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DOE OSTI2025

Analytical gradient-based optimization of CALPHAD model parameters

The calibration of CALPHAD (CALculation of PHAse Diagrams) models involves the solution of a very challenging high-dimensional multiobjective optimization problem. Traditional approaches to parameter fitting predominantly rely on gradient-free methods, which while robust, are computationally inefficient and often scale poorly with model complexity. In this work, we introduce and demonstrate a generalizable framework for analytic gradient-based optimization of the parameters of the CALPHAD model enabled by the recently formalized Jansson derivative technique. This method allows for efficient evaluation of gradients of thermodynamic properties at equilibrium with respect to model parameters, even in the presence of arbitrarily complex internal degrees of freedom. Leveraging these semi-analytic gradients, we employ the conjugate gradient (CG) method to optimize thermodynamic model parameters for four binary alloy systems: Cu-Mg, Fe-Ni, Cr-Ni, and Cr-Fe. Across all systems, CG achieves comparable or superior optimality relative to Bayesian ensemble Markov Chain Monte Carlo (MCMC) with improvements in computational efficiency ranging from one to three orders of magnitude. Furthermore, our results establish a new paradigm for CALPHAD assessments in which high fidelity data-rich model calibration becomes tractable using deterministic gradient-informed algorithms.

CALPHAD↗

DOE OSTI2025

Modeling Protein–Protein and Protein–Ligand Interactions by the ClusPro Team in CASP16

ABSTRACT In the CASP16 experiment, our team employed hybrid computational strategies to predict both protein–protein and protein–ligand complex structures. For protein–protein docking, we combined physics‐based sampling—using ClusPro FFT docking and molecular dynamics—with AlphaFold (AF)‐based sampling, followed by AF‐based refinement. Our method produced numerous high‐accuracy complex models, including cases where AF alone failed, underscoring the critical role of physics‐based sampling alongside deep learning‐based refinement. For protein–ligand docking, we integrated the ClusPro LigTBM template‐based approach with a machine learning‐based confidence model for rescoring. The method preserves conserved interaction fragments derived from homologous complexes, followed by local resampling using physics‐based sampling and a diffusion model. Our template‐based strategy achieved a mean lDDT‐PLI of 0.69 across 233 targets, which was highly competitive. These results demonstrate that combining physics‐based modeling with AI‐driven refinement can significantly enhance the accuracy of both protein–protein and protein–ligand structure predictions.

Ashizawa, Ryota [Department of Applied Mathematics↗

DOE OSTI2021

Quantifying the Multi-Objective Cost of Uncertainty

Various real-world applications involve modeling complex systems with immense uncertainty and optimizing multiple objectives based on the uncertain model. Quantifying the impact of the model uncertainty on the given operational objectives is critical for designing optimal experiments that can most effectively reduce the uncertainty that affect the objectives pertinent to the application at hand. In this paper, we propose the concept of mean multi-objective cost of uncertainty (multi-objective MOCU) that can be used for objective-based quantification of uncertainty for complex uncertain systems considering multiple operational objectives. We provide several illustrative examples that demonstrate the concept and strengths of the proposed multi-objective MOCU. Furthermore, we present a real-world example based on the mammalian cell cycle network to demonstrate how the multi-objective MOCU can be used for quantifying the operational impact of model uncertainty when there are multiple, possibly competing, objectives.

42 ENGINEERING↗

DOE OSTI2021

AI-Batt (Autonomous Identification of Battery Life Models) [SWR 21-36]

Autonomous Identification of Battery Life Models (AI-Batt) AI-Batt is a MATLAB code base for developing lifetime models for batteries from accelerated aging data. The code base provides many functions for processing, visualizing, and modeling battery aging data, making the data processing, exploration, and modeling workflow substantially faster. These tools are tailored for working with battery aging data sets, which usually consist of many separate time-series for each cell, with many test conditions and possible replicates at each condition, which makes it difficult to simply process or visualize the data set. Complex modeling tasks, such as cross-validation, sensitivity analysis, and uncertainty quantification have been implemented to enable thorough statistical investigation of model predictions. Additionally, several machine-learning algorithms are implemented to autonomously identify suitable models via symbolic regression. Data processing functions automatically cast data from the struct data type, which is commonly used to store experimental data, but is not an acceptable input for most algorithms, to the table data type, which can be easily used as input to any optimization algorithm. Also, the data can be separated into time-invariant and time-variant data tables, which is helpful for exploring the data set as well as developing separate models for time-variant and time-invariant aging mechanisms. For example, in aging tests with constant temperature, temperature is a time-invariant experimental condition. Visualization tools enable plotting of data, model fits, and model simulations possible with single-line function calls, empowering data exploration of complex data sets with both time-varying and time-invariant trends. Plots can be automatically generated for the whole data set, or separated by data group (groups of test replicates) or individual data series. Data points or data series can be automatically colored by the value of a variable with a variety of color maps, and model predictions can also be colored by the value of a fit statistic. Comparisons between data sets and the predictions/simulations of different models on the same data set can be easily plotted as well. Distributions of parameter values from bootstrap resampling can be plotted to visualize the reliability of parameter estimation, or determine any correlations between parameters. Modeling tools handle the complex task of creating and parsing symbolic equations for modeling battery lifetime. Equations are parsed to grab relevant data variables, parameter values, or specified sub-models for input into optimization, evaluation, or simulation functions. Models can be optimized locally (one set of parameters for each data series), bi-level (some parameters shared across the data set), or globally (single set of parameters for all data). Functions implementing symbolic regression algorithms help users to discover effective model equations, even in poorly sampled, high-dimensional data.

Smith, Kandler↗

DOE OSTI2026

A score-based diffusion model approach for adaptive learning of stochastic partial differential equation solutions

In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Postmortem and Antemortem Forensic Assessment of Pediatric Fracture Healing from Radiographs and Machine Learning Classification

A timeline of pediatric bone healing using fracture healing characteristics that can be assessed solely using radiographs would be practical for forensic casework, where the fracture event may precede death by days, months, or years. However, the dating of fractures from radiographs is difficult, imprecise, and lacks consensus, as only a few aspects of the healing process are visible on radiographs. Multiple studies in both the clinical and forensic literature have attempted to develop a usable scale to assess pediatric bone healing on radiographs using various healing characteristics. In contrast to the orthopedic definition, a fracture in forensic casework is only considered to be healed when the area around the fracture has been remodeled to the point that the fracture is difficult to detect on a radiograph or on the surface of the bone itself, a process that can take several years. We subjectively assessed visible characteristics of healing in radiograms of fractures occurring in 942 living children and adolescents. By dividing these assessments into learning and test (validation) sets, the accuracy of a newly proposed fracture healing scale was compared to a previous study. Two machine learning models were used to test predictions of the new scale. All three models produced similar estimates with substantial imprecision. Results corroborate the Malone model with an independent dataset and support the efficacy of using less complex models to estimate fracture age in children.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2023

Encoding nonlinear and unsteady aerodynamics of limit cycle oscillations using nonlinear sparse Bayesian learning

This article investigates the applicability of a recently proposed, nonlinear sparse Bayesian learning (NSBL) algorithm to identify and estimate the complex aerodynamics of limit cycle oscillations. NSBL provides a semi-analytical framework for determining the data-optimal sparse model nested within a (potentially) over-parameterized model. This is particularly relevant to nonlinear dynamical systems where modelling approaches involve the use of physics-based and data-driven components. In such cases, the data-driven components, where analytical descriptions of the physical processes are not readily available, are often prone to overfitting, meaning that the empirical aspects of these models will often involve the calibration of an unnecessarily large number of parameters. While an overparameterized model may fit the observed data well, such models may be inadequate for making predictions in regimes that are different from those wherein the data were recorded. In view of this, it is desirable to not only calibrate the model parameters, but also identify the optimal compromise between data fit and model complexity. In this article, we exhibit the optimal model discovery for an aeroelastic system wherein the structural dynamics are well-known and described by a differential equation model, coupled with a semi-empirical aerodynamic model for laminar separation flutter, resulting in low-amplitude limit cycle oscillations (LCO). To illustrate the performance of the algorithm, in this article, we use synthetic data and demonstrate the ability of the algorithm to correctly rediscover the optimal model and model parameters, given a known data-generating model. The synthetic data are generated from a forward simulation of a known differential equation model with parameters selected so as to mimic the dynamics observed in wind-tunnel experiments. Subsequently, we demonstrate the performance of the algorithm for model selection using noisy LCO data from wind tunnel experiments. As there is no ground truth available for the experimental data case, we provide a comparison between NSBL and Bayesian model selection to validate the results, and demonstrate the use of NSBL as an efficient alternative to traditional methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Evaluating Lyman- α constraints for general dark-matter velocity distributions: Multiple scales and cautionary tales

One of the most important observational constraints on possible models of dark-matter physics exploits the Lyman-α absorption spectrum associated with photons traversing the intergalactic medium. Because these data allow us to probe the linear matter power spectrum with great accuracy down to relatively small distance scales, finding ways of accurately evaluating such Lyman-α constraints across large classes of candidate models of dark-matter physics is of paramount importance. While such Lyman-α constraints have been evaluated for dark-matter models that give rise to relatively simple dark-matter velocity distributions, more complex models—particularly those whose dark-matter velocity distributions stretch across multiple scales—have recently been receiving increasing attention. In this paper, we undertake a study of the Lyman-α constraints associated with general dark-matter velocity distributions. Although such Lyman-α constraints are difficult to evaluate in principle, in practice there currently exist two classes of methods in the literature through which such constraints can be recast into forms which are easier to evaluate and which therefore allow a more rapid determination of whether a given dark-matter model is ruled in or out. Accordingly, we utilize both of these recasts in order to determine the Lyman-α bounds on different classes of dark-matter velocity distributions. Here we also develop a general method by which the results of these different recasts can be compared. For relatively simple dark-matter velocity distributions, we demonstrate that these two classes of recasts tend to align and give similar results. However, we find that the situation is far more complex for distributions involving multiple velocity scales: while these two classes of recasts continue to yield similar results within certain regions of parameter space, they nevertheless yield dramatically different results within precisely those regions of parameter space which are likely to be phenomenologically relevant. This, then, serves as a cautionary tale regarding the use of such recasts for complex dark-matter velocity distributions.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Prediction of impact sensitivity, heat of formation and heat of explosion using atomic connectivity

In these proceedings we revisit a large collection of explosives and explosive descriptors with the goal of predicting impact sensitivity using only local atomic environments that can be deciphered from molecular SMILES strings as descriptors without utilizing empirically measured values or computationally expensive electronic structure calculations. From the original database of nearly 500 descriptors, removing empirically measured and electronic structure values decreased the number of descriptors to 135, which we reduced to 18 the most important descriptors using Random Forests. The condensed model predicted impact sensitivity with essentially the same accuracy as the existing, more complex model (R 2 = 0.788 and RSME = 0.312), while remaining applicable to all types of explosives (Peroxides, azides, C-Nitros, Nitroamines, Nitrate Esters, etc.). In addition to impact sensitivity, we proposed similar models to accurately predict values heat of formation (ΔH f ) and heat of explosion (Q), with R 2 = 0.966 and 0.916, respectively. In conclusion, the work in these proceedings allows for prediction of explosive performance and sensitivity with only chemical structure information and an estimate of density.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Foundational Science to Accelerate Nuclear Energy Innovation [Brochure]

The foundational science gaps inhibiting the advancement of nuclear energy technologies are identified and tackled in five priority research opportunities. These opportunities pave the way to accelerate the development and ultimately the adoption of new nuclear energy systems. They include the fundamental aspects of ion-electron interactions; novel properties of next-generation coolants and solvents; interfacial dynamics, not only in solids, but in other aspects of nuclear reactors; novel operando and in-situ monitoring and sensing; and artificial intelligence to accelerate condensed phases discovery. Building on the foundation established by previous BES workshops, these opportunities encompass recent advances in fundamental knowledge and focus on the experimental and computational methods needed to resolve major technical challenges for nuclear energy technologies. Through developing fundamental scientific insight as well as pushing the frontiers of modeling complex systems and probing the operation of materials and chemical systems in extreme environments, research motivated by the priorities identified here will further develop the promise, potential, and utilization of nuclear energy for a clean energy future. The PROs are as follows: (1) Master complex electronic structures to tailor thermochemical reactivity, transport, and microstructural evolution; (2) Interrogate and direct the physics and chemistry underpinning next-generation coolants and solvents; (3) Elucidate and control the underlying physics and chemistry of interfaces in complex nuclear environments; (4) Bridge multi-fidelity multi-resolution experiments, computational modeling, and data science to control dynamic behavior; and (5) Harness artificial intelligence to design inherently resilient condensed phases.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

AN INITIAL LOOK AT THE HEAT PIPE RESILIENCY TO REACTOR OPERATION

Several special purpose reactor designs are aiming to utilize heat pipes due to its inherently passive features allowing safe heat removal to the power conversion systems. There is insufficient data on heat pipe survivability in reactor environments, although heat-pipe failures are predicted to have low failure rates. In this paper, we perform a coupled neutronics and thermo-mechanics analyses for a 45 kWth HALEU fueled, hydride moderated homogenous design to evaluate the transient effects during both startup and a heatpipe-failure scenario. The heatpipe-failure study includes both a single failure case and a failure-propagation (cascading) case. While the model only evaluates a homogenous core, the approach could be applied to more complex models for any heat pipe cooled small reactor.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2026

Neural Scaling Laws for Jet Generation

Recently observed empirical scaling laws describe the performance of foundation-type models as three independent key quantities -- dataset size, compute, and model parameters -- are modified. Extracting these scaling laws informs the training of large complex models for which the tuning of hyperparameters in traditional ways is not feasible. This work for the first time explores if scaling laws can also be observed for the task of particle jet generation -- both relevant as a pre-training objective for foundation models and as in-situ simulation by itself. We indeed replicate the key logarithmic scaling law behavior for model-size scaling. Beyond studying the next token prediction validation loss of the generative model, we also study the sliced Wasserstein distance of five physical quantities that are not immediately available to the model during training. Our study shows that this quantity is monotonically related to the next token prediction validation loss, meaning that this loss is indeed a good proxy for the physics performance. For the scaling with dataset size and compute, we observe substantially weaker scaling behavior of both the loss and the sliced Wasserstein distance. We analyze this behavior by introducing the concept of a learnable window, and argue that autoregressive next token prediction on jet constituents exhibits comparatively rapid saturation relative to language-model studies. We discuss possible origins of this behavior, including the stochastic nature of QCD radiation and differences between generative and supervised learning tasks in collider physics.

Amram, Oz [Fermilab]↗

DOE OSTI2024

Comparison of Projections for a Short-Term Release, CAP88 vs NARAC

The purpose of this study was to compare the projected dose using different plume models, evaluating a short duration release of tritium to the 16 compliance sectors and 4 additional points of interest using local meteorology. This report is written as guidance to the decision makers when reviewing this specific Gaussian plume model intended for radiological dose assessment and regulatory compliance, called CAP88 1 , as compared to a more-complex model designed for emergency response. The emergency response model, NARAC 2 , can be used to supplement the CAP88 compliance model evaluations, since NARAC is intended for use in situations where releases are shorter in duration and have increased complexity in terrain and meteorology.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Science &Technology Review (September 2022)

Computer modeling is essential to scientific research. Models simulate natural phenomena to aid scientists in understanding their underlying principles. While the most complex models running on supercomputers may contain millions of lines of code and generate billions of data points, models never simulate reality perfectly. Experiments—in contrast—have been fundamental to the study of natural phenomena from science’s earliest days. However, some of today’s complex experiments generate too much data for the human mind to interpret.

42 ENGINEERING↗

DOE OSTI2025

Direction of impact for explainable risk assessment modeling

Abstract Several graphical indicators have been recently introduced to help analysts visualize the marginal effects of inputs in complex models. The insights derived from such tools may help decision‐makers and risk analysts in designing interventions. However, we know little about the adequacy and consistency of different indicators. This work investigates popular marginal effect indicators to understand whether they yield indications consistent with the properties of the quantitative model under inspection. Specifically, we examine the notions of monotonicity, Lipschitz, and concavity consistency. Surprisingly, only PD functions satisfy all these notions of consistency. However, when selecting the indicators, in addition to consistency, analysts need to consider the risk of model extrapolation. For situations where such risk is under control, we utilize individual conditional expectations together with PD plots. Two applications, on a NASA space risk assessment model and a susceptible exposed infected recovered (SEIR) model for the COVID‐19 pandemic illustrate the insights obtained from these indicators.

Mathematical Methods In Social Sciences↗

DOE OSTI2024

Improving the reliability of machine learned potentials for modeling inhomogeneous liquids

The atomic-scale response of inhomogeneous fluids at interfaces and surrounding solute particles plays a critical role in governing chemical, electrochemical, and biological processes. Classical molecular dynamics simulations have been applied extensively to simulate the response of fluids to inhomogeneities directly, but are limited by the accuracy of the underlying interatomic potentials. Here, we use neural network potentials (NNPs) trained to ab initio simulations to accurately predict the inhomogeneous responses of two distinct fluids: liquid water and molten NaCl. Although NNPs can be readily trained to model complex bulk systems across a range of state points, we show that to appropriately model a fluid's response at an interface, relevant inhomogeneous configurations must be included in the training data. In order to sufficiently sample appropriate configurations of such inhomogeneous fluids, we develop protocols based on molecular dynamics simulations in the presence of external potentials. We demonstrate that NNPs trained on inhomogeneous fluid configurations can more accurately predict several key properties of fluids—including the density response, surface tension and size-dependent cavitation free energies—for liquid water and molten NaCl, compared to both empirical interatomic potentials and NNPs that are not trained on such inhomogeneous configurations. This work therefore provides a first demonstration and framework to extract the response of inhomogeneous fluids from first principles for classical density-functional treatment of fluids free from empirical potentials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Representing Socio‐Economic Uncertainty in Human System Models

Abstract Socio‐economic development pathways and their implications for the environment are highly uncertain, and energy transitions will involve complex interactions among sectors. Here, traditional Monte Carlo analysis is paired with scenario discovery techniques to provide a richer portrait of these complexities. Modeled uncertain input variables include costs of advanced energy technologies, energy efficiency trends, fossil fuel resource availability, elasticities of substitution for labor, capital, and energy across economic sectors, population growth, and labor and capital productivity. The sampled values are simulated through a multi‐sector, multi‐region, recursively dynamic model of the world economy to explore a range of possible future outcomes. We find that many patterns of energy and technology development are possible for various long‐term environmental pathways and that sectoral output for most sectors is little affected through 2050 by the long‐term temperature target, but with tight constraints on emissions, emission intensities must fall much more rapidly. Scenario discovery techniques are applied to the large uncertainty ensembles to explore if there are prevailing storylines behind outcomes of interest. An illustrative investigation focused on different levels of economic growth shows many combinations of pathways and no single storyline emerging for a given economic outcome. This method can be extended to other outcomes of interest, exploring the nature of scenarios with both tail and median outcomes. Sampling from a Monte Carlo generated ensemble provides a rich set of scenarios to investigate, and potentially aids in avoiding heuristic biases in less structured scenario approaches.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2024

Implementation of a Drift Flux Model into SAM with Development of a Verification and Validation Test Suite for Modeling of Noncondensable Gas Mixtures

The advanced thermal-hydraulic system code, System Analysis Module (SAM), was originally developed for the modeling of single-phase flow in advanced reactors. It has since been expanded to include a four-equation drift flux model for the modeling of two-phase flows containing a noncondensable gas. The model was expanded to support the modeling of molten salt reactor (MSR) designs in which the fuel is directly dissolved in the circulating coolant. These designs have shown that circulating gas bubbles can play an important role in the management of fission products and the operational behavior of the reactor. A drift flux model was implemented to more accurately capture the localized behavior of the void in the core and its impact on the mass transfer of fission products. A thorough assessment of the new model was performed by developing a verification and validation test suite. Verification problems were designed to test all major terms in the new governing equations. The new model converged to the correct solution at the expected order of accuracy for all verification cases. The validation cases included a wide range of flow and void conditions in different pipe geometries. Although higher void experiments show a slight underprediction of void by the drift flux model, experiments that aim to reproduce Molten Salt Reactor Experiment (MSRE) experimental conditions show good agreement with the model. The gas transport model was activated for a SAM model of the MSRE to demonstrate that it can be used in a more complex model. Finally, this gas transport model will be used along with an interfacial area transport equation being implemented in SAM for the prediction of mass transport behavior in MSR conditions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗