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An Adaptive-Horizon Graph Neural Operator for coupled surrogate morphodynamic modelling

Ying Cao, Yifan Yang, Junqiang Xia, Julia C. Mullarney, Mário J. Franca

arXiv:2610.22432v2physics.comp-phcs.LG

TL;DR

Repeated process-based morphodynamic simulations are costly, and learned approaches may not provide distributed bed updates within a coupled solver. AH-GNO adapts its temporal history and write-back horizon while retaining TELEMAC-2D feedback; across the tested cases it preserves main bed-evolution patterns and substantially accelerates bed updating.

  • Problem

    Repeated process-based morphodynamic calculations are costly for large domains and multi-scenario studies, while decoupled bed prediction can drift from the coupled trajectory through cumulative errors.

    Source: §1 · p. 2

  • Method

    AH-GNO predicts bed-elevation increments on unstructured meshes, adaptively selecting history and write-back horizon from flow-bed state while retaining TELEMAC-2D feedback.

    Source: §5 · p. 25

  • Results

    Across Bump, Yen, and Waiho, AH-GNO preserved main bed-evolution patterns and achieved approximately 346, 150, and 360 times speedups, respectively, relative to 4-core GAIA.

    Source: §5 · p. 25

  • Takeaways & Limitations

    AH-GNO provides an accelerated bed-updating component for coupled simulations while retaining hydrodynamic feedback from TELEMAC-2D.

    Source: §5 · p. 25

    AH-GNO omits explicit sediment-state variables, so its supported scope is bed updating under the sediment closures and state assumptions of the reference GAIA simulations.

    Source: §4.1 · p. 21

Abstract

from arXiv · show

Morphodynamic simulations require repeated coupling between hydrodynamic solvers, sediment transport modules, and bed updating. For long duration, multi-scenario simulations on large unstructured meshes, such coupling is computationally demanding. This study proposes an Adaptive-Horizon Graph Neural Operator (AH-GNO) that formulates bed evolution as a graph operator learning problem from recent hydrodynamic and topographic states to predict future bed elevation increments. The model operates directly on the native unstructured meshes. The approach integrates area-weighted graph learning, historical state selection, and forecast horizon estimation, allowing the effective history length (K) and update interval (B) to vary with the evolving flow and bed state. Using Telemac2D/GAIA solutions as supervised numerical references, the framework is evaluated on the official Bump and Yen bend benchmarks and on a field-scale application (Waiho River, New Zealand). Results show that the AH-GNO reproduces the main patterns of bedform migration, bend-scale erosion and deposition, and localized bed adjustment. Across the three cases, the tested CPU-GPU deployment reduced post-training bed-update workflow time from 12~1204 s with GAIA to 0.08~3.34 s with AH-GNO. This improvement corresponds to deployment-specific accelerations of approximately 150~360 times relative to 4-core GAIA CPU configurations, and with 105~186 times gains for 20-core CPU configurations. These results suggest that, while retaining hydrodynamic feedback from TELEMAC-2D, a learned operator for bed updating can provide an efficient acceleration component for morphodynamic scenario analysis and rapid coupled simulation.

1 Introduction

River morphodynamic simulation is computationally demanding, while many existing learning approaches predict local sediment or hydraulic quantities rather than distributed bed updates inside a coupled solver. This study introduces AH-GNO to adapt its temporal history and forecast horizon to evolving flow and bed states.

1 Introduction

  • Repeated hydrodynamic, sediment-transport, and bed-update calculations make large-domain and multi-scenario process-based morphodynamic simulations costly.The burden is especially pronounced for refined or unstructured meshes and realistic river geometries.Source: §1 · p. 2
  • Existing sediment-learning models often target point or cross-section quantities, not mesh-based bed updates within a coupled solver; decoupled bed prediction can drift under cumulative errors.Embedding a surrogate as an accelerated bed update retains hydrodynamic feedback from the process model.Source: §1 · p. 2
  • Neural operators represent spatially distributed mappings, while graph-based approaches can work with irregular meshes and their connectivity.Neural operators are described as largely discretization-independent in principle, unlike mappings tied to a fixed grid or node set.Source: §1 · pp. 2–3
  • Fixed temporal windows apply one time scale to different evolutionary states, although rapid adjustment calls for shorter forecasts and stable evolution can support longer horizons.This mismatch can waste computation during stable periods and risk unreliable extrapolation during rapid adjustment.Source: §1 · p. 3
  • AH-GNO predicts bed-elevation changes on native unstructured meshes and adaptively selects effective history and forecast horizon within a TELEMAC-2D/GAIA workflow.The study evaluates it on Bump and Yen benchmarks and the Waiho River, including comparison with a non-adaptive one-step graph-operator counterpart.Source: §1 · p. 3

2 Adaptive-Horizon Graph Neural Operator

AH-GNO replaces only the bed-evolution update within the TELEMAC-2D/GAIA workflow, learning bed-elevation increments from coupled flow–bed histories on the native mesh. Its area-weighted graph operator and state-dependent history and write-back horizons tailor updates to evolving conditions.

2.1 Reference morphodynamic solver: TELEMAC-2D/GAIA

  • AH-GNO replaces GAIA’s bed-evolution update by mapping recent coupled flow–bed states to future bed-elevation increments, while TELEMAC-2D continues solving hydrodynamics.Predicted increments are accumulated and written back to the TELEMAC bed field.Source: §2.1 · p. 4, §2.6 · p. 10

2.2 Graph formulation and input-output representation

  • Each mesh node receives a lumped control area used in graph aggregation, training loss, and evaluation, approximating physical-domain integration and reducing sensitivity to mesh density.The area weighting reduces the influence of nonuniform mesh density and local refinement compared with simple node averaging.Source: §2.2 · p. 5

2.3 Adaptive-Horizon Graph Neural Operator (AH-GNO)

  • The encode–process–decode architecture lifts historical nodal states, selects their temporal contributions, applies graph integral layers, and decodes bed increments and a write-back horizon.The temporal selector and horizon head make history length and forecast horizon state-dependent.Source: §2.3 · p. 5

2.4 Adaptive temporal bundling method

  • AH-GNO infers effective history and write-back length from the current state, using shorter horizons during rapid adjustment and longer horizons during slow or near-equilibrium evolution.The horizon head separates predicting a full increment sequence from deciding how many increments to apply, balancing fewer calls in slow periods against long-extrapolation risk during rapid adjustment.Source: §2.3 · p. 7, §2.4 · p. 8

2.5 Loss function

  • Training combines an area-weighted prediction loss with horizon supervision, while activity weighting emphasizes changing bed regions and a Huber penalty moderates localized large residuals.The horizon pseudo-label records how far the bundled prediction remains within tolerance of the reference.Source: §2.5 · pp. 8–9

2.6 Online coupling

  • During online coupling, TELEMAC-2D advances flow over the updated bed and remains in the loop, preserving feedback between hydrodynamics and bed evolution.AH-GNO predicts bed changes that are written back to TELEMAC-2D; it is not an open-loop neural time-series generator.Source: §2.6 · p. 10

2.7 Implementation details

  • The coupled framework uses TELEMAC-MASCARET V8P4R0 and AH-GNO implemented in Python 3.12 and PyTorch 2.5.1, with production runs on an RTX 4090 GPU and 20 allocated CPU cores.The implementation runs under Ubuntu 22.04 with CUDA 12.4 and exchanges fields through a Python interface using Selafin format.Source: §2.7 · p. 10

3 Benchmark Design and Evaluation Results

Across the Bump, Yen bend, and Waiho cases, AH-GNO reproduces major bed-change patterns while reducing bed-update runtime. Its evaluation also tests cross-mesh performance, which remains sensitive to mesh layout and localized change.

3.1 Benchmark cases, scenario design, and data construction

  • The evaluation uses two official TELEMAC-2D/GAIA benchmarks and a field-scale Waiho case, with scenario-level splits and native unstructured-mesh bed-increment predictions.Bump and Waiho each use six training, one validation, and one test scenario; Yen uses 12, 4, and 4, respectively.Source: §3.1 · pp. 10–12, Figure 3 · p. 11, Figure 4 · p. 12

3.2 Benchmark 1: flow over a bump

  • AH-GNO reproduces the Bump bedform’s migration and lateral spreading; RMSE relative to GAIA rises from 0.0002 m at 1500 min to 0.0007 m at 6000 min.Its spreading angle is 26.04° versus GAIA’s 25.76°, while both exceed the 21.787° analytical reference.Source: §3.2 · p. 13, Figure 6 · p. 15

3.3 Benchmark 2: Yen 180° bend

  • In the Yen bend, AH-GNO captures outer-bank erosion and inner-bank deposition; its area-weighted RMSE relative to GAIA stabilizes at 10^-4 to 10^-3 m.Both AH-GNO and GAIA underrepresent large changes near the 90° section edges relative to laboratory measurements, which AH-GNO learns from GAIA rather than experiments.Source: §3.3 · pp. 13, 15, Figure 8 · p. 17

3.4 Benchmark 3: braided river

  • At 30 h in Waiho, AH-GNO preserves the main erosion corridors and depositional belts, with domain-mean bed change of -0.027 m versus GAIA’s -0.028 m.Transects retain main peaks and erosion features, but localized extremes are smoother; the study’s controlled setup excludes external sediment supply.Source: §3.4 · pp. 15, 17, Figure 9 · p. 18, Figure 10 · p. 19

3.5 Runtime performance in coupled simulations

  • AH-GNO ran in 0.66 s (Bump), 0.08 s (Yen), and 3.34 s (Waiho), with 4-core GAIA speedups of approximately 346, 150, and 360 times, respectively.These are post-training online bed-update workflow comparisons; speedups vary with hardware configuration and case.Source: §3.5 · p. 19, Figure 11 · p. 20

3.6 Discretization consistency

  • Across four Yen meshes, mean area-weighted R2 ranges from approximately 0.951 to 0.998, with an overall mean of about 0.987; the irregular mesh averages 0.981.The test does not establish strict mesh independence: predictions remain sensitive to node distribution and local irregularity, especially for localized bed changes.Source: §3.6 · p. 21

4 Discussion

AH-GNO is presented as a bed-update operator for controlled sediment settings, with limits tied to omitted sediment state, conservation, and reference-model assumptions. The discussion proposes richer sediment inputs, stronger error control, broader testing, and more efficient coupling as future work.

4.1 Limitations

  • AH-GNO omits explicit sediment-state inputs and is best interpreted under the sediment closure and controlled conditions of its GAIA training cases, not across all sediment regimes.The study identifies bed-load-dominated benchmarks and a controlled field-scale redistribution test as the conditions supporting the present results.Source: §4.1 · pp. 21, 23, 24
  • The Waiho experiment excludes external sediment replenishment, so it compares erosion and deposition patterns against GAIA rather than predicting the river’s natural sediment budget.The upstream supply cutoff was used because field inputs, transport relations, and boundary supply are uncertain.Source: §4.1 · p. 24
  • GAIA serves as a process-based numerical reference, not observational truth, and systematic GAIA bias or omitted external supply can carry into the surrogate comparison..Source: §4.1 · p. 24
  • Because AH-GNO predicts bed increments without sediment flux or flux divergence, it does not enforce Exner mass conservation; long rollouts warrant monitoring accumulated volume and boundary errors.Source: §4.1 · p. 24
  • Online hydrodynamic feedback limits but does not eliminate accumulated bed error; systematic surrogate bias can persist, with larger errors expected in shallow, boundary, wetting-drying, and localized active-bed areas.Source: §4.1 · p. 24
  • The Yen multi-mesh results indicate practical mesh robustness, not strict mesh independence; error control remains important for localized bed change or target meshes far from training discretizations.Coordinates, relative-position kernels, and area weights support parameter reuse across different node counts and mesh densities.Source: §4.1 · p. 24

4.2 Future Work

  • Future work proposes adding sediment-state and transport-capacity features, conservation constraints and error monitors, and state- and error-informed adaptation of the K/B policy.Source: §4.2 · pp. 24–25
  • Broader tests across river settings and sediment conditions are needed; a coupled hydrodynamic surrogate could further improve efficiency but would make stability and error control harder.Source: §4.2 · p. 25

5 Conclusions

Across the Bump, Yen, and Waiho cases, AH-GNO preserves the main bed-evolution patterns and substantially accelerates post-training bed updates. It operates as an online bed-update operator within TELEMAC-2D, while its demonstrated scope remains bed-load-dominated conditions under a fixed transport closure.

5 Conclusions

  • The method predicts bed-elevation increments on native unstructured meshes using area-weighted graph integration and adaptive history and forecast horizons inferred from the current flow-bed state.TELEMAC-2D remains in the loop and recomputes hydrodynamics after bed updates.Source: §5 · p. 25
  • AH-GNO achieved speedups of approximately 346, 150, and 360 times over 4-core GAIA for Bump, Yen, and Waiho, and approximately 186, 112, and 105 times over 20-core GAIA.These are post-training bed-update workflow speedups.Source: §5 · p. 25
  • AH-GNO preserves main bed-evolution patterns across the three cases, while smoothing sharp scour troughs and depositional margins; mean area-weighted R2 across four Yen meshes is 0.981 to 0.993.Source: §5 · p. 25
  • The evidence supports AH-GNO as a bed-update acceleration component under fixed, bed-load-dominated transport conditions, not as a complete replacement for morphodynamic models.The model does not explicitly predict sediment flux or impose Exner mass conservation.Source: §5 · p. 25

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