rpm=v⋅ω/1000,ftemp-rpm=θm⋅ω/1000(2)

fpress-temp=P⋅θm/100,Δθ=θm−θa(3)

Degradation indicator: rmaint-press=hm/(P+1). Total feature set: 19 dimensions.

3.4 Data Preprocessing

The failure classes are balanced by having an 80/20 split. Statistics are calculated on the training set and then used for normalization (z-score). The test split follows strictly a temporal order and the latter 20% of the time series of each machine is used as the test set, which means that no information from the future is used in the training process. The cross validation folds are built from non-overlapping period of time. Each fold has its own held-out portion of the records, and normalization statistics are recalculated on the basis of the held-out proportion of the records, respectively. This design is to avoid leakage across time series folds. The nearly identical mean RMSE of 21.52 h observed in both the five-fold cross-validation and the held-out test set arises from the deterministic nature of the synthetic degradation curves. Any temporal subset effectively samples the same underlying distribution. This statistical regularity is a property of the synthetic data generator rather than an indication of data leakage. Temporal sequences of L=10 are formed by a sliding window Xiseq=[xi,…,xi+L−1].

3.5 Temporal Transformer

The transformer encoder (Table 1) serves as the neural component of the neuro-symbolic integration: it learns data-driven degradation representations that are then constrained by the symbolic physics loss module described below.

Input embedding with positional encoding at dimension d=128:

zt(0)=Wembxt+bemb+PE(t)(4)

where PE(t,2k)=sin⁡(t/100002k/d), PE(t,2k+1)=cos⁡(t/100002k/d).

Multi-head self-attention (H=4, dk=32):

MHA(Z)=Concat(head1,…,headH)WO(5)

headh=softmax(QhKhTdk)Vh(6)

Two encoder layers each apply:

Z~(l)=LN(Z(l)+MHA(Z(l)))(7)

Z(l+1)=LN(Z~(l)+FFN(Z~(l)))(8)

Task-specific prediction heads operate on the final state zT(2):

y^RUL=WrReLU(Wr(1)zT(2))(9)

y^fail=softmax(WfReLU(Wf(1)zT(2)))(10)

y^cost=WcReLU(Wc(1)zT(2))(11)

3.6 Physics-Informed Constraint Module

The neuro-symbolic integration is achieved by four differentiable constraint terms that enforcing known physical laws as soft penalties in the training objective bridges neural pattern recognition with domain-grounded symbolic rules. These constraints are the symbolic layer of the neuro-symbolic architecture, which directly relates the learned representations of the transformer to thermodynamic, mechanical and degradation physics.

Four differentiable constraints act as targeted regularizers:

ℒvib-rpm=1B∑i|vi−αωi/ωmax|,α=1.0(12)

ℒpress-temp=1B∑i|θm,i−(θ0+βPi)|,β=0.01(13)

ℒbounds=∑i[ReLU(θmin−θm,i)+ReLU(θm,i−θmax)](14)

ℒmono=∑tReLU(RULt−RULt−1−ε),ε=0.5(15)

Combined: ℒphys=λ1ℒvib-rpm+λ2ℒpress-temp+λ3ℒbounds+λ4ℒmono with [λi]=[1.0,0.01,1.0,0.5]. The weight values reflect the relative physical significance of each constraint. λ1=1.0 and λ3=1.0 enforce vibration-RPM coupling and sensor boundary conditions with equal priority, since violations of either represent physically impossible predictions. λ2=0.01 is deliberately small because the linear pressure-temperature relationship is an approximation with a higher tolerable deviation in practice. λ4=0.5 moderately enforces the RUL monotonicity, which means that only the transient load changes cause short-term fluctuations, and the sustained RUL increases are penalised. They were chosen by coarse grid searching the {0.001,0.01,0.1,0.5,1.0} per weight set on the validation fold, and the combination minimizing the validation RMSE while keeping the prediction distribution physically plausible was kept.

3.7 Counterfactual VAE

The CVAE is another connection between the symbolic and neural components of the system. It encodes the current machine state into a latent representation, which also captures the operating conditions. This representation can then be decoded under hypothetical interventions to generate realistic counterfactual next states. The resulting states are simulated transitions for the Q-learning agent, allowing a model-based reinforcement learning environment without the need for “real” exploration.

Encoder maps (xt,ct) to approximate posterior:

μ, log⁡σ2=WμReLU(We[xt;ct]), WσReLU(We[xt;ct])(16)

Reparameterization: z=μ+σ⊙ε, ε∼𝒩(0,I), z∈R32. Decoder reconstructs counterfactual state with modified conditions ct′:

x^t′=WdReLU(Wd(1)[z;ct′])(17)

Training objective (β=0.001):

ℒCVAE=E[‖x−x^‖2]+βKL(qϕ‖p)(18)

CVAE reconstruction quality was assessed on the held-out test set, yielding a mean reconstruction RMSE of 0.043 (normalized units), an MSE of 0.0018, and a Fréchet distance of 1.82 between the distribution of generated counterfactual samples and real held-out sensor states, confirming that generated states reside within the observed sensor manifold.

3.8 Multi-Objective Reinforcement Learning

The RL action space 𝒜 comprises four decisions that map directly to industrial maintenance practice: no-action (continue monitoring), reduce-load (lower operating intensity), maintenance (schedule an immediate maintenance window), and both (combined load reduction and maintenance). These actions are not derived from any labeled action column in the dataset; they are defined analytically as the Cartesian product of two binary operator decisions (schedule maintenance: yes/no; reduce load: yes/no). Their effects on machine state are simulated through the CVAE decoder conditioned on the corresponding intervention context vector ct′.

State space: |𝒮|=125 states from 5-bin discretization of (RUL, Pfail, cost). To quantify the policy degradation caused by this discretization resolution, a sensitivity analysis was conducted by varying the number of bins per state dimension across {3,5,7,10}, yielding Q-table sizes of 27, 125, 343, and 1000 states, respectively. The results are reported in Table 4.

Failure rate under the learned policy changed by less than ±1.4 percentage points across all configurations, and episode reward varied by less than ±0.018, confirming that the 5-bin discretization captures the dominant state structure. Residual discretization error at bin boundaries motivates future deep RL extensions with continuous state encodings.

Multi-objective reward ([wi]=[1.0,2.0,1.5,0.5,−0.3]):

R=w1RULt+1−RULtRULmax+w2⋅2(Pfail,t−Pfail,t+1)−w3Caction+Crepair,t+1Cmax+w4Rpro+w5Runnec(19)

Q-learning update (α=0.1, γ=0.95, ε=0.2):

Q(st,at)←Q(st,at)+α[Rt+γmaxa′Q(st+1,a′)−Q(st,at)](20)

3.9 Training Configuration

Multi-task supervised loss:

ℒ=ℒRUL+0.5ℒfail+0.3ℒcost+0.1ℒphys(21)

AdamW optimizer, lr 10−3, batch 64, dropout 0.1, gradient clipping 1.0. Transformer trained 50 epochs; CVAE 30 epochs; RL policy 500 episodes. Experiments run on Kaggle notebook with NVIDIA Tesla T4 ×2 GPU (16 GB each) and 30 GB RAM.

4  Algorithm

Algorithm 1 summarizes the three-stage training procedure. Algorithm 2 details the inference-time pipeline.

5  Experimental Setup

Random Forest (100 trees, depth 15), XGBoost (100 estimators, depth 8, lr 0.1), LSTM (2 layers, 128 units, dropout 0.2, sequence length 10), and a standard Transformer without physics constraints serve as baselines. All share identical preprocessing pipelines, stratified splits, and sequence generation, ensuring performance differences reflect architecture rather than data preparation. Hyperparameters for Random Forest and XGBoost were selected by grid search over a held-out validation fold; LSTM units were matched to the transformer’s representational capacity. The four baselines were designed to isolate the incremental contribution of each proposed component: Random Forest and XGBoost represent strong non-sequential tabular methods; LSTM represents the sequential deep-learning baseline; and the physics-unconstrained Transformer isolates the gain from the physics constraint module. Regression evaluation uses RMSE, MAE, and R2; RMSE is the primary ranking metric. Classification evaluation uses Precision, Recall, F1, and ROC-AUC; F1 is primary given 8.7% class imbalance. RL policy evaluation tracks failure rate, average maintenance cost, and equipment utilization across 200 greedy evaluation episodes.

6  Results

6.1 Overall Performance

Table 5 compares all methods, and Fig. 5 visualizes the results. The full framework achieves RUL RMSE 21.52 h, which are improvements of 25.1% over RF, 18.2% over XGBoost, 14.3% over LSTM, and 6.0% over the Transformer without physics; R2=0.918 confirms the strong fit across the entire RUL range. The fact that RMSE gains are due to the reduction of outliers and not an enhancement in central-tendency alone is confirmed by MAE of 15.84 h. On failure prediction, the framework attains F1 0.916, precision of 0.923, and a recall of 0.909. RMSE of cost prediction of 456 (15.9% better than RF). The monotonic improvement of the RMSE of RF → XGB → LSTM → Transformer → Trans.+Physics → Full confirms the additive contribution of each component.

Figure 5: Comparison of performance on different model variants: (a) RUL RMSE on all model variants. The entire structure has a 21.52 h, 25.1% mimic of RF. (b) Variants of model prediction F1-score vs. failure prediction. The entire structure attains 0.916, which is an improvement of 9.8% as compared to RF.

6.2 Ablation Study

Table 6 (plotted in Fig. 6) decomposes component contributions. The most significant contributor is multi-head attention (H=4): replacing it with single-head attention increases RMSE to 28.45 h (+32.2%) and lowers F1 to 0.846. Multi-task learning contributes 24.4%. Positional encoding contributes 20.3%, consistent with Fig. 4 showing temporally ordered sensor trends. Physics constraints contribute 11.7%, primarily by eliminating outlier predictions outside physically meaningful ranges.

Figure 6: Ablation study: RUL RMSE and percent degradation by component removal; multi-head attention contributes most (32.2%).

6.3 Error Analysis and Failure Prediction Horizons

The error distribution varies systematically with operating conditions, consistent with EDA findings. Peak-mode RMSE (24.76 h) is 34.2% higher than idle (18.45 h), consistent with the EDA finding that peak-mode machines exhibit compressed and more variable RUL distributions. Intermediate accuracy (21.89 h RMSE) is obtained under normal operating conditions. Machine-type error is nearly uniform (CNC 20.34 h, Pump 22.12 h, Compressor 21.98 h, Robotic Arm 21.44 h, std 0.89 h), confirming that machine-type embeddings transfer across equipment categories. Error for overdue-maintenance states (25.89 h, +34.6% vs. recent-maintenance 19.23 h) reflects distributional shift on degradation paths that extend beyond normal operating periods.

Table 7 confirms failure prediction F1 above 0.916 at all horizons up to 24 h, with AUC above 0.972 throughout. Precision above 0.92 ensures fewer than eight unnecessary maintenance alerts per 100 forecasts. Recall above 0.90 ensures that fewer than 10% of real failure events are missed. The F1 gradient (0.979 at 0–6 h to 0.916 at 18–24 h) reflects the progressive weakening of discriminative degradation signal with increasing prediction distance.

6.4 Counterfactual Interventions and RL Policy

The quantifications of intervention trade-offs are done on average of 100 test-set machines and represented in Table 8. The maintenance costs are about 2.4 times higher per hour, but about 13 times higher in absolute terms, as compared to the load reduction effect; the combined intervention extends RUL by 24.9 h at 520, which is approximately 2.3 times more efficient per hour, but about 17 times more efficient in absolute terms, than the load reduction effect.

The Q-learning policy reduces the failure rate by 51.7 percentage points (2.1% failure rate compared with 4.2% failure rate of the rule-based policy), saves costs by 13.5 percentage points (2.1% failure cost vs. 4.2% failure cost for the rule-based policy), and improves utilization by 7.3 percentage points (2.1% failure utilization vs. 4.2% failure utilization for the rule-based policy). All the reported 51.7% failure rate improvement in RL policy training and reported transition of the policy occur due to the generation of counterfactual transitions by CVAE and not from actual interaction with an equipment or simulation. The outcome is based on the simulated performance of the policies within the learned counterfactual model. This measure cannot be considered as a direct operational guarantee without being validated on the deployed physical systems. Episode reward 0.387 is 167% above rule-based (0.145) and 265% above random (−0.234). The action distribution (no-action 32%, maintenance 28%, combined 22%, reduce-load 18%) demonstrates state-dependent intelligence.

6.5 Computational Performance

Mean inference latency: 23.1 ms (std 3.2 ms) on Tesla T4 ×2, supporting 1–10 Hz industrial rates. Training: 4.5 h total (2.8 h transformer, 1.2 h CVAE, 0.5 h RL). Peak inference memory: 1.6 GB. Five-fold cross-validation: RMSE 21.52±1.34 h, F1 0.916±0.023, cost RMSE $456 ± $29. Folds were constructed respecting temporal order within each machine’s time series, and normalization statistics were recomputed from the training portion of each fold. The near-identical mean cross-validation and held-out test RMSE of 21.52 h arises because the synthetic dataset follows deterministic parametric degradation curves: any temporally ordered partition of the data draws samples from the same underlying statistical distribution. This is a property of the synthetic data generator and does not indicate data leakage.

7  Discussion

There are 3 complementary mechanisms behind the performance gains. Temporal transformers increase the effective receptive field, connecting current signals with shifts in the operation mode of the preceding dozen (or more) timesteps. The physics constraints help to prevent unrealistic predictions (such as RUL increase under constant peak load), resulting in an RMSE improvement of 6.0% and working in tandem with attention-based learning. Multi-task learning also boosts generalization: the degradation of 24.4% RMSE for training the RUL head alone demonstrates that failure and cost heads regularize the shared encoder. The goal of counterfactual analysis is to change predictions into economically viable choices. For instance, a 10-h maintenance deferral leads to a 15.7 h of RUL saving (1.57 h/dollar) and joint interventions result in a 24.9 h extension compared to a naive 31.0 h sum, which is a strong confirmation of the subadditivity of the RUL from shared thermomechanical pathways. The learned policy is 32% no-action; by being selective, the learned policy will reduce the number of failures by 51.7% instead of just increasing the number of interventions. Peak mode RMSE is 34.2% higher than idle mode RMSE, as there are nonlinear degradation dynamics that are not well represented (e.g., thermomechanical coupling, accelerated wear).

Future studies will be conducted in three directions: (i) augmenting the training data with physics-based simulations of degradation in high severity, (ii) adding mode-specific or conditional sub-models that characterize different operation conditions and regimes and (iii) implementing adaptive uncertainty estimation to broaden prediction intervals in the presence of distributional shift. The larger the increase in the number of overdue-maintenance states (34.6%), the greater the sensitivity to distributional shift, and transfer learning from accelerated aging experiments is a promising strategy for improvement.

Limitations and Generalizability.

The data used for this study is completely synthetic and mimics industrial degradation. Physically grounded data (sensor ranges, temporal degradation, correlated failures) can capture only a small portion of the complexities of the real world, including noise and drift and calibration artifacts. So the fact that they saw a 51.7% reduction in failures does not mean they achieved a guaranteed increase in real-world performance. Testing in actual industrial applications (such as CNC, pumps, compressors, robotic arms, etc.) is still required before use.

There are other deployment restrictions. Model training takes 6–12 months of historical failure data and tail events are restricted by the 8.7% failure rate. The discretised 125-state Q-table also does not have sufficient resolution at bin boundaries, leading to the motivation of deep reinforcement learning with continuous representations (Table 4). Mitigation measures need to be taken before the autonomous deployment of these challenges occurs [5].

8  Conclusion

This paper presents an end-to-end hybrid neuro-symbolic digital twin system for industrial predictive maintenance, combining temporal transformer-based prognostics, differentiable physics constraints, conditional VAE counterfactual generation, and multi-objective Q-learning for policy optimization. The framework is evaluated on 24,042 synthetic sensor records from CNC machines, pumps, compressors, and robotic arms. It achieves an RUL RMSE of 21.52 h (R2 0.918), a failure prediction F1 score of 0.916 consistently across 24-h prediction horizons, and a 51.7% reduction in failure rate compared to rule-based scheduling (based on CVAE-generated counterfactual simulations), with an inference latency of 23.1 ms on dual Tesla T4 GPUs. Ablation studies show that multi-head attention, multi-task learning, positional encoding, and physics constraints each contribute meaningfully to overall performance, with multi-head attention providing the largest individual improvement at 32.2%. Future work could focus on incorporating uncertainty quantification to produce calibrated prediction intervals, exploring deep reinforcement learning methods for continuous state-action spaces to move beyond Q-table discretization, and validating the approach on real-world industrial sensor data to assess how well these performance gains transfer beyond synthetic settings.

Acknowledgement: This work was supported by the Princess Nourah Bint Abdulrahman University Researchers supporting project, Princess Nourah Bint Abdulrahman University, Riyadh Saudi Arabia. The authors also thank Prince Sultan University, Riyadh Saudi Arabia for APC support. The authors used Gemini (v3.5, Jan 2026) and ChatGPT (GPT-4 Turbo, Jan 2026) tools for English language editing, grammar improvement, and AI-assisted diagramming tools for figure preparation. AI was not used for data collection, experimental design, data analysis, or interpretation of results.The authors reviewed and approved the final manuscript in its entirety and are fully responsible for all content.

Funding Statement: This work was funded by the Princess Nourah Bint Abdulrahman University Researchers Supporting Project number PNURSP2026R733, Princess Nourah Bint Abdulrahman University, Riyadh Saudi Arabia.

Author Contributions: Nada Alzaben: Conceptualization, Methodology, Software, Validation, Writing original draft, Writing—review & editing. Muhammad I. Khan: Conceptualization, Formal analysis, Investigation, Writing original draft. Hafeez Ur Rehman Siddiqui: Methodology, Validation, Visualization, Writing review & editing. Abeer Rashad Mirdad: Formal analysis, Investigation, Visualization, Writing review & editing. Saeed Ali Bahaj: Software, Resources, Supervision, Project administration. All authors reviewed and approved the final version of the manuscript.

Availability of Data and Materials: The dataset analyzed during the current study is openly available on Kaggle: Industrial Machine Predictive Maintenance (syn), version 3.0, updated February 2026. Available at: https://www.kaggle.com/datasets/tatheerabbas/industrial-machine-predictive-maintenance (accessed on 1 February 2026).

Ethics Approval: Not Applicable.

Conflicts of Interest: The authors declare no conflicts of interest.

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