Predicting fuel assembly bow in pressurized water reactors requires solving tightly coupled fluid-structure interaction problems, whose direct simulations can be computationally prohibitive, making large-scale uncertainty quantification (UQ) very challenging. This work introduces a general mathematical framework for coupling Gaussian process (GP) surrogate models representing distinct physical solvers, aimed at enabling rigorous UQ in coupled multiphysics systems. A theoretical analysis establishes that the predictive variance of the coupled GP system remains bounded under mild regularity and stability assumptions, ensuring that uncertainty does not grow uncontrollably through the iterative coupling process. The methodology is then applied to the coupled hydraulic-structural simulation of fuel assembly bow, enabling global sensitivity analysis and full UQ at a fraction of the computational cost of direct code coupling. The results demonstrate accurate uncertainty propagation and stable predictions, establishing a solid mathematical basis for surrogate-based coupling in large-scale multiphysics simulations.

翻译：预测压水反应堆中燃料组件的弯曲行为需要求解强耦合的流固相互作用问题，其直接模拟计算成本极高，使得大规模不确定性量化面临严峻挑战。本研究提出了一种通用的数学框架，用于耦合代表不同物理求解器的高斯过程代理模型，旨在实现耦合多物理场系统中严格的不确定性量化。理论分析表明，在温和的正则性与稳定性假设下，耦合高斯过程系统的预测方差保持有界，从而确保不确定性不会在迭代耦合过程中无限制增长。该方法随后应用于燃料组件弯曲的耦合水力-结构模拟，以远低于直接代码耦合的计算成本实现了全局敏感性分析和完整的不确定性量化。结果证明了准确的不确定性传播与稳定的预测性能，为大规模多物理场模拟中基于代理模型的耦合方法奠定了坚实的数学基础。