This study investigates the dynamic regulation of the sodium cold trap purification temperature at Argonne National Laboratory’s liquid sodium test facility, employing long short-term memory (LSTM) system identification techniques. The investigation introduces an innovative hybrid approach by integrating model predictive control (MPC) based on first principles dynamic models with a multi-step time–frequency LSTM model in predicting the temperature profiles of a sodium cold trap purification system. The long short-term memory–model predictive controller (LSTM-MPC) model employs a sliding window scheme to gather training samples for multi-step prediction, leveraging historical data to construct predictive models that capture the non-linearities of the complex system dynamics without explicitly modeling the underlying physical processes. The performance of the LSTM-MPC and MPC were evaluated through simulation experiments, where both models were assessed on their capacity to maintain the cold trap temperature within predefined set-points while minimizing deviations and overshoots. Results obtained show how the data-driven LSTM-MPC model demonstrates stability and adaptability. In contrast, the traditional MPC model exhibits irregularities, particularly evident as overshoots around set-point limits, which can potentially compromise its effectiveness over long prediction time intervals. The findings obtained offer valuable insights into integrating data-driven techniques for enhancing real-time monitoring systems.

This study develops an optimized scientific framework to identify least-cost energy mixes while enabling scale-invariant energy security assessment for Puerto Rico’s clean-energy transition. A nonlinear programming model is formulated to minimize total energy cost, and a Gaussian Process Regression (GPR) surrogate with explainability is employed to identify key cost drivers and quantify techno-economic uncertainty. To address the complexity of hybrid energy systems, fifteen relevant Nuclear–Renewable Hybrid Energy System (N-RHES) features are systematically aggregated into six energy security variables representing system capacity, storage, renewable penetration, and demand characteristics. Using these variables, a dimensional-scaling framework based on the Buckingham $$\pi$$ -theorem is developed to construct three dimensionless $$\pi$$ -groups corresponding to Reliability, Resilience, and Renewability (3R). These metrics transform system-specific optimization outputs into transferable, scale-invariant engineering performance indicators suitable for comparing islanded energy systems of different sizes. The GPR surrogate provides posterior mean predictions $$\mu (\textbf{x}^*)$$ and predictive variance $$\sigma ^2(\textbf{x}^*)$$ to characterize uncertainty in Levelized Cost of Energy (LCOE) and energy security metrics. SHapley Additive exPlanations (SHAP) analysis indicates that nuclear capacity reduces LCOE by 1.4 ¢/kWh, whereas wind increases cost by 0.9 ¢/kWh in high-penetration scenarios. Under techno-economic uncertainty, the predicted LCOE is $$9.6\pm 2.3$$ ¢/kWh, with the optimal nuclear–hybrid solution achieving 9.6 ¢/kWh while remaining below the 11.0 ¢/kWh policy constraint. Five hybrid configurations combining wind, solar PV, geothermal generation, battery storage, and hydrogen fuel-cell systems are analyzed, with selected cases integrating Small Modular Reactor (SMR) base-load supply. Optimization identifies three recommended configurations, with an SMR–renewables hybrid emerging as the least-cost solution. Configuration 5 achieves an LCOE of 10.0 ¢/kWh, delivers 70% renewable contribution, and reduces total energy cost by 18% relative to fossil-dominant mixes. By integrating techno-economic optimization with $$\pi$$ -based dimensional scaling, the proposed framework provides physically interpretable and transferable energy security metrics applicable to heterogeneous hybrid energy systems and hurricane-exposed island grids.