arXiv:2604.07292cs.LG2026-04

用图神经网络与微分方程建模反应堆热工状态,实现毫秒级预测且能补全无传感器位置。

Graph Neural ODE Digital Twins for Control-Oriented Reactor Thermal-Hydraulic Forecasting Under Partial Observability

论文配图:Graph Neural ODE Digital Twins for Control-Oriented Reactor Thermal-Hydraulic Forecasting Under Partial Observability
图 1 · 摘自论文原文
  • 构建带物理约束的图神经网络-微分方程模型,通过消息传递模拟流热耦合关系。
  • 在未测点上300秒内平均误差仅2.18K,R²高达0.995,推理速度超仿真105倍。
  • 可迁移至真实实验数据,学习到符合经典公式的传热规律,适合控制闭环应用。

先进反应堆实时监控需准确预测全厂热工状态,包括无传感器位置。本文提出物理信息引导的图神经网络-神经常微分方程(GNN-ODE)模型,同时满足高精度、毫秒级推理和部分可观测性鲁棒性。系统以有向传感器图为结构,边编码流/热传递连通性,通过可控神经ODE连续演进隐状态。采用拓扑引导的缺失节点初始化器重建起始状态,后续完全自回归推演。在保留仿真瞬态测试中,未测点60秒平均绝对误差为0.91K,300秒为2.18K,缺失状态重建的R²最高达0.995。单卡推理速度比仿真快约105倍,支持64样本集合推演用于不确定性量化。通过仅30条序列的分层判别微调,模型成功适配实验设施数据,学习到与雷诺数相关性一致的传热系数指数,体现超越轨迹拟合的物理规律学习能力。模型能准确追踪陡峭功率变化,预测未测点轨迹。

原文摘要 · Abstract (English)

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 $R^2$ 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.

图神经网络热工预测数字孪生控制应用

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