Conservative Hybrid Graph Networks for Process Systems with Learned Routing

Paolo Guida

cs.LGAug 28, 2026

Conservative Hybrid Graph Networks for Process Systems with Learned Routing

Authors: Paolo Guida

Organizations: Physical Science and Engineering King Abdullah University of Science and Technology (KAUST) Thuwal, Saudi Arabia

Abstract

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 $\downarrow$	Gate MAE $\downarrow$	Regime acc. $\uparrow$
Joint CHGN	$0.01267\pm 0.00108$	$0.01225\pm 0.00234$	$96.37\pm 1.18\%$
State only	$0.01564\pm 0.00294$	$0.02985\pm 0.01535$	$45.26\pm 8.00\%$
Gate supervision	$0.01337\pm 0.00199$	$0.01357\pm 0.00189$	$42.08\pm 10.06\%$
Regime supervision	$0.01690\pm 0.00246$	$0.02639\pm 0.00745$	$93.51\pm 2.58\%$
Fixed routing	$0.05293\pm 0.00454$	$0.20051$	$73.74\pm 2.97\%$
Fixed regimes	$0.01221\pm 0.00303$	$0.01499\pm 0.00208$	$30.66\%$

Table 1: Mechanism ablations. Mean

\pm

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 $\downarrow$	Gate MAE $\downarrow$	Regime acc. $\uparrow$	Balance disc. $\downarrow$
CHGN	$0.01267\pm 0.00108$	$0.01225\pm 0.00234$	$96.37\pm 1.18\%$	$0.01983\pm 0.00394$
LSTM	$\mathbf{0.00520\pm 0.00035}$	$\mathbf{0.00621\pm 0.00037}$	$94.34\pm 0.22\%$	$\mathbf{0.01091\pm 0.00082}$
MLP	$0.01630\pm 0.00131$	$0.01661\pm 0.00218$	$92.97\pm 0.31\%$	$0.01574\pm 0.00121$
Dynamic GNN	$0.03421\pm 0.00035$	$0.01072\pm 0.00020$	$\mathbf{96.57\pm 0.11\%}$	$0.11376\pm 0.00157$
NHA-inspired	$0.03437\pm 0.00037$	$0.01061\pm 0.00028$	$96.35\pm 0.12\%$	$0.11430\pm 0.00133$
NRI-inspired	$0.05192\pm 0.00032$	$0.05263\pm 0.00378$	$91.64\pm 0.63\%$	$0.11667\pm 0.00220$

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

\mathbf{1}^{\top}B\hat{\mathbf{F}}

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	$4.115\times 10^{-4}$	$4.627\times 10^{-4}$	$1.084\times 10^{-4}$
Oracle: both	$4.239\times 10^{-4}$	$4.847\times 10^{-4}$	$0.778\times 10^{-4}$
Oracle: routing only	$4.240\times 10^{-4}$	$4.847\times 10^{-4}$	$0.786\times 10^{-4}$
Oracle: regimes only	$4.115\times 10^{-4}$	$4.627\times 10^{-4}$	$1.079\times 10^{-4}$
Fixed: regimes only	$4.441\times 10^{-4}$	$4.622\times 10^{-4}$	$3.890\times 10^{-4}$
Fixed: routing only	$1.932\times 10^{-3}$	$2.710\times 10^{-3}$	$9.620\times 10^{-4}$

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 $\downarrow$	Gate MAE $\downarrow$	Regime acc. $\uparrow$
CHGN (zero-shot)	$\mathbf{(2.118\pm 0.230)\times 10^{-3}}$	$\mathbf{(7.861\pm 1.218)\times 10^{-3}}$	$\mathbf{94.27\pm 0.49\%}$
Retrained per graph
MLP	$0.07483\pm 0.00712$	$0.12386\pm 0.01117$	$55.71\pm 9.13\%$
LSTM	$0.05374\pm 0.00951$	$0.09535\pm 0.01492$	$59.82\pm 7.15\%$
Fixed GNN	$0.04395\pm 0.01769$	$0.32299\pm 0.02731$	$92.84\pm 2.13\%$
Dynamic GNN	$0.03051\pm 0.00924$	$0.02101\pm 0.00832$	$95.62\pm 1.14\%$

Appendix

Table 4: Secondary graph-specific reference. CHGN is evaluated zero-shot on the eight held-out topologies (mean

\pm

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

\pm

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).

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HGRP: Heterogeneous Graph Neural Network for Routability Prediction

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Open paper AskPDF arXiv

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.

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