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

arXiv: https://arxiv.org/abs/2604.07292 · HTML: https://mlsanity.com/paper/2604.07292/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 49 references that are in the map.
- First posted on arXiv 8 Apr 2026.

## Builds on (most cited first, 11 of 11)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [Development and Assessment of a Nearly Autonomous Management and Control System for Advanced Reactors](https://mlsanity.com/paper/2008.12888/) (2020)
- [An AI-Driven Thermal-Fluid Testbed for Advanced Small Modular Reactors: Integration of Digital Twin and Large Language Models](https://mlsanity.com/paper/2507.06399/) (2025)
- [A Safe Reinforcement Learning Algorithm for Supervisory Control of Power Plants](https://mlsanity.com/paper/2401.13020/) (2024)
- [Design of a Supervisory Control System for Autonomous Operation of Advanced Reactors](https://mlsanity.com/paper/2209.04334/) (2022)
- [Stable and Safe Human-aligned Reinforcement Learning through Neural Ordinary Differential Equations](https://mlsanity.com/paper/2401.13148/) (2024)
- [Automating Data-Driven Modeling and Analysis for Engineering Applications using Large Language Model Agents](https://mlsanity.com/paper/2510.01398/) (2025)
- [AutoSAM: an Agentic Framework for Automating Input File Generation for the SAM Code with Multi-Modal Retrieval-Augmented Generation](https://mlsanity.com/paper/2603.24736/) (2026)

## Abstract (arXiv)

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.