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DOE OSTI2024

RandONets: Shallow networks with random projections for learning linear and nonlinear operators

Deep neural networks have been extensively used for the solution of both the forward and the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space of parameters and hyperparameters. This fact, along with the requirement of substantial computational resources, pose a barrier to achieving high numerical accuracy, but also interpretability. Here, to address the above challenges, we present Random Projection-based Operator Networks (RandONets): shallow networks with random projections and tailor-made numerical analysis methods that learn accurately and fast linear and nonlinear operators. Building on previous works, we prove that RandOnets are universal approximators of linear and nonlinear operators. Due to their simplicity, RandONets provide a one-step transformation of the input space, facilitating interpretability. For the evaluation of their performance, we focus on operators of PDEs. We show, that RandONets outperform by several orders of magnitude, both in terms of numerical approximation accuracy and computational cost, the “vanilla” DeepONets. Hence, we believe that our method will trigger further developments in the field of scientific machine learning, for the development of new ‘’light”schemes that will provide high accuracy while reducing dramatically the computational cost. A MATLAB toolbox for RandONets, including demos, is available on GitHub at https://github.com/GianlucaFabiani/RandONets.

Interpretable machine learning↗

DOE OSTI2025

Leveraging interpolation models and error bounds for verifiable scientific machine learning

Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and methods involved. Error bounds for classical interpolation techniques can provide mathematically rigorous estimates of accuracy, but often are difficult or impractical to determine computationally. Here, in this work, we present a best-of-both-worlds approach to verifiable scientific machine learning by demonstrating that (1) multiple standard interpolation techniques have informative error bounds that can be computed or estimated efficiently; (2) comparative performance among distinct interpolants can aid in validation goals; (3) deploying interpolation methods on latent spaces generated by deep learning techniques enables some interpretability for black-box models. We present a detailed case study of our approach for predicting lift-drag ratios from airfoil images. Code developed for this work is available in a public Github repository.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Structure-preserving neural networks for the regularized entropy-based closure of a linear, kinetic, radiative transport equation

The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural network-based approximation to the entropy-based closure method to accurately compute the solution of the multi-dimensional moment system with a low memory footprint and competitive computational time. We extend methods developed for the standard entropy-based closure to the regularized entropy-based closures. The main idea is to interpret structure-preserving neural network approximations of the regularized entropy-based closure as a two-stage approximation to the original entropy-based closure. We conduct a numerical analysis of this approximation and investigate optimal parameter choices. Our numerical experiments demonstrate that the method has a much lower memory footprint than traditional methods with competitive computation times and simulation accuracy. The code and all trained networks are provided on GitHub.

entropy closure↗

DOE OSTI2025

rcsb-api : Python Toolkit for Streamlining Access to RCSB Protein Data Bank APIs

The Protein Data Bank (PDB) was founded in 1971 as the first open-access digital data resource in biology to serve as the single global archive for three-dimensional (3D) macromolecular structure data. Current PDB holdings exceed 230,000 experimentally determined structures of proteins, nucleic acids, viruses, and macromolecular machines. The RCSB Protein Data Bank RCSB.org research-focused web portal facilitates search, analyses, and visualization of every PDB structure along with more than one million Computed Structure Models from AlphaFold DB and the ModelArchive. It is powered by a set of publicly available Application Programming Interfaces (APIs) that both support RCSB.org users and provide programmatic access to PDB data. Given the breadth and levels of granularity encompassed in this rich data collection, efficiently accessing the information programmatically may be challenging for new users. RCSB PDB has developed a Python software package, rcsb-api , that facilitates easy and efficient use of RCSB PDB APIs within a Python environment. This software tool is designed to streamline access to the extensive corpus of data housed within the PDB, enabling researchers to search, retrieve, and analyze 3D biostructure data seamlessly. Its use will accelerate research in structural biology, molecular biology and biochemistry, drug discovery, and bioinformatics by providing more efficient tools for data integration and analysis. The new toolkit is available on GitHub (github.com/rcsb/py-rcsb-api) and published to the public Python package repository (PyPI) to foster wider usage and support basic and applied research in fundamental biology, biomedicine, and the energy sciences.

FAIR principles↗

DOE OSTI2023

Sensitivity study of parameters important to Molten Salt Reactor Safety

This paper presents a molten salt reactor (MSR) design parameter sensitivity study using a nodal dynamic modelling methodology with explicitly modified point kinetics equation and Mann’s model for heat transfer. Six parameters that can impact MSR safety are evaluated. A MATLAB-Simulink model inspired by Thorcon’s 550MW th MSR is used for parameter evaluations. A safety envelope was formed to encapsulate power, maximum and minimum temperature, and temperature-induced reactivity feedback. The parameters are perturbed by ±30%. The parameters were then ranked by their subsequent impact on the considered safety envelope, which ranks acceptable parameter uncertainty. The model is openly available on GitHub.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

On relaxations of the max k -cut problem formulations

Here, a tight continuous relaxation is a crucial factor in solving mixed integer formulations of many NP-hard combinatorial optimization problems. The (weighted) max k-cut problem is a fundamental combinatorial optimization problem with multiple notorious mixed integer optimization formulations. In this paper, we explore four existing mixed integer optimization formulations of the max k-cut problem. Specifically, we show that the continuous relaxation of a binary quadratic optimization formulation of the problem is: (i) stronger than the continuous relaxation of two mixed integer linear optimization formulations and (ii) at least as strong as the continuous relaxation of a mixed integer semidefinite optimization formulation. We also conduct a set of experiments on multiple sets of instances of the max k-cut problem using state-of-the-art solvers that empirically confirm the theoretical results in item (i). Furthermore, these numerical results illustrate the advances in the efficiency of global non-convex quadratic optimization solvers and more general mixed integer nonlinear optimization solvers. As a result, these solvers provide a promising option to solve combinatorial optimization problems. Our codes and data are available on GitHub.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

SootLib: A soot model library for combustion simulation

Soot formation in combustion is an important process that affects radiative heat transfer, flame temperatures, and emissions with health and environmental impacts. Soot formation involves complex chemistry for nucleation, growth, oxidation, and coagulation processes. The soot particles vary widely in size and accurate modeling requires representation of the particle size distribution (PSD). Modeling soot is not trivial, and is only one of several physical processes active in combustion systems. This paper presents a software package called SootLib, which is an open-source library for modeling soot formation and other aerosol systems. SootLib is written in C++, is documented with Doxygen, and is available on GitHub. The library includes several models for soot chemistry and coagulation, and it represents the PSD using either a sectional model or the method of moments (MOM). Four closure approaches for the MOM are implemented allowing up to eight moments: monodispersed, an assumed-shape lognormal distribution, the quadrature method of moments, and the method of moments with interpolative closure. SootLib provides an interface for inclusion in other combustion packages including CFD or reacting flow solvers. The range of models allows comparisons and sensitivity studies, and the modularity facilitates extension to other soot models.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

3.0 - MOOSE: Enabling massively parallel multiphysics simulations

The development of MOOSE has kept accelerating since the last release, with over 2,100 pull requests merged over the last 30 months that involved nearly fifty contributors across close to a dozen institutions internationally. The growth in MOOSE's capabilities and downstream applications is reflected in the growth of the community. User support provided on the GitHub discussions forum has steadily increased to nearly 50 daily interactions. New simulation projects, notably to model advanced nuclear reactor and fusion devices, are driving a significant expansion of the capabilities. This paper reports on these developments, with several major released features, new physics modules, and key improvements to the user experience and simulation workflow.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

HARD: A performance portable radiation hydrodynamics code based on FleCSI framework

Hydrodynamics And Radiation Diffusion (HARD) is an open-source application for high-performance simulations of compressible hydrodynamics with radiation-diffusion coupling. Built on the FleCSI (Bergen et al., 2021 [1]) (Flexible Computational Science Infrastructure) framework, HARD expresses its computational units as tasks whose execution can be orchestrated by multiple back-end runtimes, including Legion (Bauer et al., 2012 [2]), MPI (Forum, 1994 [3]), and HPX (Kaiser et al., 2020 [4]). Node-level parallelism is handled through Kokkos (Edwards et al., 2014 [5]), providing a single-source, portable code base that runs efficiently on laptops, small homogeneous clusters, and the largest heterogeneous supercomputers currently available. To ensure scientific reliability, HARD includes a regression test suite that automatically reproduces canonical verification problems such as the Sod and LeBlanc shock tubes, and the Sedov blast wave, comparing numerical solutions against known analytical results. The project is distributed under an OSI-approved license, hosted on GitHub, and accompanied by reproducible build scripts and continuous integration workflows. This combination of performance portability, verification infrastructure, and community-focused development makes HARD a sustainable platform for advancing radiation hydrodynamics research across multiple domains.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

PyHydroGeophysX: An extensible open-source platform for integrating hydrological models with geophysical measurements

Hydrological models and geophysical measurements are widely used tools for understanding subsurface hydrological processes relevant to water resource management, yet they typically remain disconnected due to technical barriers. We present PyHydroGeophysX, an open-source Python platform bridging this gap by providing standardized interfaces between hydrological modeling software (MODFLOW, ParFlow) and geophysical simulation tools (PyGIMLi, SimPEG). The platform implements bidirectional workflows: translating hydrological outputs into simulated geophysical responses through petrophysical models, and extracting hydrological information from geophysical inversions. Key features include bidirectional workflow modules, configurable petrophysical models, time-lapse inversion with temporal regularization, parallel computing, and mesh utilities for property transfer between geophysical and hydrological grids. The modular architecture of PyHydroGeophysX enables researchers to incorporate additional models and methods, fostering broader adoption of integrated hydrogeophysical approaches. The software is freely available on GitHub and is intended for researchers and practitioners working at the intersection of hydrology and geophysics.

Hydrogeophysics↗

DOE OSTI2026

GBOpt: Grain boundary structure optimization using Monte Carlo and evolutionary algorithms

Polycrystalline materials are made of many small crystals separated by grain boundaries (GBs), whose atomic structure strongly influences material properties. Because the structure of a GB determines its properties, the optimal structure must be known in order to determine those impacts. There are many ways of placing atoms in the GB region, but the optimal structure is defined as the one that gives the lowest value of a target property (typically energy). GB structure optimization has been successfully demonstrated using stochastic and evolutionary methods, but no reusable, community-maintained open-source workflow has been developed. GBOpt (Grain Boundary Optimization) is an open-source Python package that creates that workflow, where we have presently implemented two approaches: Markov Chain Monte Carlo, and genetic algorithm based on elite selection. We demonstrate this capability by successfully reproducing the known optimal structures of a specific GB in two materials, and point interested readers to the GitHub repository for additional examples, including optimization for different properties. Both of the implemented approaches recovered the known structures, with the genetic algorithm approach finding the optimal structure faster on average.

99 - GENERAL AND MISCELLANEOUS↗

DOE OSTI2020

Benchmark probabilistic solar forecasts: Characteristics and recommendations

We illustrate and compare commonly used benchmark, or reference, methods for probabilistic solar forecasting that researchers use to measure the performance of their proposed techniques. A thorough review of the literature indicates wide variation in the benchmarks implemented in probabilistic solar forecast studies. To promote consistent and sensible methodological comparisons, we implement and compare ten variants from six common benchmark classes at two temporal scales: intra-hourly forecasts and hourly resolution forecasts. Using open-source Surface Radiation Budget Network (SURFRAD) data from 2018, these benchmark methods are compared using proper probabilistic metrics and common diagnostic tools. Practical implementation issues, such as the impact of missing data and applicability for operational forecasting, are also discussed. Furthermore, we make recommendations for practitioners on the appropriate selection of benchmark methods to properly showcase state-of-the-art improvements in forecast reliability and sharpness. All code and open-source data are available on Github for reproducibility and for other researchers to apply the same benchmark methods to their own data.

14 SOLAR ENERGY↗

DOE OSTI2023

pvlib iotools—Open-source Python functions for seamless access to solar irradiance data

Access to accurate solar resource data is critical for numerous applications, including estimating the yield of solar energy systems, developing radiation models, and validating irradiance datasets. However, lack of standardization in data formats and access interfaces across providers constitutes a major barrier to entry for new users. pvlib python’s iotools subpackage aims to solve this issue by providing standardized Python functions for reading local files and retrieving data from external providers. All functions follow a uniform pattern and return convenient data outputs, allowing users to seamlessly switch between data providers and explore alternative datasets. The pvlib package is community-developed on GitHub: https://github.com/pvlib/pvlib-python. As of pvlib python version 0.9.5, the iotools subpackage supports 12 different datasets, including ground measurement, reanalysis, and satellite-derived irradiance data. The supported ground measurement networks include the Baseline Surface Radiation Network (BSRN), NREL MIDC, SRML, SOLRAD, SURFRAD, and the US Climate Reference Network (CRN). Additionally, satellite-derived and reanalysis irradiance data from the following sources are supported: PVGIS (SARAH & ERA5), NSRDB PSM3, and CAMS Radiation Service (including McClear clear-sky irradiance).

14 SOLAR ENERGY↗

DOE OSTI2023

Uncertainty quantification in machine learning for engineering design and health prognostics: A tutorial

On top of machine learning (ML) models, uncertainty quantification (UQ) functions as an essential layer of safety assurance that could lead to more principled decision making by enabling sound risk assessment and management. The safety and reliability improvement of ML models empowered by UQ has the potential to significantly facilitate the broad adoption of ML solutions in high-stakes decision settings, such as healthcare, manufacturing, and aviation, to name a few. In this tutorial, we aim to provide a holistic lens on emerging UQ methods for ML models with a particular focus on neural networks and the applications of these UQ methods in tackling engineering design as well as prognostics and health management problems. Towards this goal, we start with a comprehensive classification of uncertainty types, sources, and causes pertaining to UQ of ML models. Next, we provide a tutorial-style description of several state-of-the-art UQ methods: Gaussian process regression, Bayesian neural network, neural network ensemble, and deterministic UQ methods focusing on spectral-normalized neural Gaussian process. Established upon the mathematical formulations, we subsequently examine the soundness of these UQ methods quantitatively and qualitatively (by a toy regression example) to examine their strengths and shortcomings from different dimensions. Then, we review quantitative metrics commonly used to assess the quality of predictive uncertainty in classification and regression problems. Afterward, we discuss the increasingly important role of UQ of ML models in solving challenging problems in engineering design and health prognostics. In conclusion, two case studies with source codes available on GitHub are used to demonstrate these UQ methods and compare their performance in the life prediction of lithium-ion batteries at the early stage (case study 1) and the remaining useful life prediction of turbofan engines (case study 2).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

OpenMSI Arrayed Analysis Toolkit: Analyzing Spatially Defined Samples Using Mass Spectrometry Imaging

Mass spectrometry imaging (MSI) has primarily been applied in localizing biomolecules within biological matrices. Although well-suited, the application of MSI for comparing thousands of spatially defined spotted samples has been limited. One reason for this is a lack of suitable and accessible data processing tools for the analysis of large arrayed MSI sample sets. In this paper, the OpenMSI Arrayed Analysis Toolkit (OMAAT) is a software package that addresses the challenges of analyzing spatially defined samples in MSI data sets. OMAAT is written in Python and is integrated with OpenMSI (http://openmsi.nersc.gov), a platform for storing, sharing, and analyzing MSI data. By using a web-based python notebook (Jupyter), OMAAT is accessible to anyone without programming experience yet allows experienced users to leverage all features. OMAAT was evaluated by analyzing an MSI data set of a high-throughput glycoside hydrolase activity screen comprising 384 samples arrayed onto a NIMS surface at a 450 μm spacing, decreasing analysis time >100-fold while maintaining robust spot-finding. The utility of OMAAT was demonstrated for screening metabolic activities of different sized soil particles, including hydrolysis of sugars, revealing a pattern of size dependent activities. Finally, these results introduce OMAAT as an effective toolkit for analyzing spatially defined samples in MSI. OMAAT runs on all major operating systems, and the source code can be obtained from the following GitHub repository: https://github.com/biorack/omaat.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Improving Enzyme Optimum Temperature Prediction with Resampling Strategies and Ensemble Learning

Accurate prediction of the optimal catalytic temperature ( T opt ) of enzymes is vital in biotechnology, as enzymes with high T opt values are desired for enhanced reaction rates. Recently, a machine learning method (temperature optima for microorganisms and enzymes, TOME) for predicting T opt was developed. TOME was trained on a normally distributed data set with a median T opt of 37 °C and less than 5% of T opt values above 85 °C, limiting the method’s predictive capabilities for thermostable enzymes. Due to the distribution of the training data, the mean squared error on T opt values greater than 85 °C is nearly an order of magnitude higher than the error on values between 30 and 50 °C. Here, we apply ensemble learning and resampling strategies that tackle the data imbalance to significantly decrease the error on high T opt values (>85 °C) by 60% and increase the overall R 2 value from 0.527 to 0.632. The revised method, temperature optima for enzymes with resampling (TOMER), and the resampling strategies applied in this work are freely available to other researchers as Python packages on GitHub.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

NEXTorch: A Design and Bayesian Optimization Toolkit for Chemical Sciences and Engineering

Automation and optimization of chemical systems require well-informed decisions on what experiments to run to reduce time, materials, and/or computations. Data-driven active learning algorithms have emerged as valuable tools to solve such tasks. Bayesian optimization, a sequential global optimization approach, is a popular active-learning framework. Past studies have demonstrated its efficiency in solving chemistry and engineering problems. Here we introduce NEXTorch, a library in Python/PyTorch, to facilitate laboratory or computational design using Bayesian optimization. NEXTorch offers fast predictive modeling, flexible optimization loops, visualization capabilities, easy interfacing with legacy software, and multiple types of parameters and data type conversions. It provides GPU acceleration, parallelization, and state-of-the-art Bayesian optimization algorithms and supports both automated an d human-in-the-loop optimization. The comprehensive online documentation introduces Bayesian optimization theory and several examples from catalyst synthesis, reaction condition optimization, parameter estimation, and reactor geometry optimization. NEXTorch is open-source and available on GitHub

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Adaptive Ensemble Refinement of Protein Structures in High Resolution Electron Microscopy Density Maps with Radical Augmented Molecular Dynamics Flexible Fitting

Recent advances in cryo-electron microscopy (cryo-EM) have enabled modeling macromolecular complexes that are essential components of the cellular machinery. The density maps derived from cryo-EM experiments are often integrated with manual, knowledge or artificial intelligence driven, and physics-guided computational methods to build, fit, and refine molecular structures. Going beyond a single stationary- structure determination scheme, it is becoming more common to interpret the experimental data with an ensemble of models, which contributes to an average observation. Hence, there is a need to decide on the quality of an ensemble of protein structures on-the-fly, while refining them against the density maps. Here, we introduce such an adaptive decision making scheme during the molecular dynamics flexible fitting (MDFF) of biomolecules. Using RADICAL-Cybertools, and the new RADICAL augmented MDFF implementation (R-MDFF) is examined in high-performance computing environments for refinement of two protein systems, Adenylate Kinase and Carbon Monoxide Dehydrogenase. For the test cases, use of multiple replicas in flexible fitting with adaptive decision making in R-MDFF improves the overall correlation to the density by 40% relative to the refinements of the brute-force MDFF. The improvements are particularly significant at high, 2 - 3 Å, map resolutions. More importantly, the ensemble model captures key features of biologically relevant molecular dynamics that is inaccessible to a single-model interpretation. Finally, the pipeline is applicable to systems of growing sizes, which is demonstrated using ensemble refinement of capsid proteins from Chimpanzee adenovirus. The overhead for decision making remaining low and robust to computing environments. The software is publicly available on GitHub and includes a short user guide to install the R-MDFF on different computing environments, from local Linux based workstations to High Performance Computing (HPC) environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗