Dean Price

Will Savage, Logan Burnett, Dean Price

The validation of advanced nuclear reactor designs and fuel concepts requires critical experiments with high neutronic similarity to the target technology. Neutronic similarity is quantified by the correlation coefficient $c_k$, which captures the shared bias in $k_\text{eff}$ induced by uncertainties in nuclear data. Generally, a $c_k\geq0.9$ is needed for an experiment to be sufficiently similar to a target technology. This work presents a methodology for the inverse design of critical experiments. Deep neural network surrogate modeling and nonparametric gradient optimization are used to generate experiment geometries that maximize $c_k$. A deep neural network is trained on OpenMC-calculated sensitivity vectors for grid-based critical experiment geometries. The model architecture combines a U-Net convolutional encoder-decoder with a novel multigroup attention pooling layer, introduced to capture the differing spatial dependencies of sensitivities. Multigroup attention pooling is shown to achieve better performance than traditional pooling, as well as interpretable internal behavior. The differentiability of the surrogate enables gradient-based optimization of the full combinatorial design space, allowing $c_k$ to be maximized by directly changing the material assignment of each position in the geometry grid. The method is applied to the validation of the TN-Americas TN-LC transportation cask with HALEU fuel, for which existing critical experiment coverage is limited. The optimization procedure is shown to produce experiment geometries achieving $c_k$ scores of 0.97757, 0.81324, and 0.93276 for three configurations of interest. This approach demonstrates the potential of deep learning and gradient optimization to accelerate the development of advanced nuclear technology.

Stefano Riva, Carolina Introini, Antonio Cammi et al.

The demand for clean energy is ever increasing, with new nuclear technologies presenting a complementary solution to renewable energies. However, designing and operating these systems is exceptionally difficult, given the complexity of the physical phenomena that interact to form the system dynamics. While high-fidelity simulations help to understand the non-linear, multi-physics interactions within a reactor, they are computationally expensive and rarely suitable for real-time applications. Furthermore, model-based approaches are inherently sensitive to simplifying assumptions required to derive their governing equations and parameters, leading to inevitable discrepancies with real-world measurements. In contrast, Machine Learning (ML) methods have the potential to generate reliable surrogate models which may be able to quickly predict the system's behaviour. However, the number of data-driven methods that can potentially be used for this task is large and diverse. In a safety-critical setting such as nuclear engineering, a fair comparison of different ML methods, and a clear understanding of their advantages and limitations, is of paramount importance. To address this, we introduce a Common Task Framework (CTF) for ML in nuclear engineering, building upon previous efforts in dynamical systems and seismology. This CTF considers a curated set of datasets from different nuclear and nuclear-adjacent systems. The CTF evaluates the performance of a method on 12 established metrics, alongside a new paradigm focused on system monitoring from sparse measurements only. We illustrate the framework by benchmarking standard ML baselines against these datasets, revealing current method limitations. Our vision is to replace ad hoc comparisons with standardized evaluations on hidden test sets, raising the bar for rigour and reproducibility in scientific ML for the nuclear industry.

Paul Seurin, Dean Price, Luis Nunez

Microreactors, particularly heat-pipe microreactors (HPMRs), are compact, transportable, self-regulated power systems well-suited for access-challenged remote areas where costly fossil fuels dominate. However, they suffer from diseconomies of scale, and their financial viability remains unconvincing. One step in addressing this shortcoming is to design these reactors with comprehensive economic and physics analyses informing early-stage design iteration. In this work, we present a novel unifying geometric design optimization approach that accounts for techno-economic considerations. We start by generating random samples to train surrogate models, including Gaussian processes (GPs) and multi-layer perceptrons (MLPs). We then deploy these surrogates within a reinforcement learning (RL)-based optimization framework to optimize the levelized cost of electricity (LCOE), all the while imposing constraints on the fuel lifetime, shutdown margin (SDM), peak heat flux, and rod-integrated peaking factor. We study two cases: one in which the axial reflector cost is very high, and one in which it is inexpensive. We found that the operation and maintenance and capital costs are the primary contributors to the overall LCOE particularly the cost of the axial reflectors (for the first case) and the control drum materials. The optimizer cleverly changes the design parameters so as to minimize one of them while still satisfying the constraints, ultimately reducing the LCOE by more than 57% in both instances. A comprehensive integration of fuel and HP performance with multi-objective optimization is currently being pursued to fully understand the interaction between constraints and cost performance.

Omer F. Erdem, Dean Price, Paul Seurin et al.

Multiobjective optimization remains challenging for many scientific and engineering problems due to the need to balance convergence, diversity, and computational efficiency across high-dimensional objective landscapes. This work presents the Multiobjective Animorphic Ensemble Optimization (MAEO) framework, a parallelizable ensemble strategy that unifies state-of-the-art evolutionary algorithms within an island-based architecture, overcoming the limitations of relying on a single optimizer, as implied by the No Free Lunch theorem. MAEO uses a parameter-free hypervolume indicator for island performance assessment and a strict Pareto-rank-based individual scoring formulation that incorporates crowding distance and nadir-point proximity to ensure consistent selection pressure within each front. The framework is initiated using four algorithms (NSGA-III, CTAEA, AGEMOEA2, SPEA2) and evaluated through extensive benchmarking on 12 DTLZ/ZDT functions under 36 dimensionality settings using Wilcoxon signed-rank tests with both hypervolume and inverse generational distance metrics. Results show that MAEO achieves balanced convergence-diversity performance, outperforming or matching some of the leading multiobjective optimization algorithms across different benchmark problems. To demonstrate practical applicability, MAEO is applied to the equilibrium-cycle optimization of a small modular nuclear reactor. Eight discrete design variables (and three objectives (levelized cost of electricity, peak soluble boron concentration, fuel cycle length) are optimized under two safety constraints. The algorithm carried out roughly 40000 evaluations using computer simulations. MAEO identifies core designs that lower both the levelized cost of electricity and the peak boron concentration, while preserving fuel cycle length and meeting all safety constraints.

Paul Seurin, Dean Price

Heat-pipe microreactors (HPMRs) are compact and transportable nuclear power systems exhibiting inherent safety, well-suited for deployment in remote regions where access is limited and reliance on costly fossil fuels is prevalent. In prior work, we developed a design optimization framework that incorporates techno-economic considerations through surrogate modeling and reinforcement learning (RL)-based optimization, focusing solely on minimizing the levelized cost of electricity (LCOE) by using a bottom-up cost estimation approach. In this study, we extend that framework to a multi-objective optimization that uses the Pareto Envelope Augmented with Reinforcement Learning (PEARL) algorithm. The objectives include minimizing both the rod-integrated peaking factor ($F_{Δh}$) and LCOE -- subject to safety and operational constraints. We evaluate three cost scenarios: (1) a high-cost axial and drum reflectors, (2) a low-cost axial reflector, and (3) low-cost axial and drum reflectors. Our findings indicate that reducing the solid moderator radius, pin pitch, and drum coating angle -- all while increasing the fuel height -- effectively lowers $F_{Δh}$. Across all three scenarios, four key strategies consistently emerged for optimizing LCOE: (1) minimizing the axial reflector contribution when costly, (2) reducing control drum reliance, (3) substituting expensive tri-structural isotropic (TRISO) fuel with axial reflector material priced at the level of graphite, and (4) maximizing fuel burnup. While PEARL demonstrates promise in navigating trade-offs across diverse design scenarios, discrepancies between surrogate model predictions and full-order simulations remain. Further improvements are anticipated through constraint relaxation and surrogate development, constituting an ongoing area of investigation.

Majdi I. Radaideh, Leo Tunkle, Dean Price et al.

Reducing operation and maintenance costs is a key objective for advanced reactors in general and microreactors in particular. To achieve this reduction, developing robust autonomous control algorithms is essential to ensure safe and autonomous reactor operation. Recently, artificial intelligence and machine learning algorithms, specifically reinforcement learning (RL) algorithms, have seen rapid increased application to control problems, such as plasma control in fusion tokamaks and building energy management. In this work, we introduce the use of RL for intelligent control in nuclear microreactors. The RL agent is trained using proximal policy optimization (PPO) and advantage actor-critic (A2C), cutting-edge deep RL techniques, based on a high-fidelity simulation of a microreactor design inspired by the Westinghouse eVinci\textsuperscript{TM} design. We utilized a Serpent model to generate data on drum positions, core criticality, and core power distribution for training a feedforward neural network surrogate model. This surrogate model was then used to guide a PPO and A2C control policies in determining the optimal drum position across various reactor burnup states, ensuring critical core conditions and symmetrical power distribution across all six core portions. The results demonstrate the excellent performance of PPO in identifying optimal drum positions, achieving a hextant power tilt ratio of approximately 1.002 (within the limit of $<$ 1.02) and maintaining criticality within a 10 pcm range. A2C did not provide as competitive of a performance as PPO in terms of performance metrics for all burnup steps considered in the cycle. Additionally, the results highlight the capability of well-trained RL control policies to quickly identify control actions, suggesting a promising approach for enabling real-time autonomous control through digital twins.