Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “root”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,225 records · Page 68
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Investigation of 3D printed lightweight hybrid composites via theoretical modeling and machine learning

Hybrid composites combine two or more different fillers to achieve multifunctional or advanced material properties, such as lightweight and enhanced mechanical properties. The properties of the composites significantly depend on their microstructures, which can be tailored via advanced 3D printing processes. Understanding the process-structure-property relationships is critical to enable the design and engineering of novel hybrid composites for applications in aerospace, automotive, and protective coatings. Here, for this work, we develop 3D printable and lightweight hybrid composites and leverage the conventional design of experiments, a theoretical hybrid model, and an image-driven machine learning (ML) method to investigate their mechanical behaviors. The hybrid composites are formulated with elastomer matrix, microfillers, and thin-shell particles, enabling a significant degree of design freedom of microstructures with densities and mechanical properties varying up to 70% and 91%, respectively. Our statistical analysis indicates that the 3D printing path direction and the microfibers fraction are dominating process parameters with contribution percentages of 45.3% and 57.7% on the specific stiffness and strength, respectively. A hybrid mechanics model is developed based on a simple Weibull distribution function and classical single-filler models to effectively capture the variations in mechanical properties, however, it overestimates the values due to its statistical constraints and idealization of experimental uncertainty. The image-driven ML model leverages the microscale images directly without losing the structural details, shows more accurate predictions with experimental data, and has 48.6% lower root mean square error than the theoretical model.

3D printing↗
DOE OSTI2020

LieART 2.0 – A Mathematica application for Lie Algebras and Representation Theory

In this paper, we present LieART 2.0 which contains substantial extensions to the Mathematica application LieART (Lie Algebras and Representation Theory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. The basic procedure is unchanged—it computes root systems of Lie algebras, weight systems and several other properties of irreducible representations, but new features and procedures have been included to allow the extensions to be seamless. The new version of LieART continues to be user friendly. New extended tables of properties, tensor products and branching rules of irreducible representations are included in the supplementary material for use without Mathematica software. LieART 2.0 now includes the branching rules to special subalgebras for all classical and exceptional Lie algebras up to and including rank 15.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

NuSD: A Geant4 based simulation framework for segmented anti-neutrino detectors

NuSD: Neutrino Segmented Detector is a Geant4-based user application that simulates inverse beta decay event in a variety of segmented scintillation detectors developed by different international collaborations. This simulation framework uses a combination of cross-programs and libraries including Geant4, ROOT and CLHEP developed and used by high energy physics community. It will enable the neutrino physics community to simulate and study neutrino interactions within different detector concepts using a single program. In addition to neutrino simulations in segmented detectors, this program can also be used for various research projects that use of scintillation detectors for different physics purposes.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

A robust fourth-order finite-difference discretization for the strongly anisotropic transport equation in magnetized plasmas

We propose a second-order temporally implicit, fourth-order-accurate spatial discretization scheme for the strongly anisotropic heat transport equation characteristic of hot, fusion-grade plasmas. Following Du Toit et al. (2018), the scheme transforms mixed-derivative diffusion fluxes (which are responsible for the lack of a discrete maximum principle) into nonlinear advective fluxes, amenable to nonlinear-solver-friendly monotonicity-preserving limiters. The scheme enables accurate multi-dimensional heat transport simulations with up to seven orders of magnitude of heat-transport-coefficient anisotropies with low cross-field numerical error pollution and excellent algorithmic performance, with the number of linear iterations scaling very weakly with grid resolution and grid anisotropy, and scaling with the square-root of the implicit timestep. We propose a multigrid preconditioning strategy based on a lower-order approximation that renders the scheme efficient and scalable under grid refinement. Several numerical tests are presented that display the expected spatial convergence rates and strong algorithmic performance, including fully nonlinear magnetohydrodynamics simulations of kink instabilities in a Bennett pinch in 2D helical geometry and of ITER in 3D toroidal geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

High-performance data format for scientific data storage and analysis

Here, in this article, we present the High-Performance Output (HiPO) data format developed at Jefferson Laboratory for storing and analyzing data from Nuclear Physics experiments. The format was designed to efficiently store large amounts of experimental data, utilizing modern fast compression algorithms. The purpose of this development was to provide organized data in the output, facilitating access to relevant information within the large data files. The HiPO data format has features that are suited for storing raw detector data, reconstruction data, and the final physics analysis data efficiently, eliminating the need to do data conversions through the lifecycle of experimental data. The HiPO data format is implemented in C++ and JAVA, and provides bindings to FORTRAN, Python, and Julia, providing users with the choice of data analysis frameworks to use. In this paper, we will present the general design and functionalities of the HiPO library and compare the performance of the library with more established data formats used in data analysis in High Energy and Nuclear Physics (such as ROOT and Parquete). In columnar data analysis, HiPO surpasses established data formats in performance and can be effectively applied to data analysis in other scientific fields.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

A critical review of molybdenum sequestration mechanisms under euxinic conditions: Implications for the precision of molybdenum paleoredox proxies

The observed difference in molybdenum (Mo) mobility and isotopic fractionation under oxic versus euxinic (i.e., anoxic and sulfidic) aqueous conditions provides a sound operational basis for the use of Mo geochemical signatures in ancient sedimentary records to infer palaeoceanographic redox conditions. While Mo is known to exist predominantly as molybdate (MoO 4 2– ) in oxic waters and convert into thiomolybdate species (MoO x S 4-x 2– ) under euxinic conditions, the pathways that lead to Mo sequestration are highly debated. As mechanistic understanding of Mo sequestration is crucial for accurately reconstructing the chemistry of ancient oceans and constraining the timing and intensity of oxygenation events through Earth's history using Mo paleoproxies, we have closely examined the current proposed mechanisms for Mo sequestration across a wide range of euxinic conditions. Through compilation and comparison of such information, we aim to provide an integrated view of Mo sequestration processes, to identify the current controversies as well as the roots of such controversies, and importantly, to propose avenues for future research. Here, sequestration of Mo may occur through complexation with organic matter (OM), reactions with oxyhydroxide and sulfide mineral surfaces, incorporation into iron sulfide crystal structures, formation of Mo-sulfide, and cellular assimilation. However, several major questions remains unresolved, including whether OM complexation plays a significant role in overall sedimentary Mo accumulation, whether the reduction of Mo(VI) occurs during interaction with Fe-S clusters/precipitates and/or with OM, whether microbial enzymatic reduction of Mo(VI) is important in Mo sequestration, whether synergistic effects exist between the biological and abiotic processes in Mo sequestration, and whether differences in reactivity among the various thiomolybdate intermediate species and tetrathiomolybdate influence the Mo sequestration process. At the end of the review, the reliability of Mo paleoproxies is discussed and reevaluated.

58 GEOSCIENCES↗
DOE OSTI2021

Monitoring agroecosystem productivity and phenology at a national scale: A metric assessment framework

Effective measurement of seasonal variations in the timing and amount of production is critical to managing spatially heterogeneous agroecosystems in a changing climate. Although numerous technologies for such measurements are available, their relationships to one another at a continental extent are unknown. Using data collected from across the Long-Term Agroecosystem Research (LTAR) network and other networks, we investigated correlations among key metrics representing primary production, phenology, and carbon fluxes in croplands, grazing lands, and crop-grazing integrated systems across the continental U.S. Metrics we examined included gross primary productivity (GPP) estimated from eddy covariance (EC) towers and modelled from the Landsat satellite, Landsat NDVI, and vegetation greenness (Green Chromatic Coordinate, GCC) from tower-mounted PhenoCams for 2017 and 2018. Overall, our analysis compared production dynamics estimated from three independent ground and remote platforms using data for 34 agricultural sites constituting 51 site-years of co-located time series. Pairwise sensor comparisons across all four metrics revealed stronger correlation and lower root mean square error (RMSE) between end of season (EOS) dates (Pearson R ranged from 0.6 to 0.7 and RMSE from 32.5 to 67.8) than start of season (SOS) dates (0.46 to 0.69 and 40.4 to 66.2). Overall, moderate to high correlations between SOS and EOS metrics complemented one another except at some lower productivity grazing land sites where estimating SOS can be challenging. Growing season length estimates derived from 16-day satellite GPP (179.1 days) were significantly longer than those from PhenoCam G CC (70.4 days, p adj < 0.0001) and EC GPP (79.6 days, p adj < 0.0001). Landscape heterogeneity did not explain differences in SOS and EOS estimates. Annual integrated estimates of productivity from EC GPP and PhenoCam G CC diverged from those estimated by Landsat GPP and NDVI at sites where annual production exceeds 1000 gC/m –2 yr –1 . Based on our results, we developed a “metric assessment framework” that articulates where and how metrics from satellite, eddy covariance and PhenoCams complement, diverge from, or are redundant with one another. The framework was designed to optimize instrumentation selection for monitoring, modeling, and forecasting ecosystem functioning with the ultimate goal of informing decision-making by land managers, policy-makers, and industry leaders working at multiple scales.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Considering coasts: Adapting terrestrial models to characterize coastal wetland ecosystems

The Energy Exascale Earth System Model (E3SM) simulates fully coupled processes and interactions among water, energy, carbon and nutrient cycles. E3SM connects vegetation and soil dynamics through nutrient uptake, plant production, litterfall and decomposition as a function of abiotic parameters (e.g. temperature and moisture). However, E3SM is designed to characterize terrestrial ecosystems and connects land and open ocean systems using a single streamflow transport term, ignoring the complex dynamics of energy, water, carbon, and nutrients in coastal systems. The goals of our project were to: (1) Parameterize a point version of E3SM to capture coastal wetland habitats and (2) Determine marsh community responses to increased temperature and elevated CO 2 . We adapted a version of the E3SM land model, previously configured to represent forested bog hydrology to a coastal ecosystem using datasets from field experiments conducted at the Smithsonian Environmental Research Center's Global Change Research Wetland (GCReW). Tidal forcing in a marsh environment was simulated using a two-column system in which the columns are connected by lateral hydrologic flows. One column simulates interactions between vegetation and soil while a second column simulates variation in water level (both tidal and sea level rise). The updated model captures many aspects of the field experiments, showing that plant community responses to environmental change are non-linear, non-additive and different between plant types. Elevated CO 2 treatments increased C 3 plant biomass more than C 4 (33% vs 17%). Temperature exacerbated CO 2 responses in C 3 plants (0 °C: 26%, 5.1 °C: 56%). We were more successful at characterizing C 3 than C 4 responses and simulating above rather than belowground biomass production. Furthermore, the next steps will include updates to key physiological parameters such as root:shoot carbon allocation and the addition of mechanistic feedbacks between vegetation and biogeochemical processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Data efficiency assessment of generative adversarial networks in energy applications

This study investigates the data requirements of generative artificial intelligence (AI), particularly generative adversarial networks (GANs), for reliable data augmentation in energy applications. Generative AI, though seen as a solution to data limitations, requires substantial data to learn meaningful distributions—a challenge often overlooked. This study addresses the challenge through synthetic data generation for critical heat flux (CHF) and power grid demand, focusing on renewable and nuclear energy. Two variants of GAN employed are conditional GAN (cGAN) and Wasserstein GAN (wGAN). Our findings include the strong dependency of GAN on data size, with performance declining on smaller datasets and varying performance when generalizing to unseen experiments. Mass flux and heated length significantly influence CHF predictions. wGAN is more robust to feature exclusion, making it suitable for constrained synthetic data generation. In energy demand forecasting, wGAN performed well for solar, wind, and load predictions. Longer lookback hours and larger datasets improved predictions, especially for load power. Seasonal variations posed challenges, with wGAN achieving a relatively high error of Root Mean Squared Error (RMSE) of 0.32 for load power prediction, compared to RMSE of 0.07 under same-season conditions. Feature exclusions impacted cGAN the most, while wGAN showed greater robustness. This study concludes that, while generative AI is effective for data augmentation, it requires substantial data and careful training to generate realistic synthetic data and generalize to new experiments in engineering applications.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Dilated causal convolutional neural networks for forecasting zone airflow to estimate short-term energy consumption

Here this paper investigates the use of dilated causal convolutional neural networks for fine- grained temporal forecasting of building zone states. Specifically, we build and evaluate models using a small set of exogenous features (e.g., external temperature) to autoregressively predict zone airflow setpoints every minute for a 24-hour prediction window. We carefully explore the trade-off between generality and specificity in these models, training and evaluating them based on zone, zone type, month, season, and combinations thereof. When evaluated for a commercial office building in Eastern Washington with 16 zones served by variable air volume air handling units, we find that the highest performance comes from a zone-specific, season-agnostic approach; with it, we obtain an R 2 of 0.704 (averaged over zones) and an average normalized root mean square error (nRMSE) of 0.111. In contrast, the most general model (trained across all zones and seasons) yields an R 2 of only 0.416 and a nRMSE of 0.168, while a baseline zone-specific reduced order model obtains 0.443 R 2 and 0.159 nRMSE. We also report on factors affecting airflow forecasting performance, on the ability of models trained on a specific zone to generalize to other zones, and on the capability of those models trained on a specific month to generalize to other months.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Development, calibration, and validation of a novel gray-box energy model for residential split air conditioners

Energy models for vapor compression refrigeration in residential air conditioners have been developed through white-box, gray-box, and black-box methods in decades. However, existing white-box and gray-box models require complicated equations with detailed geometries while black-box models require substantial experimental data. Further, this paper aims to develop and validate a simple gray-box steady-state energy model without the need for detailed geometries, which can accurately predict the cooling capacity and electrical power input based on outdoor and indoor air conditions, and supply airflow rates. First three state variables, including the evaporation and condensation temperatures, and refrigerant mass flowrate, are applied to develop the energy model and are solved by three physical equations, including the energy conservations at the evaporator and condenser, and the refrigerant volume-mass flow correlation of the compressor. Secondly, seven performance property functions related to three state variables and three physical equations are identified and calibrated by simple temperature and power measurements. Finally, field experiments are conducted on a residential air conditioner to calibrate these performance property functions and validate the developed model. The validated results reveal the model can accurately predict the cooling capacity and electrical power input, with the normalized root mean square errors of 2.3% and 0.87% respectively.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Machine learning surrogate of physics-based building-stock simulator for end-use load forecasting

Building energy models are used to simulate heat and mass transfer and estimate end-use load in buildings. With the proliferation of solar photovoltaics on residential and commercial buildings, increasingly, buildings are expected to provide grid services, for which accurate and computationally efficient building energy simulations and end-use load prediction are imperative. Existing building energy simulation tools, however, have significant computational overhead that make them less practical in real-time deployment for optimization, design, uncertainty quantification and control in building energy management systems. Here this article presents a data-driven machine learning model based on light gradient boosting method (LightGBM) as a surrogate for a physics-based simulator for residential buildings to predict end-use load. The machine learning based surrogate model accounts for time-series related variables, seasonality and trend component of end-use load, and history of end-use load. The accuracy of the surrogate model is assessed on the prediction of the load profiles of 100 different houses in Cook County, Illinois, USA. The LightGBM surrogate model is shown to reduce the root-mean-squared error by 53% relative to a reference decision tree (DT) based model reported previously in the literature. Moreover, the model predicts the load spikes and high-ramp rate events throughout the year which are often the Achilles heel of other models in the literature. The machine learning based surrogate model is demonstrated to be computationally efficient, with a ten-fold reduction in the computational time compared to a physics-based building energy simulation, and suitable for uncertainty analysis and real-time control of building characteristics in response to uncertainty.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Dynamic modelling and control strategy of a temperature-driven metal hydride cooling system for buildings

A temperature-driven coupled metal hydride (MH) based thermal energy storage (TES) system can allow to shave and shift the peak energy demand in buildings. The high energy density and long-term (seasonal) energy storage capability are its major advantages over other energy storage methods. The dynamic nature of the MH operation, however, requires controlled hydrogen transfer between the coupled MHs at a rate needed to meet the building's transient load. While temperature-driven MH systems are studied in the literature, their application in buildings and control are scarcely reported. Here, this paper presents a control-based dynamic modeling of the temperature-driven coupled MH-TES system for building cooling applications. The dynamic model is developed in MATLAB(R) Simulink environment, considering the thermodynamic and kinetic behaviors of the MH systems. Based on a preliminary analysis of a property database of over 337 hydrides, we select around 1600 MH pairs suitable for building cooling applications. Each of these MH pairs is studied for their performance using the dynamic model, and among all, Zr 0.76 Ti 0.24 Ni 1.16 Mn 0.63 V 0.14 Fe 0.18 -Ti 0.85 Zr 0.15 Cr 1.2 Mn 0.8 MH pair showed fast dynamics along with high coefficient of performance (COP) of 0.71. A parametric investigation is performed on this MH pair to understand the effect of operating temperatures. Finally, three proportional-integral (PI) feedback controllers are investigated to regulate the temperature, pressure and mass exchange between the coupled MH pairs. The developed PI controller is sufficiently capable of rejecting the signal noise from the hydrogen flow and internal heat exchange processes with root mean square error of 5.78 W between reference and actual cooling load.

08 HYDROGEN↗
DOE OSTI2025

Active multi-mode data analysis to improve fault diagnosis in AHUs

Faults in heating, ventilation and air conditioning systems can lead to increased energy consumption, occupant comfort issues, and reduced equipment lifetime. Commercial fault detection and diagnosis (FDD) tools has been increasingly deployed in U.S. commercial buildings. While they are helping to achieve energy efficiency and operational reliability, there remain gaps in their fault diagnostic capabilities. The diagnostic results often contain multiple distinct candidate root causes (CRCs) or offer no insight into CRCs. This study developed a novel active rule-based multi-mode data analysis method to enhance diagnostic resolution by applying proven rule sets and additional new rules to data from multiple known operational modes. The proposed method was demonstrated using enhanced air handling unit performance assessment rule sets and validated with the simulated data of two air handling units. New metrics, namely, reduced number of CRCs and improvement ratio, were developed to quantify the improvement of fault diagnostic resolution. The validation results showed that the proposed method effectively reduced the number of CRCs in contrast to analyzing data solely for a single mode of operation. It achieved a median improvement ratio of 80% in 19 test cases.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Surrogate model evaluation and building energy benchmarking for commercial buildings

Building energy consumption benchmarking involves challenges associated with various energy patterns for different building types; heating, ventilating, and air-conditioning (HVAC) system types; and climates. Given significant variation in energy use patterns, accurate prediction of long-term energy use using surrogate models remains challenging. Multiple linear regression (MLR) is commonly used for building energy benchmarking because of its simple structure; however, it lacks accuracy compared to other black-box models. Although many studies have compared surrogate models and offer guidance on model selection based on metrics, they do not provide detailed analysis on improving the surrogate model accuracy. In this paper, we implement a surrogate model using polynomial ridge regression (i.e., MLR with interaction terms combined with ridge regularization) for small office and retail strip mall buildings across six HVAC system types and all climate zones, for electricity and natural gas in baseline and proposed scenarios. A simulation workflow is developed using OpenStudio TM /EnergyPlus TM to generate simulation data using measures over a wide range of efficiency inputs. Enhancements based on statistical insights are used for improving the model accuracy using filters, input transformations, and change points. Surrogate models achieved average coefficient of variation of the root mean squared error (CVRMSE) values of 2.17, 1.06, 2.05, and 3.26 for proposed electricity, proposed natural gas, baseline electricity, and baseline natural gas, respectively, with enhancements reducing CVRMSE by an average of 14.9% across all combinations. We provide model interpretation via Shapley additive explanations to determine which input variables most influence energy consumption and provide supportive arguments for enhancements.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Correlating and Simulating Socio-Demographically Driven Residential End-Use Activity Schedules

Incorporating socio-demographic and behavioral considerations into decision-support tools is crucial for identifying gaps and addressing consumer needs to ensure reliable and affordable energy solutions. In energy simulation models, the correlation between socio-demographics and time-use behavior is not well-captured. Thus, we developed a large-scale simulation workflow to generate schedules for 10 residential activities across 24 population segments defined by age, income, and employment status. Using pre-pandemic 2015-2019 American Time Use Survey (ATUS) data, we used ANOVA to confirm the correlation between demographic factors and time use. We explored three k-modes clustering methods-backward, forward, and a new hybrid approach-to delineate the occupancy patterns based on demographics. Using the probability of cluster membership for each population segment and a time inhomogeneous Markov chain to generate activity transition probabilities for each cluster, we simulated 50,000 schedules per segment and validated them against the ATUS data. The hybrid method produced the most socio-demographically differentiated clusters while demonstrating comparable performance to other approaches, with an overall root mean square error of 0.12 for both weekday and weekend schedules. Thus, the hybrid method, where each cluster is dominated by certain demographic segments and occupancy patterns, offers more modeling versatility in terms of scenario analysis. The new workflow improves the socio demographic differentiation of energy consumption by considering differences in time use. This approach enables future research on demographically segmented time of use (TOU) energy consumption, including impacts of TOU utility bills and rate analysis, long-run marginal emissions, and energy retrofits.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Experiments on a vapor compression air conditioner with liquid desiccants for efficient dehumidification

Buildings require air conditioning systems that not only cool and dehumidify supply air but also provide sufficient ventilation to ensure indoor air quality and occupant comfort. However, standard recirculation systems-which introduce about a 10 % to 20 % fraction of outdoor air-often fail to deliver air that is precisely cooled and dry, particularly because 80-90 % of the ventilation cooling load is latent. Mixing humid ventilation air with recirculated indoor air increases the energy and costs required to condition the air to comfortable levels. Dedicated outdoor air systems (DOASs) are designed to handle this latent dominated ventilation load and thus need to have efficient humidity removal. Many cooling cycles can perform this task. Here we describe a liquid desiccant DOAS, which combines a vapor compression cycle and a liquid desiccant absorber and desorber pair. We present its performance at 26 operating conditions and a thermodynamic model which can accurately predict the moisture removal efficiency. The model's performance predictions have a mean percentage error of 2.5 % and a coefficient of variation of the root mean square error of 7.5 %. We also compare the performance of this vapor-compression-coupled liquid desiccant system with a standard vapor compression system with the same components but no liquid desiccant. For the 26 conditions tested in this study, this comparison shows that adding liquid desiccants lowers the required evaporator cooling load by 21 %, allows for 25 % lower compressor volumetric capacity, and 25 % lower electricity use. Future work will leverage this model to quantify the reduction in annual electricity use across different climates, including the need for a standard vapor compression system to reheat the air during some of the year.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Deep learning–based digital twins for heat pumps

Heat pumps are effective cooling and heating appliances to save energy in buildings. However, traditional heat pump models are challenging to integrate with building demands in a co-simulation environment because of the nonlinear thermodynamics of refrigerants. Developing digital twin representatives for heat pumps capable of faster calculations with good accuracy is desirable. This study aimed to establish a generic deep learning–based digital twin for heat pumps with a large amount of high-fidelity data. Two refrigerants for two different heat pumps were considered: an air source heat pump with refrigerant R-410A, an air source heat pump with refrigerant CO 2 , a water source heat pump with refrigerant R-410A, and a water source heat pump with refrigerant CO 2 . Furthermore, results showed that the deep learning (long short-term memory) models effectively represented these four heat pumps as a digital twin: (a) accuracy for training and testing showed smaller than 0.02 for heating electricity and heating demands, and (b) the digital twins showed good consistency with original data for heating electricity and heating demands (root mean square errors of less than 0.12 W and 0.19 W, respectively). Therefore, deep learning–based heat pump models can be used in the co-simulation of building mechanical systems.

Air source heat pump↗