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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Workflow for Process Automation of Soil Gas Results from an Automated Soil Gas-Sampling System for Application in Carbon Storage Projects

Conference presentation at Geoconvention, Calgary, Alberta, Canada, May 12–14, 2025. The Energy & Environmental Research Center (EERC) developed an automated workflow for processing soil gas measurements collected from the automated soil gas-sampling systems deployed across the project site. Raw soil gas measurements are collected from each station every 4 hours and automatically uploaded to a cloud database. The workflow begins by writing code to download the data to a workstation automatically, then the data are published to an online dashboard that visualizes the measurements in time-series plots and a process-based decision-making framework. This automated workflow accelerates the time from data acquisition to decision-making. It supports carbon storage project operators by preparing and delivering a live, standardized dataset for quick analysis and source attribution to provide assurance of containment and overall permit compliance.

02 PETROLEUM↗
DOE OSTI2023

PFLOTRAN Development FY2021

The Spent Fuel & Waste Science and Technology (SFWST) Campaign of the U.S. Department of Energy (DOE) Office of Nuclear Energy (NE), Office of Spent Fuel & Waste Disposition (SFWD) is conducting research and development (R&D) on geologic disposal of spent nuclear fuel (SNF) and high-level nuclear waste (HLW). A high priority for SFWST disposal R&D is to develop a disposal system modeling and analysis capability for valuating disposal system performance for nuclear waste in geologic media. This report describes fiscal year (FY) 2021 advances of the PFLOTRAN Development group of the SFWST Campaign. The mission of this group is to develop a geologic disposal system modeling capability for nuclear waste that can be used to probabilistically assess the performance of generic disposal concepts. In FY 2021, development proceeded along three main thrusts: software infrastructure, code performance, and process model advancement. Software infrastructure improvements included implementing an Agile software development framework and making improvements to the QA Test Suite. Code performance improvements included development of advanced linear and nonlinear solvers as well as design of flexible smoothing algorithms for capillary pressure functions. Process modeling advancements included the addition of flexible thermal conductivity function definitions and refinement of multi-continuum reactive transport to support Sandia’s participation in DECOVALEX. This report fulfills the GDSA PFLOTRAN Development Work Package Level 3 Milestone – PFLOTRAN Development, FY2021, M3SF-21SN010304072.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

An advanced membrane-based HMX model and its application in utilizing sensible and latent heat removed in space cooling

This paper presents a comprehensive simulation model for advanced membrane-based heat and mass exchanger (HMX) components which account for three separate fluid streams with complex flow patterns. The model was implemented with various liquid desiccants and their properties (including LiCl, CaCl and ionic liquid (IL)). Preliminary model validation is presented using data from a laboratory prototype absorber. The paper also presents implementation of the model into a sorption system modeling platform and analyzes potential benefit analysis of the HMX component in utilizing the sensible and latent heat removed in space cooling to heat water. The developed model and codes are expected to enable detailed optimization studies and identify novel configurations for the three-fluid HMX maximum performance and cost effectiveness.

Gao, Zhiming↗
DOE OSTI2023

Electric Vehicles at Scale (EVs@Scale) Laboratory Consortium Deep-Dive Technical Meetings: High Power Charging (HPC) Summary Report

Electric vehicle (EV) adoption will change the composition of EV charging load to higher-power charging as more medium- (MD) and heavy-duty (HD) applications are electrified, and as all vocations, including light-duty (LD) vehicles, are capable of faster charging. These shifts provide the opportunity for high-power charging (HPC) and facility equipment to evolve and improve efficiency, cost, and space. High-Power Electric Vehicle Charging Hub Integration Platform (eCHIP) project designs and develops a high-power, interoperable charging experimental platform to research, develop, and demonstrate the integration approaches and technology solutions. The project addresses (1) interconnection and management of a grid-tied inverter; (2) development of a DC distribution system that is responsible for system energy management, interoperability, and DC protection; (3) modular DC/DC conversion for vehicle charging; (4) EV charging interface and DC/DC integration; and (5) smart charge control and vehicle-to-edge (vehicle-to-building [V2B], vehicle-to-everything [V2X]) capability. This summary presentation is the first technical progress output of the project. It provides insight for the first deep-dive technical meeting outputs in terms of research presentations and also includes summary of the discussions occurred in the follow-up breakout sessions. The summary presentation covers three technical areas: (1) HPC: State of the art power architectures and the design of the power electronics, (2) Modeling, energy management, and power control in the HPC station, and (3) Next Generation Profiles for high power charging characterization.

ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

An Evaluation of The Dynamic Physical Security Risk Assessment Methodology for Fleet-Wide Applications

The requirements for U.S. nuclear power plants to maintain a large onsite physical security force contribute to their high operational costs. The cost of maintaining the current physical security posture is approximately 10% of the overall operation and maintenance budget for commercial nuclear power plants. The goal of the Light Water Reactor Sustainability (LWRS) program’s physical security pathway is to develop tools, methods, and technologies and provide the technical basis for an optimized physical security posture. The conservatisms built into current security postures may be analyzed and minimized to reduce security costs while still ensuring adequate security and operational safety. The research performed at Idaho National Laboratory within LWRS program’s physical security pathway has successfully developed a dynamic force-on-force modeling framework using various computer simulation tools and integrating them with the dynamic assessment Event Modeling Risk Assessment using Linked Diagrams (EMRALD) tool. This integrated process for physical security analysis is named Modeling and Analysis for Safety Security using Dynamic EMRALD Framework (MASS-DEF). This document provides an update on the progress in applying the MASS-DEF process to an operating commercial nuclear power plant as well as additional industry feedback regarding use of the tool for other physical security risk-informed topics. This report is only a summary of the progress and does not contain specific modeling results as those contain sensitive security information. Previous reports described how a user could integrate their plant-specific force-on-force models with the dynamic simulation tool EMRALD, model operator actions, and integrate with probabilistic risk assessment tools, such as CAFTA (Computer Aided Fault Tree Analysis System) or SAPHIRE (Systems Analysis Programs for Hands-on Integrated Reliability Evaluations), and with thermal-hydraulic tools, such as RELAP-5 or MAAP. Previous reports applied various combinations of available simulations codes with EMRALD using generic plant models to demonstrate how to perform the analysis. This report is an update the progress of applying the dynamic computational framework to an actual nuclear facility using their security scenarios and timelines. This report also provides an update to the procedural guidance for the MASS-DEF process and an overview of the generic models available for use by utilities. This report does not contain any plant’s sensitive information and/or safeguards information. This study’s purpose was to verify that the results achieved using generic models are similar to actual plant results and refine our guidance on the use of the framework. This assessment enables further analysis, such as what-if scenarios and staff-reduction evaluation, thereby optimizing physical security at plants.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Workflow for Process Automation of Soil Gas Results from an Automated Soil Gas-Sampling System for Application in Carbon Storage Projects

Extended abstract for Geoconvention, Calgary, Alberta, Canada, May 12–14, 2025. The Energy & Environmental Research Center (EERC) developed an automated workflow for processing soil gas measurements collected from the automated soil gas-sampling systems deployed across the project site. Raw soil gas measurements are collected from each station every 4 hours and automatically uploaded to a cloud database. The workflow begins by writing code to download the data to a workstation automatically, then the data are published to an online dashboard that visualizes the measurements in time-series plots and a process-based decision-making framework. This automated workflow accelerates the time from data acquisition to decision-making. It supports carbon storage project operators by preparing and delivering a live, standardized dataset for quick analysis and source attribution to provide assurance of containment and overall permit compliance.

02 PETROLEUM↗
DOE OSTI2022

Application of FARM to an IES scenario within the FORCE ecosystem

The FARM (Feasible Actuator Range Modifier) software module is a component of the RAVEN-based FORCE framework for analysis of Integrated Energy Systems (IES). FARM supports the HERON software module in the evaluation of the optimal dispatch by evaluating feasible set-points for the different IES unit components. Set-points are required to satisfy limits on both production variables (i.e., the variables to be optimized such as the electrical power, the hydrogen production rate, etc.) and process variables tied to the service life of equipment (e.g., steam flowrate, vessel pressure, turbine firing temperature, etc.). This problem is addressed by adopting a two-stage approach. First, the HERON power dispatcher determines set-points that meet the constraints on the former variables (e.g., power levels and power ramp rate limits). These constraints are called explicit constraints. Then, FARM adjusts these set-points to ensure the respect of the limits on the latter variables given the knowledge of the system physics acquired through machine learning algorithms. These constraints are called implicit constraints. From this standpoint, FARM constitutes a bridge between the HERON power dispatcher that adopts a simplified description of the IES unit (low-resolution physics) and the HYBRID high-fidelity models (high-resolution physics). The original version of the FARM software module (FARM-Alpha) was released by Argonne National Laboratory in January 2021. In the latest version of the code released in July 2022 (FARM-Delta), the Reference Governor (RG) algorithm was upgraded to a Multi-Input Multi-Output version from its original Single-Input Single-Output form. The RG algorithm acts to enforce constraints. With this improvement an IES unit is now treated as a single dynamic system from the standpoint of control. The crosstalk among components in an IES unit is now fully considered thereby ensuring a true optimization is obtained for those units that have multiple set-points. In this report, the capabilities of FARM-Delta operating within the FORCE ecosystem are demonstrated for an IES test case. The specific configuration of IES unit for this case was selected by the IES team with consultation from the Advanced Reactor IES Expert Group. A full TEA analysis that invoked HERON, HYBRID, FARM, and RAVEN was performed and serves to demonstrate how the latest modification to FARM algorithms (i.e., state variable selection, state-space matrices derivation, set-point verification) can shape setpoints that might otherwise compromise the health of equipment through accelerated wear and tear. In this specific test case, it was demonstrated that these algorithms ensure a more efficient utilization of steam resources to be shared by two different subsystems, namely Balance of Plant (BOP) and High-Temperature Steam Electrolysis (HTSE). Finally, some code improvements that can further enhance the user-friendliness are suggested.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Field To Farm Aggregation For Agricultural Systems

The Fields to Farms methodology illustrates the generation of farm parcels from the Crop Data Layer (CDL), a raster dataset containing 133 categories representing various crop types and land uses. This methodology involves two primary steps: Field Delineation and Farm Aggregation. The code specifically addresses the aggregation of pre-delineated fields within a county to form farms, adhering to predefined criteria for farm size categories. It is assumed that the field delineation process, which involves creating vector polygons from CDL raster, has been completed beforehand, possibly through external tools or methods. Upon initialization, the script processes county-level fields, preparing them for farm aggregation. In the Farm Aggregation phase, the code iteratively combines delineated fields into farms based on specified criteria, continuing until the aggregated farm size meets predefined thresholds derived from data from the 2017 National Agricultural Statistics Service (NASS) census. Throughout this iterative process, the script dynamically adjusts the aggregation to ensure alignment with the desired distribution reported by NASS. The resulting output of the script is a GeoDataFrame containing classified farms, which are subsequently saved as GeoPackage files. These files enable further analysis and visualization, facilitating comprehensive exploration of the farm landscape generated through the methodology.

Paudel, Rajiv [Idaho National Laboratory (INL), Id↗
DOE OSTI2025

WRF-ELM v1.0: a regional climate model to study land–atmosphere interactions over heterogeneous land use regions

Abstract. The Energy Exascale Earth System Model (E3SM) Land Model (ELM) is a state-of-the-art land surface model that simulates the intricate interactions between the terrestrial land surface and other components of the Earth system. Originating from the Community Land Model (CLM) version 4.5, ELM has been under active development, with added new features and functionality, including plant hydraulics, radiation–topography interaction, subsurface multiphase flow, and more explicit land use and management practices. This study integrates ELM v2.1 with the Weather Research and Forecasting (WRF; WRF-ELM) model through a modified Lightweight Infrastructure for Land Atmosphere Coupling (LILAC) framework, enabling affordable high-resolution regional modeling by leveraging ELM's innovative features alongside WRF's diverse atmospheric parameterization options. This framework includes a top-level driver for variable communication between WRF and ELM and Earth System Modeling Framework (ESMF) caps for the WRF atmospheric component and ELM workflow control, encompassing initialization, execution, and finalization. Importantly, this LILAC–ESMF framework demonstrates a more modular approach compared to previous coupling efforts between WRF and land surface models. It maintains the integrity of ELM's source code structure and facilitates the transfer of future developments in ELM to WRF-ELM. To test the ability of the coupled model to capture land–atmosphere interactions over regions with a variety of land uses and land covers, we conducted high-resolution (4 km) WRF-ELM ensemble simulations over the Great Lakes region (GLR) in the summer of 2018 and systematically compared the results against observations, reanalysis data, and WRF-CTSM (WRF coupled with the Community Terrestrial Systems Model). In general, the coupled WRF-ELM model has reasonably captured the spatial distribution of surface state variables and fluxes across the GLR, particularly over the natural vegetation areas. The evaluation results provide a baseline reference for further improvements in ELM in the regional application of high-resolution weather and climate predictions. Our work serves as an example to the model development community for expanding an advanced land surface model's capability to represent fully-coupled land–atmosphere interactions at fine spatial scales. The development and release of WRF-ELM marks a significant advancement for the ELM user community, providing opportunities for fine-scale regional representation, parameter calibration in coupled mode, and examination of new schemes with atmospheric feedback.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Quantitative comparisons of electron-scale turbulence measurements in NSTX via synthetic diagnostics for high-k scattering.

Two synthetic diagnostics are implemented for the high-k scattering system in NSTX [D. R. Smith, E. Mazzucato, W. Lee, H. K. Park, C. W. Domier, and N. C. Luhmann Jr., Rev. Sci. Instrum., 79, 123501 (2008)] allowing direct comparisons between synthetic and experimentally detected frequency and wavenumber spectra of electron-scale turbulence fluctuations. Synthetic diagnostics were formulated in real-space and in wavenumber space, and were deployed to realistic electron-scale simulations carried out with the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186 (2003) 545]. A highly unstable ETG regime (electron temperature gradient mode) in a modest beta NSTX NBI-heated H-mode discharge was chosen for the analysis. Mapping the measured wavenumbers to field aligned coordinates showed that the high-k system is sensitive to fluctuations that are closer to the spectral peak in the density fluctuation wavenumber spectrum (streamers) than originally predicted. Analysis of synthetic spectra show that the frequency response of the detected fluctuations is dominated by Doppler shift and insensitive to the turbulence drive. The shape of the high-k density fluctuation wavenumber spectrum is sensitive to the ETG turbulence drive conditions, and can be reproduced in a sensitivity scan of the most pertinent turbulent drive terms in the simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Tuning the Radius Ratio to Enhance Thermoelectric Properties in the Zintl Compounds AM 2 Sb 2 (A = Ba, Sr; M = Zn, Cd)

Five novel Zintl phase solid solutions in the Ba 1–x Sr x Zn 2–y Cd y Sb 2 (0 ≤ x ≤ 0.13(1); 0 ≤ y ≤ 0.32(2)) system were successfully synthesized by the molten Pb metal-flux method, and the powder X-ray diffraction and single-crystal X-ray diffraction analyses proved that all five title compounds adopted the BaCu 2 S 2 -type phase having the orthorhombic Pnma space group (Z = 4, Pearson code oP20) with five crystallographically independent atomic sites. The previously studied BaCu 2 S 2 -type antimonides demonstrated a limited tolerance for doping in contrast to the CaAl 2 Si 2 -type antimonides. To understand the relatively narrower phase width and limited dopability of the title BaCu 2 S 2 -type phase than the CaAl 2 Si 2 -type phase in the overall Ba 1–x Sr x Zn 2–y Cd y Sb 2 system, the radius ratio of cations and anionic elements r + /r – for two structure types were thoroughly investigated. For the first time, the r + /r – ratio was identified as a critical factor for the phase selectivity: (1) r + /r – > 1 favored the BaCu 2 S 2 -type phase, and (2) r + /r – < 1 favored the CaAl 2 Si 2 -type phase. Further, we also revealed the structural transformation mechanism from the more widely observed CaAl 2 Si 2 -type phase to the title BaCu 2 S 2 -type phase as the relatively larger cationic elements were introduced to the system. A series of DFT calculations using the three hypothetical models indicated that a resonance peak near EF in the density of states curves was descended from the relatively flat band structure at several special symmetry points rationalizing the enhanced Seebeck coefficients of Ba 0.94(1) Sr 0.06 Zn 1.86(3) Cd 0.14 Sb 2 and Ba 0.96(1) Sr 0.04 Zn 1.68(2) Cd 0.32 Sb 2 . Electron localization function analysis rationalized the correlation between the polarity change of anionic Zn/Cd–Sb bonds and the charge carrier mobility on the anionic frameworks. Temperature-dependent thermoelectric properties were studied for the four title compounds, and the results proved that the Sr and Cd doping in the title Ba 1–x Sr x Zn 2–y Cd y Sb 2 system successfully enhanced the ZT values through the increased Seebeck coefficients and the reduced total thermal conductivities.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Model Inputs, Outputs, and Scripts associated with: “Spatial microbial respiration variations in the hyporheic zones within the Columbia River Basin”

This data package is associated with the publication “Spatial microbial respiration variations in the hyporheic zones within the Columbia River Basin” published in the Journal of Geophysical Research: Biogeosciences (Son et al. 2022) available at doi: 10.1029/2021JG006654. This data package includes the key model inputs/outputs of the river corridor model for the Columbia River Basin (CRB) and the model source codes, which were used in the manuscript. The model is a carbon-nitrogen-coupled river corridor model (RCM), and the model is used to quantify hyporheic zone (HZ) aerobic and anaerobic respiration at the NHDPLUS stream reach scales. The RCM used in this study combines empirical substrate models derived from observations and three microbially driven reactions to compute respiration of the HZ for each National Hydrography Dataset (NHD) reach within the CRB. The reactions in HZs of each NHD reach include anaerobic respiration and two-step anaerobic respiration via denitrification. Our HZ respiration estimates are limited to the lotic (or flowing) stream/river systems, and do not account for the respiration process in water column. Note that the RCM only simulates the HZ’s contribution to the dissolved carbon dioxide (CO2) concentrations in the streams, and the CO2 emissions to the atmosphere are not modelled. The model computes at hourly timesteps because of the fast reaction rates. The key input data of the model are exchange flux, residence time, and stream solute (dissolved organic carbon (DOC), dissolved oxygen (DO), and nitrate concentrations). These inputs are constant over time and represent long-term averaged values.This modeling framework successfully quantified HZ respiration components over multiple scales. It revealed key mechanisms driving the spatial variation of HZ aerobic and anaerobic respiration in reaches with varying hydrologic and substrate conditions. Thus, this modeling study offers a testing hypothesis in different river system (e.g., climate and biomes) for the HZ respiration processes, and can be used as a sampling design tool for large-scale HZ experimental studies.This dataset contains five folders: (1) model_inputs, (2) model_outputs, (3) Rscripts, (4) figures, and (5) model_codes. It also contains a readme, file level metadata (FLMD), and data dictionary (dd). Please see the FLMD for a list of all the files contained in this data package and descriptions for each. The model_inputs folder contains the model inputs used to drive the model simulations. The model_outputs folder contains key model output files from the river corridor model. The Rscripts folder contains the Rscripts for pre- and post- processing model results. The figures folder contains the raw figures associated with the manuscript. The model_codes folder includes key model source codes/input files. All files are .jpg, .jpeg, .out, .e, .od, .dat, .sub, .F90, .0, .R, .sbx, .cpg, .sbn, .shx, .shp, .dbf, .prj, .tfw, .tif, .xml, .pdf, or .csv.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Verification methods for drift–diffusion reaction models for plasma simulations

Abstract Compared to other computational physics areas such as codes for general computational fluid dynamics, the documentation of verification methods for plasma fluid codes remains under developed. Current analytical solutions for plasma are often highly limited in terms of testing highly coupled physics, due to the harsh assumptions needed to derive even simple plasma equations. This work highlights these limitations, suggesting the method of manufactured solutions (MMSs) as a potential option for future verification efforts. To demonstrate the flexibility of MMS in verifying these highly coupled systems, the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework was utilized. Thanks to the MOOSE framework’s robustness and modularity, as well as to its physics module capabilities and ecosystem applications (i.e. Zapdos and the chemical reaction network) developed for plasma physics modeling and simulation, this report lays the groundwork for a structured method of conducting plasma fluid code verification.

DeChant, Corey (ORCID:0000000293779732)↗
DOE OSTI2022

Implementing the three-particle quantization condition for π + π + K + and related systems

Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition. Specifically, we discuss the need to modify the upper limit of the cutoff function due to the fact that the left-hand cut in the scattering amplitudes for two nondegenerate particles moves closer to threshold; we describe the decomposition of the three-particle amplitude K df,3 into the matrix basis used in the quantization condition, including both s and p waves, with the latter arising in the amplitude for two nondegenerate particles; we derive the threshold expansion for the lightest three-particle state in the rest frame up to O(1/L 5 ); and we calculate the leading-order predictions in chiral perturbation theory for K df,3 in the π + π + K + and π + K + K + systems. We focus mainly on systems with two identical particles plus a third that is different (“2+1” systems). We describe the formalism in full detail, and present numerical explorations in toy models, in particular checking that the results agree with the threshold expansion, and making a prediction for the spectrum of π + π + K + levels using the two- and three-particle interactions predicted by chiral perturbation theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Cyber-Physical System Implementation for Manufacturing With Analytics in the Cloud Layer

Effective and efficient modern manufacturing operations require the acceptance and incorporation of the fourth industrial revolution, also known as Industry 4.0. Traditional shop floors are evolving their production into smart factories. To continue this trend, a specific architecture for the cyber-physical system is required, as well as a systematic approach to automate the application of algorithms and transform the acquired data into useful information. This work makes use of an approach that distinguishes three layers that are part of the existing Industry 4.0 paradigm: edge, fog, and cloud. Each of the layers performs computational operations, transforming the data produced in the smart factory into useful information. Trained or untrained methods for data analytics can be incorporated into the architecture. A case study is presented in which a real-time statistical control process algorithm based on control charts was implemented. The algorithm automatically detects changes in the material being processed in a computerized numerical control (CNC) machine. The algorithm implemented in the proposed architecture yielded short response times. The performance was effective since it automatically adapted to the machining of aluminum and then detected when the material was switched to steel. The data were backed up in a database that would allow traceability to the line of g-code that performed the machining.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Real-time Object Bounding in LiDAR Data With Computer Vision

The Multimodal Measurement System is a roadside radiation measurement testbed used to detect radiation sources in passing vehicles. It works by combining sensor signals from various modalities to produce a thorough scan of the source. A LiDAR sensor is used to measure the dimensions of the vehicle and provide a velocity estimate. However, the current LiDAR setup uses propriety software for which the source code is unavailable and cannot be updated to improve performance. Therefore, it is imperative to the accuracy of the analysis to create a custom vehicle detection that can return the dimensions and velocity of passing vehicles in real time. This new custom detection is written in C++ using the PointCloud Library, which keeps it lightweight. It also utilizes Docker and the Robot Operating System, which allows the versatility of running both on a small computer or the Lawrence Livermore National Laboratory cluster while utilizing different models of LiDAR sensors. The custom detection outperforms the current detection model, which increases the accuracy of radiation source detection.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Preconditioned least‐squares Petrov–Galerkin reduced order models

Abstract In this article, we introduce a methodology for improving the accuracy and efficiency of reduced order models (ROMs) constructed using the least‐squares Petrov–Galerkin (LSPG) projection method through the introduction of preconditioning. Unlike prior related work, which focuses on preconditioning the linear systems arising within the ROM numerical solution procedure to improve linear solver performance, our approach leverages a preconditioning matrix directly within the minimization problem underlying the LSPG formulation. Applying preconditioning in this way has the potential to improve ROM accuracy for several reasons. First, preconditioning the LSPG formulation changes the norm defining the residual minimization, which can improve the residual‐based stability constant bounding the ROM solution's error. The incorporation of a preconditioner into the LSPG formulation can have the additional effect of scaling the components of the residual being minimized to make them roughly of the same magnitude, which can be beneficial when applying the LSPG method to problems with disparate scales (e.g., dimensional equations, multi‐physics problems). Importantly, we demonstrate that an “ideal preconditioned” LSPG ROM (a ROM in which the preconditioner is the inverse of the Jacobian of its corresponding full order model) emulates projection of the full order model solution increment onto the reduced basis. This quantity defines a lower bound on the error of a ROM solution for a given reduced basis. By designing preconditioners that approximate the Jacobian inverse—as is common in designing preconditioners for solving linear systems—it is possible to obtain a ROM whose error approaches this lower bound. The proposed approach is evaluated on several mechanical and thermo‐mechanical problems implemented within the Albany HPC code and run in the predictive regime, with prediction across material parameter space. We demonstrate numerically that the introduction of simple Jacobi, Gauss‐Seidel, and ILU preconditioners into the proper orthogonal decomposition/LSPG formulation reduces significantly the ROM solution error, the reduced Jacobian condition number, the number of nonlinear iterations required to reach convergence, and the wall time (thereby improving efficiency). Moreover, our numerical results reveal that the introduction of preconditioning can deliver a robust and accurate solution for test cases in which the unpreconditioned LSPG method fails to converge.

Lindsay, Payton↗