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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Techno-Economic Analysis for the Addition of Thermal Energy Storage to a Campus With Existing Battery Storage

Rising global temperatures and increasing energy demands pose significant challenges for energy management, particularly in institutional and commercial settings. As cooling needs grow, campuses must balance operational efficiency, cost control, and grid stability. Energy storage solutions, such as thermal energy storage (TES) systems, offer a promising approach to shifting energy consumption from peak to off-peak periods, alleviating peak demand, reducing utility costs, and enhancing grid resilience. When integrated with existing battery energy storage systems (BESS), TES can further optimize load management and improve energy savings, especially in buildings with diverse energy needs. This article presents a techno-economic analysis of integrating a chilled water TES system into the central plant at California State University, Dominguez Hills, which already operates a BESS. We assess three TES sizing strategies—full storage, load leveling, and peak demand limiting—by modeling and simulations based on historical energy loads. Our findings show that we can control TES systems to complement BESS operation, with campus-level load leveling providing the greatest cost savings by reducing peak demands. Furthermore, the study also evaluates the long-term economic viability of TES, considering installation costs, energy savings, and payback periods under varying tariffs. This research offers practical guidance for institutions seeking to enhance energy resilience and reduce operational costs through energy storage solutions.

25 ENERGY STORAGE↗
DOE OSTI2021

Thermal-Mechanical Elastic-Plastic and Ductile Failure Model Calibrations for 6061-T651 Aluminum Alloy from Plate

Numerical simulations of metallic structures undergoing rapid loading into the plastic range require material models that accurately represent the response. In general, the material response can be seen as having four interrelated parts: the baseline response under slow loading, the effect of strain rate, the conversion of plastic work into heat and the effect of temperature. In essence, the material behaves in a thermal-mechanical manner if the loading is fast enough so when heat is generated by plastic deformation it raises the temperature and therefore influences the mechanical response. In these cases, appropriate models that can capture the aspects listed above are necessary. The matters of interest here are the elastic-plastic response and ductile failure behavior of 6061-T651 aluminum alloy under the conditions described above. The work was accomplished by first designing and conducting a material test program to provide data for the calibration of a modular $J_2$ plasticity model with isotropic hardening as well as a ductile failure model. Both included modules that accounted for temperature and strain rate dependence. The models were coupled with an adiabatic heating module to calculate the temperature rise due to the conversion of plastic work to heat. The test program included uniaxial tension tests conducted at room temperature, 150 and 300 C and at strain rates between 10 –4 and 10 3 1/s as well as four geometries of notched tension specimens and two tests on specimens with shear-dominated deformations. The test data collected allowed the calibration of both the plasticity and the ductile failure models. Most test specimens were extracted from a single piece of plate to maintain consistency. Notched tension tests came from a possibly different plate, but from the same lot. When using the model in structural finite element calculations, element formulations and sizes different from those used to model the test specimens in the calibration are likely to be used. A brief investigation demonstrated that the failure model can be particularly sensitive to the element selection and provided an initial guide to compensate in a specific example.

36 MATERIALS SCIENCE↗
DOE OSTI2020

HBU R and D Cask Transportation Options - 20436

The TN-32B HBU Demonstration Cask was successfully loaded in November 2017 with 32 high burnup (HBU) fuel assemblies at Dominion's North Anna Nuclear Plant and is collecting thermal data as intended. The first two phases of this very successful project sponsored by DOE and EPRI was designed to collect thermal data of HBU fuel to support extended storage. The next phase of the project requires the cask be licensed for transportation so the cask can be relocated to a site (to be determined by DOE) to facilitate long term monitoring and additional research on the fuel. This is a unique challenge given the constraints that exist for this particular bolted metal cask. The TN-32B cask is a 234,288 lb. (storage configuration) dry storage system that was selected for this project and it was modified to provide thermal data and the ability to collect gas samples after loading. Several major issues must be addressed to obtain the transport license including protecting the seven lid penetrations that were made to allow for the insertion of the thermocouples into the selected fuel assemblies after the cask was loaded. In order to protect the integrity of the research, the payload must remain as is. Therefore, the cask system must be placed into the transportation configuration without rewetting the fuel, replacing the lid and without removing the thermocouple instrumentation that is currently installed. A critical portion of the design and engineering that was performed in the first two phases of the project was to ensure that future transportation of the cask was integrated into the approach. Efforts were made to accommodate requirements such as containment boundary leakage testing, installation of impact limiter brackets and lid bolts suitable for transportation. Due to the science requirements of the project, the fuel selected was intended to yield the highest payload temperatures permitted to provide the greatest value for the researchers. This resulted in higher than usual external dose rates and surface temperatures that warranted performing as much preparatory work prior to cask loading to ensure ALARA and personnel safety to the greatest extent practical rather than working on a loaded cask. In addition to the work performed prior to cask load, there are remaining challenges such as protecting the modified lid, design and fabrication of impact limiters that accommodate the modified cask lid and preserving the thermocouple connections for continued monitoring. The project team is currently performing the necessary calculations, engineering, and design to support the licensing as required by the US NRC. Pre-application meetings have been held to inform the regulator of the planned technical approach to ensure compliance with the applicable regulations. The current plan is to obtain the transportation C of C by the end of 2021. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Chapter 6: Abuse Response of Batteries Subjected to Mechanical Impact

Electrochemical and thermal models to simulate nominal performance and abuse response of lithium-ion cells and batteries have been reported widely in the literature. Studies on mechanical failure of cell components and how such events interact with the electrochemical and thermal response are relatively less common. This chapter outlines a framework developed under the Computer Aided Engineering for Batteries program to couple failure modes resulting from external mechanical loading to the onset and propagation of electrochemical and thermal events that follow. Starting with a scalable approach to implement failure criteria based on thermal, mechanical, and electrochemical thresholds, we highlight the practical importance of these models using case studies at the cell and module level. The chapter also highlights a few gaps in our understanding of the comprehensive response of batteries subjected to mechanical crash events, the stochastic nature of some of these failure events, and our approach to build safety maps that help improve robustness of battery design by capturing the sensitivity of some key design parameters to heat generation rates under different mitigation strategies.

abuse simulations↗
DOE OSTI2024

Thermally anisotropic composites for thermal management in building environments

An improved system for thermal management is provided. The system includes thermally anisotropic composites coupled with a thermal loop to re-direct, reduce, and shape heat flows through a building envelope, having the potential to (1) significantly reduce envelope-generated heating and cooling loads and (2) provide grid services such as decreasing peak loads and shaping energy use. In one embodiment, the thermal management system includes an anisotropic composite that consists of alternating layers of thermal insulation and thermally conductive materials that are immediately adjacent to each other, including polyisocyanurate foam boards and aluminum sheets. The thermal management system also includes a thermal loop along the long edge or the entire the perimeter of the anisotropic composite, the thermal loop having dynamically controlled or floating temperature that is maintained at lower than an outdoor ambient temperature (for cooling). An interior wall structure is inwardly adjacent to the anisotropic composite.

Shrestha, Som S.↗
DOE OSTI2024

Studying Wind Loading on CSP Collectors to Improve Performance and Reliability

Electricity generation through Concentrating Solar-thermal Power (CSP) adds the advantage of thermal energy storage and heat production. CSP collector costs constitute nearly one-third of total plant costs. Managing wind loading, especially dynamic wind loading caused by the turbulent wind flow, is a significant design challenge. Traditional collector designs rely on wind tunnel experiments and numerical simulations, which do not fully capture dynamic effects. Here, we provide an overview of NREL's activities on wind loading on CSP collectors, aiming to improve their reliability and cost-efficiency. We present insights from field measurements at operational parabolic trough and power-tower CSP plants. Over two years, we measured turbulent wind fields and resulting structural loads in a parabolic trough plant, revealing wind, turbulence, and collector field interactions. Similar measurements are ongoing at the Crescent Dunes heliostat field. These campaigns show how atmospheric turbulence, wind direction, and collector orientation affect dynamic wind loading. Upwind collector structures can generate turbulent structures, causing fluctuating loads at downstream collectors, impacting fatigue lifetime and optical efficiency. Preliminary results indicate that interior collectors experience higher turning moments than those at the edges, suggesting higher drive wear. At Crescent Dunes, we use instrumented heliostats at the field's edge and interior to study the translation of turbulent wind to dynamic structural loads. The campaign is still ongoing, and we will present first findings. Another focus of our work is tying the experimental wind loading findings to optical performance of the collectors, using simulation tools. For example, we derive torsional errors of the parabolic troughs - the angular offset from the sun position along a collector row. This error is impacted by wind-induced mirror deformations. Future work will focus on continuing the measurement efforts and combining them with computational fluid dynamic simulations. By providing detailed field measurements and validated models, our efforts aim to enhance understanding of wind loading on CSP collectors, improving their structural integrity and optical performance.

CSP↗
DOE OSTI2024

An Efficient Annual-Performance Model of a Geothermal Network for Improved System Design, Operation, and Control: Preprint

Geothermal district energy systems (DES), and specifically geothermal networks, provide a viable solution for decarbonizing residential and commercial heating and cooling loads. District energy systems of all kinds enable a thermal resource with a relatively high capital cost (such as a geothermal borehole field) to be shared among a large number of users. While district heating and cooling has been studied for many years, geothermal networks, fifth generation DES that utilize water-source heat pumps and an ambient temperature loop to meet heating and cooling loads, have not been implemented extensively and thus require additional technical and economic optimization to obtain maximum benefits. This paper presents a newly developed reduced-order model that captures the flow of energy within the network, including the commercial and residential users' electrical usage, at an hourly rate over a year. The model includes building loads, heat pumps, borehole fields, and auxiliary heat/cool input, all connected with an ambient-temperature thermal loop model. In the model, operational control is possible for the borehole fields, circulation pump, and auxiliary system. For a given system, the model can output the complete state parameters for each component, the thermal loop, and the collective system, such as flow rate over time, average thermal loop temperature over time, and total electricity usage. The model can also be used to optimize the system control for maximizing system efficiency or minimizing system operational cost. For example, one initial assessment of the borehole controller for an example system showed that a controller with on/off operation of the borehole field reduces annual electrical usage by 33%, compared with continuous operation mode. Hence, the model can assist in optimizing a given system's operation to get the most value out of a geothermal network installation. Future work will consider the model's application to a demonstration project, including the model validation against operational data and system operation optimization.

ambient-temperature loop↗
DOE OSTI2020

Electrical power generation from moderate-temperature radiative thermal sources

Moderate-temperature thermal sources (100° to 400°C) which radiate waste heat are often the by-product of mechanical work, chemical or nuclear reactions, or information processing. We demonstrate conversion of thermal radiation into electrical power using a bipolar grating-coupled complementary metal-oxide-silicon (CMOS) tunnel diode. A two-step photon-assisted tunneling charge pumping mechanism results in separation of charge carriers in pn-junction wells leading to a large open-circuit voltage developed across a load. Electrical power generation from a broadband blackbody thermal source has been experimentally demonstrated with converted power densities of 27 to 61 microwatts per square centimeter for thermal sources between 250° and 400°C. Scalable, efficient conversion of radiated waste heat into electrical power can be used to reduce energy consumption or to power electronics and sensors.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2022

Enhancement of phase change material hysteresis model: A case study of modeling building envelope in EnergyPlus

Nowadays, buildings are expected to offer demand side services to the power grid to enhance the electrical load flexibility, which leads to the concepts of grid-interactive efficient buildings (GEBs). Phase change material (PCM)-based thermal energy storage has seen increasing attention in recent years for peak load shifting of grid-interactive efficient buildings (GEBs). Numerical models are critical tools for design and evaluation of PCM-integrated systems. Most industrial-grade PCMs are reported to melt/freeze over a temperature range instead of at a unique temperature. Such thermal hysteresis effect significantly affects the reliability of simulation results because not only the heat transfer process depends on melting and freezing temperatures, the PCM thermal properties change significantly during the phase change process as well. This study is aimed to develop a model for the PCMs used in the building envelope with the capability to accurately simulate hysteretic behaviors. Further, this model is based on a two-phase assumption and is implemented in a whole building energy performance simulation program (i.e., EnergyPlus). A comparison between numerical results and experimental data shows that during a complete phase transition, the two-phase model could achieve a good agreement with the experimental data. During a partial phase transition, the two-phase model could lead to significant improvements compared to other alternative PCM models, including the existing PCM model in EnergyPlus. Last, whole building simulations were performed to study this model's performance regarding heating/cooling loads and zone mean air temperature of a given building. The results show that the difference in hourly heating/cooling loads introduced by the models was less than 1% in design conditions, while significant changes were observed in both hourly heating/cooling loads and zone mean air temperature when the PCM envelope underwent partial phase transition processes.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Development of Surveillance Test Articles for Materials Degradation Management in MSR Environments

Materials in molten salt reactors (MSR) undergo accelerated degradation from corrosion, irradiation, and cyclic loads at elevated temperatures. Establishing a materials surveillance program to enable the assessment of material deterioration is critical to assure structural integrity of MSRs components. This presentation summarizes recent efforts towards the development of surveillance test articles for collecting various damages for monitoring materials degradation. Surveillance test articles with reduced dimensions were designed to capture creep-fatigue damage from cyclic loading at elevated temperatures. The strain evolution of test articles during thermal cycling was analyzed both numerically and experimentally. Out-of-reactor thermal cycling demonstrated successful capture of strain range for materials assessment. Moreover, test articles were subject to both mechanical loads and molten salt exposure, and the damage due to stress and corrosion was investigated. Additionally, damage inference models were developed to predict the remaining life of materials based on the accumulated damage in surveillance test articles.

36 - MATERIALS SCIENCE↗
DOE OSTI2021

Resilience of terrestrial and aquatic fauna to historical and future wildfire regimes in western North America

Wildfires in many western North American forests are becoming more frequent, larger, and severe, with changed seasonal patterns. In response, coniferous forest ecosystems will transition toward dominance by fire-adapted hardwoods, shrubs, meadows, and grasslands, which may benefit some faunal communities, but not others. We describe factors that limit and promote faunal resilience to shifting wildfire regimes for terrestrial and aquatic ecosystems. We highlight the potential value of interspersed nonforest patches to terrestrial wildlife. Similarly, we review watershed thresholds and factors that control the resilience of aquatic ecosystems to wildfire, mediated by thermal changes and chemical, debris, and sediment loadings. We present a 2-dimensional life history framework to describe temporal and spatial life history traits that species use to resist wildfire effects or to recover after wildfire disturbance at a metapopulation scale. The role of fire refuge is explored for metapopulations of species. In aquatic systems, recovery of assemblages postfire may be faster for smaller fires where unburned tributary basins or instream structures provide refuge from debris and sediment flows. We envision that more-frequent, lower-severity fires will favor opportunistic species and that less-frequent high-severity fires will favor better competitors. Along the spatial dimension, we hypothesize that fire regimes that are predictable and generate burned patches in close proximity to refuge will favor species that move to refuges and later recolonize, whereas fire regimes that tend to generate less-severely burned patches may favor species that shelter in place. Looking beyond the trees to forest fauna, we consider mitigation options to enhance resilience and buy time for species facing a no-analog future.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

ARC disruption physics and strategy

Commonwealth Fusion Systems (CFS) plans to operate a tokamak power plant called ARC in the early 2030s. Tokamak plasmas have stability limits that, if crossed, lead to a rapid termination of the plasma, referred to as a disruption. Disruptions pose a melt risk to the first wall resulting from thermal and non-thermal particle heat fluxes, and an electromagnetic loading risk on all metal components within the equilibrium coils. A comprehensive set of models is used herein to provide an assessment of both mitigated and unmitigated ARC disruption loads. A preliminary massive gas injection system is baselined and a runaway electron mitigation coil option is proposed to close possible gaps in the baseline. It is predicted that all ARC disruption loads are within a factor of 2 of the disruption loads in SPARC, a tokamak presently under construction by CFS, and therefore SPARC provides an opportunity to calibrate models, test solutions and inform the design of ARC. The goal for ARC is disruption-free operation, however, the pragmatic design target is to withstand one mitigated disruption per day, and to restart the plasma following mitigation in tens of seconds without interrupting the power output. Unmitigated disruptions must be rare, and experience with unmitigated disruption impacts in SPARC will better define what rare means. The implications of this strategy for plasma disruptivity and disruption prediction are discussed, and operating the ARC scenario on SPARC is expected to refine the ARC final design and operational plan.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Anomalous lattice expansion of bcc Ta in helium-loaded diamond anvil cells

Anomalous lattice expansion of bcc Ta is observed in helium-loaded diamond anvil cell (DAC) experiments near 6 GPa and above 400 K, while co-loaded W, Mo, and Au exhibit normal thermal expansion. The Ta volume expansion increases with temperature, reaching ~14% near 650 K before plateauing, and is largely retained after recovery to ambient conditions. Time-resolved measurements at 500 K reveal progressive expansion over several hours, consistent with gradual, thermally activated He incorporation. The largely retained expansion during subsequent cooling and holding at 400 K indicates that the incorporated He is predominantly kinetically trapped. The data reveal two distinct regimes: below ~550 K, modest and spatially uniform expansion consistent with interstitial He trapping at isolated, randomly distributed vacancies; above ~550 K, He-vacancy cluster growth producing dramatically larger expansion, peak broadening, and a core–shell microstructure revealed by micron-resolution X-ray diffraction mapping. These results demonstrate that He is not always a passive pressure medium in DAC experiments and reveal a previously unrecognized regime of He-mediated lattice modification in Ta, complementing conventional ion-implantation studies relevant to nuclear and fusion structural materials.

Diamond anvil cell↗
DOE OSTI2020

A MEMS dynamic mechanical analyzer for in situ viscoelastic characterization of 3D printed nanostructures

Cellular metamaterial structures with sub-micron features have shown the ability to become excellent energy absorbing materials for impact mitigation due to the enhanced mechanical properties of materials at the nanoscale. However, in order to optimize the design of these energy absorbing metamaterial structures we need to be able to measure the dynamic properties of the sub-micron features such as storage and loss moduli and the loss factor. Therefore, at scale testing is required to capture the scale, temperature, and strain rate dependent material properties of these nanoscale materials. This study presents the design, fabrication, and calibration of a MEMS-based dynamic mechanical analyzer (DMA) that can be directly integrated with the two photon lithography (TPL) process commonly used to fabricate metamaterial structures with nanoscale features. The MEMS-based DMA consists of a chevron style thermal actuator used to generate a tensile load on the structure and two differential capacitive sensors on each side of the structure used to measure load and displacement. This design demonstrated 1.5 ± 0.75 nm displacement resolution and 104 ± 52 nN load resolution, respectively. Dynamic mechanical analysis was successfully conducted on a single nanowire feature printed between the load and displacement stages of the MEMS device with testing frequencies ranging between 0.01–10 Hz and testing temperatures ranging between 22 °C–47 °C. These initial tests on an exemplar TPL part demonstrate that the printed nanowire behaves as a viscoelastic material wherein the transition from glassy to viscous behavior has already set in at the room temperature.

42 ENGINEERING↗
DOE OSTI2021

Hardware-in-the-Loop Investigation of Emissions Challenges in Hybrid Medium- and Heavy-Duty Powertrains Using a Pre-Production Diesel-Electric Parallel Hybrid System With and Without Stop-Start Operation

Hybrid electric powertrains are a growing market in medium- and heavy-duty applications. There is a lack of available information to understand the challenges in the integration of engine platforms into electrified powertrains, such as cold-start, restart, and load-reduction effects on emissions and emission control devices. Results from the Heavy Heavy-Duty Diesel Truck (HHDDT) cycle using a conventional medium-duty diesel engine were compared with those of a parallel hybrid architecture. Oak Ridge National Laboratory in collaboration with the US Department of Energy and Odyne Systems, LLC developed a powertrain in a hardware-in-the-loop environment, integrating the Odyne Systems, LLC medium-duty parallel hybrid system, which was used for the hybrid portion of this study. Experiments under the HHDDT cycle showed increasing improvements in fuel consumption and engine-out emissions with the integration of stop/start, hybrid, and hybrid with stop/start. However, the effects of load reduction and exhaust temperature on the thermal management strategy have shown an increase in fueling in the second part of the HHDDT cycle. Four configurations of medium-duty electrification were studied and contributed to building a unique data set containing combustion, emissions, and system integration data. Each electrification level was compared with the conventional baseline. The calibration of the conventional engine was not altered for this study. Opportunities to tailor the combustion process were identified with the stop/start strategy.

Lerin, Chloe↗
DOE OSTI2021

Impacts of Varying Concentrations of Cloud Condensation Nuclei on Deep Convective Cloud Updrafts—A Multimodel Assessment

Abstract This study presents results from a model intercomparison project, focusing on the range of responses in deep convective cloud updrafts to varying cloud condensation nuclei (CCN) concentrations among seven state-of-the-art cloud-resolving models. Simulations of scattered convective clouds near Houston, Texas, are conducted, after being initialized with both relatively low and high CCN concentrations. Deep convective updrafts are identified, and trends in the updraft intensity and frequency are assessed. The factors contributing to the vertical velocity tendencies are examined to identify the physical processes associated with the CCN-induced updraft changes. The models show several consistent trends. In general, the changes between the High-CCN and Low-CCN simulations in updraft magnitudes throughout the depth of the troposphere are within 15% for all of the models. All models produce stronger (~+5%–15%) mean updrafts from ~4–7 km above ground level (AGL) in the High-CCN simulations, followed by a waning response up to ~8 km AGL in most of the models. Thermal buoyancy was more sensitive than condensate loading to varying CCN concentrations in most of the models and more impactful in the mean updraft responses. However, there are also differences between the models. The change in the amount of deep convective updrafts varies significantly. Furthermore, approximately half the models demonstrate neutral-to-weaker (~−5% to 0%) updrafts above ~8 km AGL, while the other models show stronger (~+10%) updrafts in the High-CCN simulations. The combination of the CCN-induced impacts on the buoyancy and vertical perturbation pressure gradient terms better explains these middle- and upper-tropospheric updraft trends than the buoyancy terms alone.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Updated Estimate of Tritium Permeation from TPBAR Disposal Containers in ILV (U)

A tritium source term analysis was performed for TPBAR disposal in the E-Area Intermediate Level Vaults for the E-Area Low-Level Waste Facility Performance Assessment (PA). This analysis is based on an earlier source term analysis which treated the bulk oft he tritium residual as tightly bound by the TPBAR getter material, with only a small fraction existing as tritiated moisture in the lithium aluminate ceramic pellets. Together with atmospheric moisture trapped in the free volume, the tritiated water vapor is assumed to corrode steel surfaces inside the disposal container, covering them with a magnetite film while generating hydrogen. The carbon steel walls of the disposal container are permeable to hydrogen, providing a path way for tritium to escape containment. The rate of hydrogen generation is assumed to be limited by the rate of corrosion, which is assumed to be governed by parabolic reaction kinetics obtained from the literature. This relies on the further assumption that the water vapor consumed by the corrosion reaction is continually replaced by moisture from the lithium aluminate pellets until all of that moisture is gone. In addition to tritium permeation, the analysis also includes a slow leak through the disposal container walls at the maximum allowable leak rate, 1 x 1CH standard cm3/s. Results were obtained for four different combinations of internal and container wall temperatures, established in an earlier thermal analysis that considered two different vault loadings and two different TPBAR activity levels. Instantaneous release rates for these four cases are plotted in Figure ES-1 below

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

A data-driven peridynamic continuum model for upscaling molecular dynamics

Nonlocal models, including peridynamics, often use integral operators that embed lengthscales in their definition. However, the integrands in these operators are difficult to define from the data that are typically available for a given physical system, such as laboratory mechanical property tests. In contrast, molecular dynamics (MD) does not require these integrands, but it suffers from computational limitations in the length and time scales it can address. To combine the strengths of both methods and to obtain a coarse-grained, homogenized continuum model that efficiently and accurately captures materials’ behavior, we propose a learning framework to extract, from MD data, an optimal Linear Peridynamic Solid (LPS) model as a surrogate for MD displacements. To maximize the accuracy of the learnt model we allow the peridynamic influence function to be partially negative, while preserving the well-posedness of the resulting model. To achieve this, we provide sufficient well-posedness conditions for discretized LPS models with sign-changing influence functions and develop a constrained optimization algorithm that minimizes the equation residual while enforcing such solvability conditions. This framework guarantees that the resulting model is mathematically well-posed, physically consistent, and that it generalizes well to settings that are different from the ones used during training. We illustrate the efficacy of the proposed approach with several numerical tests for single layer graphene. Our two-dimensional tests show the robustness of the proposed algorithm on validation data sets that include thermal noise, different domain shapes and external loadings, and discretizations substantially different from the ones used for training.

homogenization↗