Grounding Time-Series Foundation Models in Digital Twin Topology for Predictive Maintenance

• Multivariate pretraining is a key driver of TSFM robustness across operating conditions.Source: Highlights · p. 1
• The three sources of cross-channel dependencies available downstream of a digital twin prove complementary.Source: Highlights · p. 2
• Topology-constrained attention lowers NRMSE by 2.7–4.2% compared with unconstrained fusion.Source: Highlights · p. 2
• A topology-grounded frozen TSFM matches end-to-end models and narrows the multi-condition performance gap.Source: Highlights · p. 2

• Digital-twin analytics include multivariate time-series tasks, while growing sensing and operating complexity expands the burden of maintaining separately designed models.TSFMs offer a potentially scalable backbone, but their forecasting-oriented pretraining differs from health-state inference tasks.Source: §1 · pp. 2–3
• Cross-channel dependencies rooted in physical coupling remain comparatively stable as operating conditions vary, unlike raw sensor measurements.The benchmark tests whether pretrained cross-channel structure is sufficient for reliable downstream predictive maintenance.Source: §1 · p. 4
• The paper frames pretrained weights, task adaptation, and digital-twin knowledge as distinct possible sources of cross-channel dependency.Twin knowledge specifies sensor-component links and physical interactions, whereas learned sources derive relationships from observations.Source: §1 · pp. 4–5
• Topology-informed fusion constrains cross-attention using asset-graph structure, so fused representations reflect local physical connectivity rather than all-to-all interactions.Source: §1 · pp. 5–6
• The ablation finds the three dependency sources complementary, and reports that topology-constrained attention outperforms unconstrained attention.The introduction concludes that a frozen TSFM informed by digital-twin representations matches or exceeds dedicated state-of-the-art models on this regression task.Source: §1 · pp. 5–6
• Five frozen TSFMs are benchmarked on C-MAPSS remaining-useful-life estimation across subsets of varying operational complexity.Source: §1 · pp. 4, 6

2.1. Landscape of Time-Series Foundation Models

• TSFMs span varied architectures and pretraining strategies, but most emphasize temporal continuation rather than the health-state tasks common in predictive maintenance.Whether pretrained cross-channel patterns suffice for cross-condition health assessment remains an open empirical question.Source: §2.1 · pp. 7–8

2.2. Knowledge Fusion with Time-Series Model in Digital Twins

• Digital-twin knowledge ranges from schemas and physics-based models to graphs that encode physical connectivity and support asset-specific reasoning.Source: §2.2 · pp. 8–9
• Prior attention-based fusion can use global all-to-all interactions, which conflict with the sparse, local nature of physical component interactions.Topology offers explicit locality constraints for fusing digital-twin representations with TSFMs.Source: §2.2 · p. 10

2.3. Modeling Cross-Channel Dependencies in Predictive Maintenance

• Pretrained weights capture cross-channel co-variation from heterogeneous corpora, but its physical origins cannot be traced or verified against the deployed system.Source: §2.3 · pp. 10–11
• Target-task adaptation learns channel relationships from available training samples, so its patterns may not reflect physical reality or generalize beyond observed conditions.Source: §2.3 · p. 11
• Digital-twin structure directly specifies asset-specific physical interdependencies, assuming the twin faithfully represents the system and requiring twin infrastructure.Source: §2.3 · p. 11

Case study and dataset choice

• C-MAPSS supports analysis of RUL prediction with multivariate sensor data, documented physical interdependencies, varied operating conditions, and established state-of-the-art comparisons.The study uses it for frozen-TSFM benchmarking and digital twin-informed fusion ablations.Source: §3 · pp. 11–12

C-MAPSS subsets

• FD001 and FD003 use one operating regime, whereas FD002 and FD004 span six; FD003 and FD004 also include a second fault mode.The subsets vary by operational conditions and fault variability, supporting robustness analysis across distinct scenarios.Source: §3 · p. 12

Engine structure

• The turbofan flow path links the fan, compressors, combustion chamber, turbines, and nozzle, with component degradation manifesting as correlated deviations across sensors.The engine has thermodynamic and mechanical interdependencies among components.Source: Figure 2 · p. 12, §3 · p. 13

Sensors and component mapping

• C-MAPSS provides 21 sensor channels, of which seven stable sensors are excluded, leaving 14 inputs distributed across six engine components.The inputs measure temperatures, pressures, rotational speeds, and flow rates; Table 3 maps sensors to components.Source: §3 · p. 13, Table 3 · p. 14

Prediction setup

• RUL is the number of cycles until failure, clipped at 125; models predict a normalized scalar from 30-cycle single-regime or 15-cycle multi-regime windows.Training uses all trajectory windows with step size 1, while testing uses each engine's final window; normalization statistics are computed from training data by subset.Source: §3 · p. 13

4.1. Benchmark Setup

• The evaluation uses ten-fold cross-validation over engine trajectories and reports test-set RMSE and NASA scoring function results.Each fold trains for 25 epochs, validates on the held-out fold, and evaluates once on the test set; proposed-model results are mean and standard deviation over folds.Source: §4.1 · p. 15
• Frozen TSFM embeddings are mean-pooled and passed to a linear probe for scalar RUL prediction; Moirai encodes channels jointly while other models process them independently.Linear probing is used as an efficient evaluation tool for the information in frozen embeddings, not as the proposed optimal deployment strategy.Source: §4.1 · pp. 15–16, Figure 3 · p. 15

4.2. Benchmark Results and Discussion

• TSFMs approach or match some state-of-the-art models on single-condition subsets, but lag substantially across six-condition subsets.Table 5 benchmarks TSFMs across the C-MAPSS subsets alongside dedicated state-of-the-art methods.Source: §4.2 · p. 17, Table 5 · p. 18
• Moirai performs best across all four subsets; its Any-variate Attention jointly encodes 14 channels with fewer than 400 trainable parameters.Its advantage over models without learned cross-channel dependencies is especially large on complex multi-condition subsets.Source: §4.2 · p. 17
• On complex subsets, Chronos is strongest among univariate TSFMs, but all four largely fall short of state-of-the-art performance.The paper attributes Chronos’ relative robustness to quantization, which makes representations partially insensitive to operating-condition magnitude shifts [45].Source: §4.2 · p. 19
• The observed cross-channel advantage leaves open whether pretrained weights, task-specific adaptation, and digital-twin-derived dependencies contribute complementary information.This question motivates the later fusion approach and ablation study.Source: §4.2 · p. 19

5.1. Encoding Asset Topology via Hierarchical Message Passing

• The hierarchical graph has sensor, component, and single-asset nodes, with directed edges between levels and undirected links between interacting components.Source: §5.1 · p. 19
• Edge construction varies by domain, but derives from asset structure already recorded in digital-twin information models.Examples include material flow in manufacturing, electrical connectivity in energy systems, and thermodynamic flow paths in aerospace.Source: §5.1 · p. 20
• Hierarchical message passing produces component embeddings that combine each component’s learned embedding with associated sensor states and adjacent-component context.Source: §5.1 · p. 20

5.2. Informing TSFM Embeddings via Topology-Informed Attention

• Cross-attention uses sensor-level TSFM embeddings as queries over component embeddings, retaining temporal information while adding topology-constrained cross-channel dependencies.Source: §5.2 · pp. 20–21
• The binary attention mask lets each sensor attend to its associated component and that component’s one-hop neighbors, excluding other connections.This constrains fusion to local physical connectivity rather than unconstrained all-to-all interactions.Source: §5.2 · p. 20
• The fusion applies to TSFMs with or without pretrained cross-channel dependencies, adding relational structure for MOMENT and asset-specific dependencies for Moirai.Source: §5.2 · pp. 21–22

6.1. Ablation Study Setup

• The ablation separately toggles pretrained mixing, target-task channel mixing, and topology-derived fusion while keeping the MOMENT and Moirai backbones frozen.For the connectivity test, alternative graphs preserve node degrees and neighbor counts while changing component links or sensor assignments.Source: §6.1 · pp. 22–23

6.2. Ablation Results and Discussion

• Weighted-average NRMSE rises from 0.1774 under ground-truth connectivity to 0.1810 under incorrect component coupling and 0.1895 under incorrect sensor-component coupling.Incorrect sensor grounding degrades performance more than incorrect component links; both errors matter more under six interleaved regimes.Source: §6.2 · pp. 23–24, Table 6 · p. 24
• Pretrained Moirai cross-channel mixing reduces NRMSE in all six configuration pairs on every subset, by about 7% on multi-condition and 4% on single-condition subsets.With all dependency sources disabled, Moirai's weighted-average NRMSE is 0.2930 versus MOMENT's 0.3444.Source: §6.2 · pp. 24, 26, Figure 6 · p. 26
• Target-task channel mixing reduces NRMSE by 2.9% for MOMENT and 4.7% for Moirai across digital-twin fusion scenarios.The reduction averages 6.6% versus 1.4% for MOMENT and 8.8% versus 3.1% for Moirai on single- versus multi-condition subsets.Source: §6.2 · pp. 26–27, Figure 7 · p. 27
• The topology mask lowers weighted-average NRMSE by 4.2% for MOMENT and 2.7% for Moirai versus unmasked fusion.Masked fusion also outperforms the GNN-alone reference and either source alone; its advantage over unmasked fusion is limited.Source: Table 7 · p. 25, §6.2 · pp. 27–28, Figure 8 · p. 29
• Digital-twin fusion adds to pretrained cross-channel mixing and target-task adaptation rather than duplicating either source.Under masked fusion, both interactions are positive for both backbones across all four subsets.Source: §6.2 · p. 28, Figure 9 · p. 30
• On single-condition subsets, the proposed method reaches the lowest reported RMSE; on multi-condition subsets, it closes most of the gap to state-of-the-art baselines without reaching them.The proposed method uses ten-fold results, while cited baselines use full training sets; the proposed models see only 14 sensor measurements, unlike some baselines that use operating-condition information.Source: §6.2 · pp. 28–29, Table 8 · p. 30

7. Conclusion

• Multivariate TSFMs substantially outperform univariate architectures, particularly under varying operating conditions, while dedicated end-to-end models remain ahead of every off-the-shelf backbone.The benchmark evaluated five frozen TSFMs on C-MAPSS RUL prediction.Source: §7 · p. 30
• Pretrained weights, target-task adaptation, and digital-twin topology are complementary, and topology-constrained attention beats unconstrained fusion by a limited margin.Replacing ground-truth sensor-component connectivity with same-size alternatives degrades performance, especially under varying operating conditions.Source: §7 · p. 30
• On single-condition subsets, a frozen multivariate TSFM matches or exceeds dedicated end-to-end models and closes roughly four-fifths of the remaining distance on multi-condition subsets.The comparison is for RUL regression, a task fundamentally different from the TSFM's pretraining objectives.Source: §7 · p. 31
• Evidence is limited to one task, one asset type, one dataset, and a limited set of backbones; transfer to other industrial domains and general robustness remain unestablished.The connectivity comparison does not isolate topology completely, and the graph is static and binary [72].Source: §7 · p. 31
• The paper identifies interpreting analytical objectives expressed in natural language as a future direction for moving digital-twin platforms beyond predefined tasks.The stated aim is to support varied operational queries.Source: §7 · p. 32

CRediT Author Contributions

• Sizhe Ma led data curation, formal analysis, investigation, software, validation, visualization, and the original draft.Ma also contributed to conceptualization, methodology, and writing review and editing.Source: CRediT Author Contributions · p. 32
• Katherine A. Flanigan contributed funding acquisition, project administration, resources, and supervision.Flanigan also contributed to conceptualization, methodology, and writing review and editing.Source: CRediT Author Contributions · p. 32
• Mario Bergés contributed funding acquisition, project administration, resources, and supervision.Bergés also contributed to conceptualization, methodology, and writing review and editing.Source: CRediT Author Contributions · p. 32

Appendix A. Pretraining Corpora of the Evaluated Backbones

• Table A.1 lists the pretraining corpora of the five evaluated TSFMs as reported by their source publications.The appendix uses the table to describe how far each corpus goes toward familiarity with the study data.Source: Appendix A · p. 32, Table A.1 · p. 33
• The appendix grades familiarity by whether pretraining data share the test channels' modality, similar generating dynamics, or the test dataset itself.For this study, these correspond to turbofan gas-path measurements, engine operation and degradation, and C-MAPSS, respectively.Source: Appendix A · p. 32
• All five evaluated corpora reach modality-level familiarity, but none reaches dynamics-level or dataset-level familiarity with C-MAPSS.The corpora include measurements such as temperature and pressure, but none is documented as covering thermo-mechanical machinery dynamics or C-MAPSS itself.Source: Appendix A · pp. 32–33, Table A.1 · p. 33

Appendix B. Structures Drawn for the Ablation Study

• For each fold, random alternatives preserve the ground-truth coupling counts while testing either component couplings or sensor-to-component assignments.The alternatives are drawn from fixed sets to avoid relying on a potentially unrepresentative inaccurate structure.Source: Appendix B · p. 33
• Table B.1 marks component pairs coupled under the ground truth and ten alternatives, one per fold.The component-coupling alternatives preserve each component's number of couplings and the graph's number of sensor connections.Source: Appendix B · p. 33, Table B.1 · p. 34
• Table B.2 lists ground-truth and alternative sensor-component couplings, with ten alternatives drawn per fold.Each alternative moves every sensor to a different component while preserving each component's sensor count.Source: Appendix B · p. 33, Table B.2 · p. 34