Industrial process networks do not maintain a single effective topology while operating: streams are throttled or bypassed, and units move between idle, transition, and active regimes. Models of such systems are typically trained on measured state trajectories while the operating mechanisms that generated them remain latent, and an unconstrained graph network can fit such a trajectory without assigning stable physical meaning to the recovered routing. We address both problems with the Conservative Hybrid Graph Network (CHGN), which learns routing, regime assignment, and removal rates as data-driven surrogates and inserts them into a fixed transport equation, so that the mass balance holds by construction for any predicted routing. CHGN trained on networks of 10-20 nodes transfers zero-shot to unseen graphs of 25-40 nodes without retraining, reaching an RMSE of 2.1e-3 against 6e-2 to 9e-2 for GNN baselines under the same protocol, with a gate MAE of 7.9e-3 and regime accuracy of 94.3% (1.2e-2 and 96.4% respectively on the fixed training topology). On a fluid-mixing pilot plant, CHGN improves on a persistence baseline for held-out physical faults but does not predict manual interventions, for which the governing valve actions are unobserved. The model therefore transfers across process topologies without retraining and exposes the latent mechanisms governing plant behaviour to inspection.
Figures & tables
Figure 1: One-step CHGN update. The spatial encoder maps the state history, unit types, external inputs and static process graph into topology-dependent node representations used by the routing head. Local heads infer the unit regimes and bounded removal rates from the corresponding state histories and unit information. The predicted quantities are then inserted into the fixed incidence-based transport law and advanced by one time step.
Figure 2: Zero-shot transfer across unseen process graphs. CHGN and two shared-weight baselines are trained on the same 10 – 20 -node graph distribution and evaluated without retraining on unseen 25 – 40 -node topologies. Points and bars show the mean and 95% Student- t interval across seeds; faint points are individual-seed means. Node count orders graphs.
Figure 3: Calibration of the three predicted quantities. Predicted versus true (a) inventory and (b) routing gate, shown as hexagonally binned log-count densities; the dashed line is parity. (c) Row-normalised regime confusion matrix. Gates are calibrated across (0,1) , and regime errors occur only between adjacent classes.
Variant
State RMSE ↓
Gate MAE ↓
Regime acc. ↑
Joint CHGN
0.01267±0.00108
0.01225±0.00234
96.37±1.18%
State only
0.01564±0.00294
0.02985±0.01535
45.26±8.00%
Gate supervision
0.01337±0.00199
0.01357±0.00189
42.08±10.06%
Regime supervision
0.01690±0.00246
0.02639±0.00745
93.51±2.58%
Fixed routing
0.05293±0.00454
0.20051
73.74±2.97%
Fixed regimes
0.01221±0.00303
0.01499±0.00208
30.66%
Table 1: Mechanism ablations. Mean ± s.d. across five independently trained seeds. Entries without intervals are clamped and constant across seeds.
Figure 4: Mechanism ablations, five seeds per variant. Circles show seeds; diamonds and bars show the mean and two-sided 95% Student- t interval. The dashed line marks the joint-model mean. Red indicates an interval separated from the reference in the worst direction; grey indicates no separation.
Model
State RMSE ↓
Gate MAE ↓
Regime acc. ↑
Balance disc. ↓
CHGN
0.01267±0.00108
0.01225±0.00234
96.37±1.18%
0.01983±0.00394
LSTM
0.00520±0.00035
0.00621±0.00037
94.34±0.22%
0.01091±0.00082
MLP
0.01630±0.00131
0.01661±0.00218
92.97±0.31%
0.01574±0.00121
Dynamic GNN
0.03421±0.00035
0.01072±0.00020
96.57±0.11%
0.11376±0.00157
NHA-inspired
0.03437±0.00037
0.01061±0.00028
96.35±0.12%
0.11430±0.00133
NRI-inspired
0.05192±0.00032
0.05263±0.00378
91.64±0.63%
0.11667±0.00220
Table 2: Fixed-graph benchmark, five seeds per model. Bold marks the best mean, not statistical separation. Balance discrepancy measures agreement with the known full balance model and is distinct from the internal transport residual 1⊤BF^ .
Figure 5: Structure-preserving architecture on held-out fluid-mixing conditions. (a) State MSE for persistence and CHGN on three anomaly categories held out from training; leakage+clogging and stirring error each contain one session, while manual mode contains eight. (b) Autoregressive rollout on the leakage+clogging session.
Appendix figures & tables7 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 6: Full-trajectory state reconstruction. (a) Ground-truth inventory for all twenty units; (b) CHGN rollout on the same scale; (c) signed residual on a scale two orders of magnitude finer. The dashed line marks the end of the conditioning history. (d) State RMSE versus forecast horizon: median and 10–90th percentile band over the test split, with the displayed trajectory dashed.
Figure 7: Recovered mechanism on the plant graph , held-out trajectory 255 at t=0.20 . Node labels show inventory and, for regime-bearing units, true and predicted regime; a red border marks disagreement. Edge colour shows absolute gate error (green <0.08 , orange 0.08 – 0.20 , red >0.20 ), and the inset lists true and predicted gate values. Because all columns are rounded independently, the printed error at S1 and S5 differs by 0.01 from the difference between the printed gate values. This instant was chosen to show the dryer and S2 errors; aggregate accuracy is reported in Table 2 .
Substitution
All units
Switch destinations
Regime-bearing units
Learned
4.115×10−4
4.627×10−4
1.084×10−4
Oracle: both
4.239×10−4
4.847×10−4
0.778×10−4
Oracle: routing only
4.240×10−4
4.847×10−4
0.786×10−4
Oracle: regimes only
4.115×10−4
4.627×10−4
1.079×10−4
Fixed: regimes only
4.441×10−4
4.622×10−4
3.890×10−4
Fixed: routing only
1.932×10−3
2.710×10−3
9.620×10−4
Appendix
Table 3: Teacher-forced one-step intervention audit, 7488 samples. Values are RMSE after substituting mechanism variables into the same trained operator; ratios are relative to the learned mechanism. Single seed ; see § 4 .
Figure 8: Zero-shot transfer as a function of graph size. State rollout RMSE, routing-gate MAE and regime accuracy for CHGN, the Shared Conservative GNN and the Shared Dynamic GNN on unseen 25 – 40 -node process graphs. Dashed lines are descriptive least-squares trends. CHGN remains substantially more accurate across the full range of graph sizes.
Figure 9: Seed robustness of zero-shot transfer. Circles show independently trained model seeds; diamonds and bars show the mean and 95% Student- t interval. CHGN retains a lower state-rollout RMSE and routing-gate MAE, and higher regime accuracy, than both shared-weight baselines across seeds.
Method
State RMSE ↓
Gate MAE ↓
Regime acc. ↑
CHGN (zero-shot)
(2.118±0.230)×10−3
(7.861±1.218)×10−3
94.27±0.49%
Retrained per graph
MLP
0.07483±0.00712
0.12386±0.01117
55.71±9.13%
LSTM
0.05374±0.00951
0.09535±0.01492
59.82±7.15%
Fixed GNN
0.04395±0.01769
0.32299±0.02731
92.84±2.13%
Dynamic GNN
0.03051±0.00924
0.02101±0.00832
95.62±1.14%
Appendix
Table 4: Secondary graph-specific reference. CHGN is evaluated zero-shot on the eight held-out topologies (mean ± s.d. across five seeds, each averaged over all graphs). In contrast, the listed comparators are retrained from scratch on each held-out graph (mean ± s.d. across eight single-seed fits). Bold marks the zero-shot reference row; values in the two blocks are not directly comparable. These values complement, but do not replace, the matched shared-weight zero-shot comparison of § 3.1 .
Figure 10: Fixed-graph predictive benchmark. Circles show independent seeds; diamonds and bars show the mean and 95% Student- t interval. Error metrics use logarithmic axes. On this fixed graph, the LSTM leads panels (a), (b), and (d).
Physics-informed graph neural networks encode equations, conservation laws, and boundary conditions into graph models for scientific prediction and simulation.
Routability prediction enables rapid evaluation of placement quality without routing, providing effective feedback for routability-driven placement optimization. Recent machine learning methods have achieved efficient routability prediction through data-driven approach. However, their prediction performance highly depends on the capability of input representations to capture essential circuit information. To address the limitations of existing circuit representations in simultaneously preserving logical topology, physical layout and routing resource information, this paper proposes HGRP, a heterogeneous graph neural network for routability prediction. HGRP models the cells, nets, and routing grids as distinct types of nodes and explicitly represents topological connectivity, spatial mapping, and grid adjacency, thereby constructing a heterogeneous graph representation that preserves multi-level circuit semantics. Based on the representation, a heterogeneous message passing mechanism is developed to enable information interaction and feature fusion among distinct types of nodes, effectively learning the complex correlations between circuit structures and routing behaviors. Experimental results on the CircuitNet dataset show that HGRP improves F1-score by 18.69% relative improvements compared with the state-of-the-art in the congestion prediction task. The source code is publicly available at https://github.com/ShenShan123/HGPR.
Yule Sheng, Yue Yuan, Shan Shen +1
Nanjing University of Science and Technology, Nanjing, China
Real-time supervisory control of advanced reactors requires accurate forecasting of plant-wide thermal-hydraulic states, including locations where physical sensors are unavailable. Meeting this need calls for surrogate models that combine predictive fidelity, millisecond-scale inference, and robustness to partial observability. In this work, we present a physics-informed message-passing Graph Neural Network coupled with a Neural Ordinary Differential Equation (GNN-ODE) to addresses all three requirements simultaneously. We represent the whole system as a directed sensor graph whose edges encode hydraulic connectivity through flow/heat transfer-aware message passing, and we advance the latent dynamics in continuous time via a controlled Neural ODE. A topology-guided missing-node initializer reconstructs uninstrumented states at rollout start; prediction then proceeds fully autoregressively. The GNN-ODE surrogate achieves satisfactory results for the system dynamics prediction. On held-out simulation transients, the surrogate achieves an average MAE of 0.91 K at 60 s and 2.18 K at 300 s for uninstrumented nodes, with R2 up to 0.995 for missing-node state reconstruction. Inference runs at approximately 105 times faster than simulated time on a single GPU, enabling 64-member ensemble rollouts for uncertainty quantification. To assess sim-to-real transfer, we adapt the pretrained surrogate to experimental facility data using layerwise discriminative fine-tuning with only 30 training sequences. The learned flow-dependent heat-transfer scaling recovers a Reynolds-number exponent consistent with established correlations, indicating constitutive learning beyond trajectory fitting. The model tracks a steep power change transient and produces accurate trajectories at uninstrumented locations.
Akzhol Almukhametov, Doyeong Lim, Rui Hu +1
Department of Nuclear Engineering, Texas A&M University, College Station, TX 77843, USA · Argonne National Laboratory, Nuclear Science and Engineering Division, USA
Building machine-learning models for estimating traffic flows from OD matrices requires an appropriate design of the training process and a training dataset spanning over multiple regimes and dynamics. As machine-learning models rely heavily on historical data, their predictions are typically accurate only when future traffic patterns resemble those observed during training. However, their performance often degrades when there is a significant statistical discrepancy between historical and future conditions. This issue is particularly relevant in traffic forecasting when predictions are required for modified versions of the network, where the underlying graph structure changes due to events such as maintenance, public demonstrations, flooding, or other extreme disruptions. Ironically, these are precisely the situations in which reliable traffic predictions are most needed. In the presented work, we combine a machine-learning model (graph convolutional neural network) with a meta-learning architecture to train the former to quickly adapt to new graph structures and demand patterns, so that it may easily be applied to scenarios in which changes in the road network (the graph) and the demand (the node features) happen simultaneously. Our results show that the use of meta-learning allows the graph neural network to quickly adapt to unseen graphs (network closures) and OD matrixes while easing the burden of designing a training dataset that covers all relevant patterns for the practitioners. The proposed architecture achieves a R^2 of around 0.85 over unseen closures and OD matrixes.
Serio Agriesti, Guido Cantelmo, Francisco Camara Pereira
Department of Technology, Management and Economics, Technical University of Denmark, Lyngby, Denmark