Learning nonlinear operators in latent spaces for real-time prediction of coolant temperature in small modular high-temperature gas-cooled reactors

In the field of nuclear thermal propulsion reactor engineering, real-time prediction of complex multi-physics temperature fields remains a critical challenge. To address this issue, this study proposes a latent space neural operator (L-DeepONet)-based approach for real-time prediction of temperature fields in nuclear thermal propulsion reactors. A lightweight "encoder-operator learning-decoder" framework is constructed by coupling an autoencoder (AE) with a deep operator network (DeepONet). First, high-dimensional temperature fields are compressed into a 100-dimensional latent space using AE. Subsequently, DeepONet is trained in the low-dimensional space to learn coolant dynamic evolution patterns. Finally, high-fidelity reconstruction of predictions is achieved through the decoder. Validation using OpenFOAM-generated coolant temperature field datasets demonstrates that the method achieves average relative errors below 1% for fuel temperature fields in both 40-second iterative predictions and 100-second long-term predictions, with errors for coolant and cladding below 0.5%. The training time of 79.23-192.83 seconds represents a two-order-of-magnitude acceleration compared to traditional CFD simulations, enabling real-time single-step long-term prediction with error distributions concentrated in gradient-sensitive regions. This work innovatively introduces latent space operator learning into multi-physics modeling of nuclear thermal propulsion reactors and achieves real-time prediction. The framework provides insights for real-time simulation and decision-making under extreme operating conditions, and can be extended to neutronics-thermomechanical coupling scenarios, offering new pathways for digital twin applications in advanced nuclear systems.

在核热推进反应堆工程领域，复杂多物理场温度场的实时预测仍是一项关键挑战。针对这一问题，本研究提出了一种基于隐空间神经算子（Latent Space Neural Operator，L-DeepONet）的核热推进反应堆温度场实时预测方法。本研究将自动编码器（Autoencoder，AE）与深度算子网络（Deep Operator Network，DeepONet）相结合，构建了轻量化的「编码器-算子学习-解码器」框架。首先，通过自动编码器将高维温度场压缩至100维隐空间；随后，在低维隐空间中训练深度算子网络，以学习冷却剂的动态演化规律；最终通过解码器实现预测结果的高保真重建。利用OpenFOAM生成的冷却剂温度场数据集进行验证的结果表明：该方法在40秒迭代预测与100秒长期预测场景下，燃料温度场的平均相对误差均低于1%，冷却剂与包壳温度场的误差则低于0.5%。该方法的训练时长为79.23~192.83秒，相较于传统计算流体动力学（Computational Fluid Dynamics，CFD）模拟实现了两个数量级的加速，可实现实时单步长期预测，且误差分布集中于梯度敏感区域。本研究创新性地将隐空间算子学习引入核热推进反应堆的多物理场建模中，实现了温度场的实时预测。该框架为极端工况下的实时模拟与决策提供了理论参考，且可拓展至中子学-热机械耦合场景，为先进核系统的数字孪生应用开辟了新路径。