Development and Assessment of Machine Learning Techniques for Non-Intrusive Probabilistic Surrogate Modeling of High-Fidelity Nuclear Reactor Simulations

Abstract

With the continuing advancement of computational resources, high-fidelity simulations of neutron transport play an increasingly important role in the design and analysis of nuclear reactor cores. Because of the inherent non-linear interdependency of the flux solution on the coolant properties, neutron transport solvers are often coupled to subchannel thermal-hydraulics or computational fluid dynamic solvers to capture the necessary physics.

The challenges present in numerical simulations required for nuclear reactor design, specifically the high computational cost and dimensionality encountered, are not unique to nuclear engineering. A full-order model is often expensive to evaluate in many engineering disciplines, particularly if the governing equations contain non-linear terms. The discretization of these partial differential equations leads to large systems of coupled equations.

This limitation has led to the development and deployment of reduced-order modeling techniques. For decades, reduced-order models (ROM) have experienced a wide variety of successes in many fields and have been demonstrated for a wide range of applications. These techniques are not typically applied in the nuclear engineering field, particularly in production environments. Importantly, they have not been applied to high-fidelity multiphysics simulations of nuclear reactors.

This work investigates the current state-of-the-art of ROMs and investigates their applicability to commonly encountered nuclear reactor design applications. Specifically, multi-stage convolutional neural network-based ROMs and the newly proposed Non-Linear Independent Dual System (NIDS) algorithm. The following chapters contain a discussion of traditional intrusive projection-based ROMs and works its way to non-intrusive neural network-based ROM methods. This work includes discussions on the theory, merits, challenges, and limitations associated with various methodologies. Furthermore, the uncertainty associated with reducing high-dimensional multiphysics problems is quantified using probabilistic modeling techniques combined with neural network-based ROMs. Specifically, variational inference approaches were applied to the ROMs.

Using current state-of-the-art methods in non-intrusive ROMs, coupled with variational inference methods, ROMs are developed for two representative classes of nuclear engineering problems. The first application is a coupled MPACT/CTF model representing a single-assembly configuration experiencing a reactivity insertion accident via rod ejection. The state variables of interest are time-dependent relative pin powers. The second application is a 3D quarter-core MC21 depletion model. The state variables of interest are isotopic depletion trajectories. The performance of associated ROMs are assessed to evaluate the efficacy of using non-intrusive neural network-based ROMs in production design environments. In all contexts analyzed, NIDS methods are shown to outperform convolutional neural network-based algorithms for nuclear engineering applications and perform to a level acceptable in certain production design environments. Finally, a new Python package, Parody, is introduced to facilitate the assessment of ROMs and its potential use for further study of ROMs for nuclear applications is presented and discussed.