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DOE OSTI2024

Inverse prediction of PuO2 processing conditions using Bayesian seemingly unrelated regression with functional data

Over the past decade, a variety of innovative methodologies have been developed to better characterize the relationships between processing conditions and the physical, morphological, and chemical features of special nuclear material (SNM). Different processing conditions generate SNM products with different features, which are known as “signatures” because they are indicative of the processing conditions used to produce the material. These signatures can potentially allow a forensic analyst to determine which processes were used to produce the SNM and make inferences about where the material originated. This article investigates a statistical technique for relating processing conditions to the morphological features of PuO 2 particles. We develop a Bayesian implementation of seemingly unrelated regression (SUR) to inverse-predict unknown PuO 2 processing conditions from known PuO 2 features. Model results from simulated data demonstrate the usefulness of the technique. Applied to empirical data from a bench-scale experiment specifically designed with inverse prediction in mind, our model successfully predicts nitric acid concentration, while results for Pu concentration and precipitation temperature were equivalent to a simple mean model. Our technique compliments other recent methodologies developed for forensic analysis of nuclear material and can be generalized across the field of chemometrics for application to other materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Refining T c Prediction in Hydrides via Symbolic‐Regression‐Enhanced Electron‐Localization‐Function‐Based Descriptors

Hydrogen‐based materials are able to possess extremely high superconducting critical temperatures, T c s , due to hydrogen's low atomic mass and strong electron–phonon interaction. Recently, a descriptor based on the Electron Localization Function (ELF) has enabled the rapid estimation of the T c of hydrogen‐containing compounds from electronic networking properties, but its applicability has been limited by the small size and homogeneity of the training dataset used. Herein, the model is re‐examined, compiling a publicly available combined dataset of 244 binary and ternary hydride superconductors. The analysis shows that though ELF‐based networking remains a valuable descriptor, its predictive power declines with increasing compositional complexity. However, by introducing the molecularity index, defined as the highest value of the ELF at which two hydrogen atoms connect, and applying symbolic regression, the accuracy of the predictions can be substantially enhanced. These results establish a more robust framework for assessing superconductivity in hydride materials, facilitating accelerated screening of novel candidates through integration with crystal structure prediction methods or high‐throughput searches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Stress intensity factor models using mechanics-guided decomposition and symbolic regression

The finite element method can be used to compute accurate stress intensity factors (SIFs) for cracks with complex geometries and boundary conditions. In contrast, handbook solutions act as surrogate SIF models that provide significantly faster evaluation times. However, the development of conventional surrogate SIF models relies on manual development based on low-order parameterizations. This limits surrogate model accuracy and generalizability. Here, in this paper, we develop a framework for the automated development of mechanics-guided handbook SIF solutions by using interpretable machine learning via genetic programming for symbolic regression (GPSR). Formalizing the mechanics-based approach of Raju and Newman, SIF training data is decomposed into multiple subsets. This decomposition enables parallel GPSR model development of subfunctions, each of which accounts for specific geometrical corrections with respect to a known analytical model. Using this mechanics-based approach with GPSR allows for equations to be learned with improved accuracy and reduced complexity relative to the Raju Newman equations while maintaining the inherent interpretability of mathematical expressions. In this paper, we present equations that match the complexity of the Raju Newman equations while having reduced error, as well as equations with similar errors and reduced complexity.

42 ENGINEERING↗

DOE OSTI2024

Utilizing waste heat in wastewater treatment plants for water desalination: Modeling and Multi-Objective optimization of a Multi-Effect desalination system using Decision Tree Regression and Pelican optimization algorithm

This paper examines the feasibility of using waste heat from wastewater treatment plants (WWTPs) for water desalination. A model was developed to utilize waste heat from the gensets at As Samra WWTP in Jordan, using real data and TRNSYS® software to calculate available waste heat. The desalination process was then modeled with ASPEN PLUS® software, focusing on multi-effect desalination (MED). Both series and parallel configurations for the MED system were compared. The study investigated the effects of system feeding flow rate, feeding pressure, and heat input on productivity, performance ratio, and recovery ratio. The study also introduces a novel optimization technique combining machine learning and modern optimization algorithms to maximize system productivity and performance. Initially, a decision tree regression (DTR) model is developed to establish relationships between key independent variables (flow rate, feed pressure, and heat input) and dependent variables (productivity, performance ratio, and recovery ratio). The Pelican Optimization Algorithm (POA) is then used to identify the optimal values of the independent variables for maximum productivity and performance. The results show that using a series configuration yields a system productivity of 3984.2 kg/hr, a performance ratio of 3.78, and a recovery ratio of 0.991 at a feed flow rate of 4000 kg/hr, feed pressure of 3 bars, and heat input of 719 kW. Optimal productivity (4421 kg/hr), performance ratio (3.81), and recovery ratio (0.851) are achieved at a feed flow rate of 5166 kg/hr, feed pressure of 3.2 bars, and heat input of 794 kW. In conclusion, the techno-economic assessment indicates a levelized cost of water of 1.63 USD/m 3 for parallel configurations and 1.65 USD/m 3 for series configurations, with a payback period of less than two years.

42 ENGINEERING↗

DOE OSTI2025

Accelerating Instanton Theory with the Line Integral Nudged Elastic Band Method and Gaussian Process Regression

Quantum tunneling plays a fundamental role in many chemical reactions, particularly proton transfer processes. Ring polymer instanton theory offers a practical framework for computing tunneling rates in complex molecular systems. However, applying the ring polymer instanton method with a potential energy surface generated on-the-fly using electronic structure calculations can be computationally demanding. Here, in this work, we present a new efficient implementation of the ring polymer instanton method by combining the Line Integral Nudged Elastic Band (LI-NEB) approach with Gaussian Process Regression (GPR). We benchmarked this method on prototypical ground-state proton transfer systems, including the benchmark gas-phase hydrogen abstraction reaction H + CH 4 → H 2 + CH 3 , malonaldehyde, and Z-3-amino-propenal (aminopropenal). Our results show that this approach is an order of magnitude faster than traditional instanton algorithms while maintaining excellent agreement with their tunneling rates. This development opens the door to studying proton transfer in larger systems with improved efficiency.

chemical physics↗

DOE OSTI2025

Understanding Peelle’s Pertinent Puzzle bias in generalized least squares regression through eigenspectrum analysis

Certain correlation structures in the data covariance matrix (DCM) used for generalized least squares (GLS) regression can result in biased estimates, commonly known in the field of nuclear data evaluation as Peele’s Pertinent Puzzle (PPP). This article introduces a generative, forward modeling framework within which the PPP bias is characterized through an eigenspectrum analysis of the DCM. This analysis highlights the root cause of the bias, generalizes the problem beyond the nuclear data field, and provides insight to the problem regimes where it can occur. What follows is an understanding that the bias can show up for any experimental neutron time-of-flight data for which systematic uncertainties have been quantified. Lastly, a discussion of the adaptation of cross validation approaches that require pre-whitening to incorporate the known ‘fix’ to the PPP bias in the GLS estimator.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Quantifying mean, variability, and uncertainty in indoor radon exposure in Pennsylvania using random forest and quantile regression forest models

Radon is a naturally occurring radioactive gas that poses a serious health risk as the primary cause of lung cancer in non-smokers. Despite the well-known adverse association with health outcomes, current radon exposure assessments are limited to county-level or average-level estimates, which fail to capture regional variability. This study uses Machine Learning models, including Random Forest (RF) and Quantile Regression Forest (QRF), to estimate the indoor radon concentrations at the ZCTA (Zip code tabulation area)-level and characterize uncertainties in model estimates. Incorporating geological, meteorological, and building-specific data, the models aim to improve radon risk assessment by capturing mean exposure, variability, and extreme concentration levels. Processed radon test data (n = 718,111) were analyzed using average, variability, and quantile prediction methods. Models that estimate the average radon exposure at the ZCTA-level can yield promising model-fit results, but they do not capture the underlying variability of indoor radon exposure within a ZCTA. We utilize volatility analyses to identify characteristics indicative of high variability of indoor radon exposure. We also show that a QRF model can be used to estimate upper quantiles of residential radon exposure, thereby uncovering localized areas of elevated exposure that were not apparent in mean estimates. The results highlighted the need for a deep characterization of exposure risk and show that regions with moderate average exposure levels could still harbor extreme outliers with implications for evaluating health risks. Utilizing multiple radon exposure models allows for a deeper characterization of radon risk within a geographic area and can better identify high-risk areas. The results from this study provide a foundation for developing mitigation strategies and examining associations between radon exposure and health outcomes at fine scales. Future research should extend the geographic scope and incorporate additional environmental risk factors to establish a comprehensive framework for risk assessment.

Lee, Heechan [ORNL]↗

DOE OSTI2024

Modeling of the metal–insulator transition temperature in alio-valently doped VO 2 through symbolic regression

The correlated semiconductor vanadium dioxide (VO 2 ) exhibits an insulator–metal transition (IMT) near room temperature, which is of interest in various device applications. Precise IMT temperature control is crucial to determine the use cases across technologies such as thermochromic windows, actuators for robots or neuronal oscillators. Doping the cation or anion sites can modulate the IMT by several tens of degrees and control hysteresis. However, modeling the effects of control parameters (e.g., doping concentration, type of dopants) is challenging due to complex experimental procedures and limited data, hindering the use of traditional data-driven machine learning approaches. Symbolic regression (SR) can bridge this gap by identifying nonlinear expressions connecting key input parameters to target properties, even with small data sets. In this work, we develop SR models to capture the IMT trends in VO 2 influenced by different dopant parameters. Using experimental data from the literature, our study reveals a dual nature of the IMT temperature with varying tungsten (W) doping concentrations. The symbolic model captures data trends and accounts for experimental variability, providing a complementary approach to first-principles calculations. Our feature-driven analysis across a broader class of dopants informs selectivity and provides qualitative insights into tuning phase transition properties valuable for neuromorphic computing and thermochromic windows.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Desmearing Bonse–Hart USANS data using Bayesian Gaussian process regression

Ultra-small-angle neutron scattering (USANS) enables access to micrometer-scale structures but is intrinsically affected by strong, anisotropic resolution smearing arising from slit-geometry optics. As a result, recovery of the intrinsic scattering intensity constitutes an ill-posed inverse problem, and commonly used iterative desmearing methods lack rigorous uncertainty quantification. We present a Bayesian desmearing framework for slit-geometry USANS based on Gaussian process regression. In this approach, the scattering intensity is modeled as a smooth random function, and the instrumental point spread function is incorporated explicitly as a forward operator. The resulting formulation yields a closed-form maximum a posteriori solution with well-defined credibility intervals. Computational benchmarks and experimental validation using combined USANS and small-angle neutron scattering (SANS) measurements demonstrate that the framework enables stable desmearing, suppresses experimental noise, and preserves physically meaningful structural features under realistic conditions.

Tung, Chi-Huan [Oak Ridge National Laboratory (ORN↗

DOE OSTI2025

Neural network-based classification and regression of magnetohydrodynamic modes in tokamaks

We present a machine learning-based magnetohydrodynamic (MHD) classifier and regressor that utilizes real or complex-valued 3D magnetic sensor array data to determine neoclassical tearing mode (NTM) onset times in tokamaks with millisecond accuracy. The input dataset consists of poloidal profiles of complex Fourier amplitudes with an n = 1 toroidal mode number from 144 human-labeled ITER Baseline Scenario discharges in the DIII-D tokamak, spanning both tearing-dominated and sawtooth-dominated regimes. Since m, n = 2,1 NTMs frequently emerge alongside sawteeth at the same frequency in this scenario, the focus is on isolating the m = 1 and m = 2 components of the n = 1 MHD mode near the tearing onset. To improve model regularization and prediction stability, singular value decomposition was applied to balance the sawtooth and tearing datasets. The enriched datasets facilitated training neural networks that learn the key distinguishing features of sawtooth and tearing modes in the poloidal profiles of their magnetic amplitude and phase. When the modes occur independently, the networks achieve perfect classification due to the modes’ distinct characteristics and low measurement noise. In the more experimentally relevant case where both modes coexist, the networks maintain exceptional performance across key metrics. Tests on synthetic data with known ground truth demonstrate the superior accuracy of the neural network trained on complex-valued input compared to models using real amplitude, phase, or pseudo-complex data, achieving both a mean time delay and standard deviation below 1 ms. Notably, standard linear regression methods fitting the dominant singular modes to the data closely match the neural network’s performance. Applying these methods across a broad range of H-mode scenarios will enable future studies to systematically identify dominant NTM triggers as scenario-specific variables, paving the way for more effective tearing mode avoidance strategies in future fusion reactor designs.

machine learning↗

DOE OSTI2025

SymbolNet: neural symbolic regression with adaptive dynamic pruning for compression

Abstract Compact symbolic expressions have been shown to be more efficient than neural network (NN) models in terms of resource consumption and inference speed when implemented on custom hardware such as field-programmable gate arrays (FPGAs), while maintaining comparable accuracy (Tsoi et al 2024 EPJ Web Conf. 295 09036). These capabilities are highly valuable in environments with stringent computational resource constraints, such as high-energy physics experiments at the CERN Large Hadron Collider. However, finding compact expressions for high-dimensional datasets remains challenging due to the inherent limitations of genetic programming (GP), the search algorithm of most symbolic regression (SR) methods. Contrary to GP, the NN approach to SR offers scalability to high-dimensional inputs and leverages gradient methods for faster equation searching. Common ways of constraining expression complexity often involve multistage pruning with fine-tuning, which can result in significant performance loss. In this work, we propose S y m b o l N e t , a NN approach to SR specifically designed as a model compression technique, aimed at enabling low-latency inference for high-dimensional inputs on custom hardware such as FPGAs. This framework allows dynamic pruning of model weights, input features, and mathematical operators in a single training process, where both training loss and expression complexity are optimized simultaneously. We introduce a sparsity regularization term for each pruning type, which can adaptively adjust its strength, leading to convergence at a target sparsity ratio. Unlike most existing SR methods that struggle with datasets containing more than O ( 10 ) inputs, we demonstrate the effectiveness of our model on the LHC jet tagging task (16 inputs), MNIST (784 inputs), and SVHN (3072 inputs).

Tsoi, Ho Fung (ORCID:0000000225502184)↗

DOE OSTI2026

Stellarator Design Exploration Using Symbolic-Regression Neutronics Surrogates

Systems codes require fast, simplified models to rapidly evaluate fusion power plant concepts, but neutronics analyses are often a computational bottleneck. Here, to address this, surrogate models for key neutronics responses have been developed using 3-D neutronics-ready models built with the open-source code ParaStell from a database of stellarator equilibria. Neutronics responses such as tritium breeding ratio (TBR), nuclear heating, and neutron-induced radiation damage displacements per atom (dpa) were simulated using OpenMC. Through sensitivity analysis and symbolic regression (SR), simple power-law formulas were derived connecting these neutronics responses to global stellarator parameters, including fusion power, plasma surface area, and plasma elongation. Validation shows these formulas can predict the simulation results with low error, enabling quick and accurate assessment of neutronics requirements in stellarator design exploration activities with systems codes.

Modeling↗

DOE OSTI2024

chemostat_regression

Automatically detect chemostat optical density dilution cycles and calculate growth rate regression slopes.

Koehler, Samuel I↗

DOE OSTI2025

Bayesian Linear Regression for Hugoniot Data

This repository provides the code and datasets used in the paper Bayesian Analysis of Linear Shock Compression Data. This paper analyzes publicly available shock compression datasets on copper, argon, and nickel from Marsh (1980) using Bayesian linear regression, and compares the results with those obtained using bootstrapping methods. References: - Marsh, S. P. (1980). LASL shock Hugoniot data (Vol. 5). Univ of California Press.

Bernstein, JasonA [Lawrence Livermore National Lab↗

DOE OSTI2025

Evaluating the Trustworthiness of Explainable Artificial Intelligence (XAI) Methods Applied to Regression Predictions of Arctic Sea Ice Motion

Abstract Recent advances in explainable artificial intelligence (XAI) methods show promise for understanding predictions made by machine learning (ML) models. XAI explains how the input features are relevant or important for the model predictions. We train linear regression (LR) and convolutional neural network (CNN) models to make 1-day predictions of sea ice velocity in the Arctic from inputs of present-day wind velocity and previous-day ice velocity and concentration. We apply XAI methods to the CNN and compare explanations to variance explained by LR. We confirm the feasibility of using a novel XAI method [i.e., global layerwise relevance propagation (LRP)] to understand ML model predictions of sea ice motion by comparing it to established techniques. We investigate a suite of linear, perturbation-based, and propagation-based XAI methods in both local and global forms. Outputs from different explainability methods are generally consistent in showing that wind speed is the input feature with the highest contribution to ML predictions of ice motion, and we discuss inconsistencies in the spatial variability of the explanations. Additionally, we show that the CNN relies on both linear and nonlinear relationships between the inputs and uses nonlocal information to make predictions. LRP shows that wind speed over land is highly relevant for predicting ice motion offshore. This provides a framework to show how knowledge of environmental variables (i.e., wind) on land could be useful for predicting other properties (i.e., sea ice velocity) elsewhere. Significance Statement Explainable artificial intelligence (XAI) is useful for understanding predictions made by machine learning models. Our research establishes trustability in a novel implementation of an explainable AI method known as layerwise relevance propagation for Earth science applications. To do this, we provide a comparative evaluation of a suite of explainable AI methods applied to machine learning models that make 1-day predictions of Arctic sea ice velocity. We use explainable AI outputs to understand how the input features are used by the machine learning to predict ice motion. Additionally, we show that a convolutional neural network uses nonlinear and nonlocal information in making its predictions. We take advantage of the nonlocality to investigate the extent to which knowledge of wind on land is useful for predicting sea ice velocity elsewhere.

Hoffman, Lauren [Scripps Institution of Oceanograp↗

DOE OSTI2025

Dataset for ASME VVUQ Symposium Workshop on Regression of Validation Data to an Application Point

This dataset consists of a collection of Excel spreadsheets that contain output from analysis specified in the workshop. The analysis involves ASME V&V 20-style validation as well as the application of a supplement methodology for regression of validation comparison error and validation uncertainty to application points where experimental data does not exist for comparison. The simulation results and experimental data are provided by the workshop organizers and a NASA report, respectively.

Kirsch, Jared Roelof [Sandia National Laboratories↗

DOE OSTI2025

Data and code from: Multivariate bayesian regression model for predicting disposed ash composition at U.S. coal fired power stations

This dataset contains the code and data files needed for implementation of a Multivariate Bayesian Regression model, described in Jin et al. (2025), for the historical prediction of the chemical composition of disposed coal ash at U.S. coal fired power plants as a function of annualized coal purchase data. The integrated coal supply data file (CoalSupplyDataset.csv) represents a compilation of monthly fuel purchase records for the period 1973-2022 at major U.S. power stations. These records were obtained from the U.S. Energy Information Administration. The CSV file also contains, for each coal purchase record, the coal region of the mine as defined by the U.S. Geological Survey. Data entry errors and data gaps in the EIA records were corrected as described in Jin et al. This CSV file represents the integrated coal supply data after corrections were made. The model structure and fitting parameters are encoded in pickle file format (Bayesian.pkl). The model was developed with the coal supply data and coal ash composition data, apportioned according to the Stratified Shuffle Split for training and testing subsets. The model was built using Python and the PyMC library. Reference Publication: Jin, Z.; Huang, J.; Hower, J.C.; Hsu-Kim, H.(2025). Predictive Assessment of the Chemical Composition of Coal Ash in Reserve at U.S. Disposal Sites. Environmental Science & Technology.

Coal ash composition↗

DOE OSTI2024

FORCE Regression Testing

Via programs including the Light Water Reactor Sustainability and Integrated Energy Systems, the U.S. Department of Energy has invested in the Framework for Optimization of ResourCes and Economics (FORCE) software framework (Idaho National Laboratory 2024a) for the technical and economic analysis of nuclear-integrated energy systems (IES). Nuclear IES expand the use of nuclear from traditional baseload electricity generation to a flexible and adaptive source of combined heat and power. Nuclear heat can be used in the production of a variety of energy currencies such as hydrogen and ammonia as well as other heat applications including water desalination and district heating. FORCE is designed with the intent to provide interconnected analysis tools that enable the accurate technical and economic assessment of specific nuclear IES configurations for individual energy markets. FORCE consists of three main analysis pathways: HYBRID (Idaho National Laboratory 2024b), which contains high-resolution physical models for IES; Holistic Energy Resource Optimization Network (HERON) (Idaho National Laboratory 2024c), which analyzes IES long-term economic viability; and Optimization of Real-time Capacity Allocation (ORCA) (Idaho National Laboratory 2024d), designed for real-time control of IES via digital twins and optimal decision making, including autonomous and remote operation research. Development of the FORCE ecosystem is guided by three pillars: capability, which assures that the computational requirements of IES analysis are met by the software tools; reliability, which provides for consistent code performance and expected behaviors; and accessibility, which lowers the barrier to entry for using the software and accelerates analysis by users beyond the FORCE primary developers. Reliability of the FORCE ecosystem is established according to the American Nuclear Society?s Nuclear Quality Assurance (NQA-1) program [American Society of Mechanical Engineers 1982], with specific levels of software quality assurance (SQA) within NQA-1 applied to each software tool in FORCE. As the tools within FORCE have matured, some integration algorithms to accurately connect the software tools for holistic analysis have been developed and deployed within the FORCE software repository. In accordance with NQA-1 standards, regression tests are required to guarantee the software performs consistently even when new capabilities are added to the software. In this report, we document the deployment of both unit tests, which test the consistent behavior of small pieces of the FORCE code base, as well as integration tests, which test the consistent performance of full use cases for the FORCE integration algorithms. We further document the encapsulation of these tests within a test harness, which collectively checks for each successful test completion on demand. Finally, we document the automation of the test harness using GitHub Actions [GitHub 2024], which require all tests succeed before any new capability or other changes can be added to the FORCE integration software

97 MATHEMATICS AND COMPUTING↗