Uncertainty Quantification in Coupled Multiphysics Systems via Gaussian Process Surrogates: Application to Fuel Assembly Bow

TL;DR

The paper tackles uncertainty quantification for tightly coupled multiphysics systems by embedding Gaussian Process surrogates for each solver into a fixed-point coupling framework, and proving that the coupled predictive variance remains bounded under mild regularity via a contraction with modulus $\varrho<1$. A theoretical analysis connects GP posterior variance to fill distance for Matérn kernels and establishes Lipschitz stability of the coupled solution map, yielding a finite-sample, high-probability bound on Monte Carlo outputs. The methodology is validated on an analytical benchmark and then applied to fuel-assembly bow in a two-solver hydraulic–mechanical FSI setting, showing that surrogate-induced uncertainty is small (e.g., $\sim$0.26 mm) compared with input-driven deformation scales and that using GP mean predictors is both accurate and computationally efficient. Overall, the work provides a rigorous, surrogate-based pathway for large-scale UQ in coupled multiphysics simulations with practical implications for reactor safety analyses.

Abstract

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.

Figures (17)

• Figure 1: Surrogates for the two scalar codes in the benchmark example, for smallDOE ($n=20$) and largeDOE ($n=200$). Deterministic training data, GP means and $\pm2\upsigma$ bands are shown together with the true responses.
• Figure 2: Distribution of the coupled solution $y$ for Method 2 (rigorous trajectory-conditioned sampling) and Method 3 (mean-path constant offsets) on the benchmark example, for smallDOE ($n=20$, left) and largeDOE ($n=200$, right). The vertical line indicates the reference solution $y^\star$.
• Figure 3: Schematic view of a fuel assembly (around 4m high) with spacer grids abboudd2025
• Figure 4: Hydraulic network model for a row of 15 fuel assemblies under reactor operation (inlet and outlet) conditions delam2021
• Figure 5: Uncertainty of the coupled GP in a simulation of a row of 15 fuel assemblies

Theorems & Definitions (20)

• Definition 1: Computational solvers
• Definition 2: Transfer operators
• Definition 3: Coupling operator
• Proposition 1: Banach fixed-point theorem zeidler1986nonlinear
• Definition 4: Iterative termination
• Definition 5: Fill distance
• Theorem 1: Posterior mean and covariance for multi-output GP regression micchelli2005alvarez2012
• Proposition 2: RKHS of Matérn kernels kanagawa2018
• Theorem 2: Scalar fill-distance bound, Kanagawa et al. kanagawa2018
• Theorem 3: Using LMC representation a lift of Kanagawa’s scalar bound to multi-output GPs