Development of statistical mechanics emulators for system analysis and uncertainty quantification in nuclear engineering

Abstract

Despite the tremendous growth of computational resources in recent years, the "curse of dimensionality'' associated with the canonical evolutionary partial differential equations in nuclear reactor engineering and thermal-hydraulics such as the direct solution to non-linear Navier-Stokes equations is still a challenge to tackle. To solve this fundamental problem and to get a reasonable answer in the time-constrained engineering design and optimization process, reduced spatio-temporal complexity models are required. Typically, this is done by linearization and spatio-temporal averaging of parameters in the context of thermal-hydraulic applications. This procedure may lead to an inaccurate depiction of the system behavior--with a number of structural errors in the model. These structural errors can also arise because of the principles on which the model relies. Since it is almost impossible to completely decipher the principles on which the model rests, and a certain degree of distortion is always required to build a system of equations. This approximated view of the reality is the basis of many engineering system simulations toolboxes such as RELAP and TRACE--which can lead to a tremendous amount of uncertainties in the quantities of interests. The gap between the reality and approximated system is typically bridged by uncertainty quantification routes which rely on black-box approaches, such as constructing low-cost regression surrogates or emulators and conducting sensitivity studies with those surrogates.\par To tackle these uncertainties, this work takes a unique approach of using the high-resolution datasets to learn the dynamics of uncertainties with a statistical mechanics approach. While doing so, it is inherently assumed that the Navier-Stokes equation is a structurally perfect and correct model. The unique contribution in the general context of nuclear engineering is the constraining of non-linear Langevin equation on the high-resolution datasets via the non-equilibrium statistical mechanics route. This is achieved by computing the parameters of the model via solving an inverse problem through the utilization of the Kramers-Moyal expansion method. These statistical mechanics equations are used to quantify uncertainties in the scalar dispersion. A similar approach is used to emulate grid load pattern and renewable energy generation, and the emulators are integrated with established reactor system models to design a novel stochastic control strategy.