SEARCH · Engineering Papers

Results for “Integrated mean squared error”

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.

SourceResearch connectionFrom yearThrough year

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

At least 91 records · Page 5

All sources NASA NTRS DOE OSTI

DOE OSTI2025

Machine learning and process-based modeling of spatiotemporal changes in active layer thickness across Alaska

Permafrost degradation poses a growing threat to infrastructure stability and ecosystem resilience in the rapidly warming Arctic. We investigated the spatiotemporal dynamics of active layer thickness (ALT) across Alaska by integrating field observations, environmental datasets, a physically based Stefan model, and machine learning (ML) techniques. Using weather projections from the Coupled Model Intercomparison Project Phase 6 under two Shared Socioeconomic Pathways (SSP 2-4.5 and SSP 5-8.5), we assessed ALT sensitivity to projected future weather conditions. The random forest (RF) model outperformed the Stefan approach in predicting ALT on the training dataset (R² = 0.84 vs. 0.53) but demonstrated lower generalizability on the test dataset (R² = 0.24 vs. 0.54). The root mean square error (RMSE) for the RF model for training and testing ranged from 14 to 22 cm, compared to 17 and 18 cm for the Stefan model. Variable importance analysis revealed that mean annual temperature and slope angle were the strongest predictors of ALT, accounting for 19% and 18% of the variance, respectively, followed by sediment transport index (14%) and stream power index (11%). Comparative analysis of baseline ALT predictions showed the Stefan model tended to project a thicker active layer (mean ± SD: 65 ± 16 cm), compared to the RF model (mean ± SD: 59 ± 8.8) cm). Both models indicated a latitudinal gradient in ALT, with shallower depths at higher latitudes. Projected ALT increases by 2100 were estimated at 3.3 ± 2.2 cm under SSP 2-4.5 and 5.9 ± 4.0 cm under SSP 5-8.5 for the ML model, whereas the Stefan model projected substantially larger increases of 13 ± 2.6 cm (SSP 2-4.5) and 28 ± 4.4 cm (SSP5-8.5). Spatial analysis showed the greatest ALT increases in northern Alaska, with relatively smaller changes in southern regions. These findings highlight the complex, multifactorial nature of ALT dynamics and the value of hybrid modeling approaches. As rising temperatures accelerate permafrost thaw, changes in ALT can disrupt ecosystems, damage infrastructures, and enhance the release of stored soil carbon, highlighting the urgent need for improved predictive capabilities to inform adaptation strategies in the Arctic.

Climate sciences↗

DOE OSTI2025

Active Learning of Microgrid Frequency Dynamics Using Neural Ordinary Differential Equations

Accurate frequency modelling of inverter‐based resource (IBR)‐dominated power systems is crucial for ensuring stable, reliable and resilient operations, particularly given their inherent low‐inertia characteristics and fast dynamics that traditional swing equation‐based models inadequately capture. This paper explores neural ordinary differential equations (Neural ODEs) as a computationally efficient, data‐driven framework for modelling power system frequency dynamics, specifically within microgrids integrating high penetrations of distributed energy resources (DERs). The developed neural ODEs framework incorporates a neural network architecture designed to capture input dynamics. By actively perturbing the system with a known signal, the Python‐based neural ODEs framework was trained using measured system states and inputs, without the need for detailed system information. The framework, tested on a model of the Cordova, AK, microgrid, achieved a goodness of fit ranging from 60% to 99% across different state variables and maintained a mean square error in the 10 -6 p.u. range under square and step excitation signals. The proposed approach demonstrated robustness to measurement noise and initial condition variations while maintaining low computational complexity suitable for real‐time power system control applications. Furthermore, transfer learning enabled the neural ODEs model to adapt to the following changes in system topology or generator dispatch, highlighting its effectiveness for dynamic microgrids with frequently evolving configurations and diverse DERs.

Aryal, Tara [South Dakota State Univ., Brookings, ↗

DOE OSTI2025

Navigating the Noise: Bringing Clarity to ML Parameterization Design With O $\boldsymbol{\mathcal{O}}$(100) Ensembles

Abstract Machine‐learning (ML) parameterizations of subgrid processes (here of turbulence, convection, and radiation) may one day replace conventional parameterizations by emulating high‐resolution physics without the cost of explicit simulation. However, uncertainty about the relationship between offline and online performance (i.e., when integrated with a large‐scale general circulation model) hinders their development. Much of this uncertainty stems from limited sampling of the noisy, emergent effects of upstream ML design decisions on downstream online hybrid simulation. Our work rectifies the sampling issue via the construction of a semi‐automated, end‐to‐end pipeline for size ensembles of hybrid simulations, revealing important nuances in how systematic reductions in offline error manifest in changes to online error and online stability. For example, removing dropout and switching from a Mean Squared Error to a Mean Absolute Error loss both reduce offline error, but they have opposite effects on online error and online stability. Other design decisions, like incorporating memory, converting moisture input from specific humidity to relative humidity, using batch normalization, and training on multiple climates do not come with any such compromises. Finally, we show that ensemble sizes of may be necessary to reliably detect causally relevant differences online. By enabling rapid online experimentation at scale, we can empirically settle debates regarding subgrid ML parameterization design that would have otherwise remained unresolved in the noise.

Lin, Jerry [Department of Earth System Sciences Un↗

DOE OSTI2026

Digital Twin-Enabled Adaptive Control for Hydroelectric Systems: Turbine Governor and Voltage Regulation

This paper presents a comprehensive digital twin (DT) framework for hydroelectric systems that enables adaptive control of turbine governors and excitation systems without requiring detailed manufacturer specifications. The proposed framework integrates neural network-based system identification with stabilizing adaptive control laws for the installed turbine controller and middle-branch adaptive tuning for the installed voltage regulator. Using real operational data from Unit C-8 at Rocky Reach Dam (1,349 MW capacity), highfidelity neural network models are developed to capture turbine and generator dynamics without requiring detailed manufacturer specifications. The DT enables safe controller synthesis and validation in simulation before deployment. For turbine control, the proposed method achieves a 79.9% mean square error (MSE) reduction compared with that of an optimal controller. For voltage regulation, the adaptive excitation controller achieves approximately 42.6% MSE reduction while preserving installed protection logic. The results demonstrate that DT technology provides a practical pathway for modernizing hydropower control systems with minimal operational disruption.

Gui, Yonghao [ORNL] (ORCID:0000000250435534)↗

NASA NTRS2016

Snow Process Estimation Over the Extratropical Andes Using a Data Assimilation Framework Integrating MERRA Data and Landsat Imagery

A data assimilation framework was implemented with the objective of obtaining high resolution retrospective snow water equivalent (SWE) estimates over several Andean study basins. The framework integrates Landsat fractional snow covered area (fSCA) images, a land surface and snow depletion model, and the Modern Era Retrospective Analysis for Research and Applications (MERRA) reanalysis as a forcing data set. The outputs are SWE and fSCA fields (1985-2015) at a resolution of 90 m that are consistent with the observed depletion record. Verification using in-situ snow surveys showed significant improvements in the accuracy of the SWE estimates relative to forward model estimates, with increases in correlation (0.49-0.87) and reductions in root mean square error (0.316 m to 0.129 m) and mean error (-0.221 m to 0.009 m). A sensitivity analysis showed that the framework is robust to variations in physiography, fSCA data availability and a priori precipitation biases. Results from the application to the headwater basin of the Aconcagua River showed how the forward model versus the fSCA-conditioned estimate resulted in different quantifications of the relationship between runoff and SWE, and different correlation patterns between pixel-wise SWE and ENSO. The illustrative results confirm the influence that ENSO has on snow accumulation for Andean basins draining into the Pacific, with ENSO explaining approximately 25% of the variability in near-peak (1 September) SWE values. Our results show how the assimilation of fSCA data results in a significant improvement upon MERRA-forced modeled SWE estimates, further increasing the utility of the MERRA data for high-resolution snow modeling applications.

SWE↗

NASA NTRS2013

Evaluation of MODIS Albedo Product (MCD43A) over Grassland, Agriculture and Forest Surface Types During Dormant and Snow-Covered Periods

This study assesses the Moderate-resolution Imaging Spectroradiometer (MODIS) BRDF/albedo 8 day standard product and products from the daily Direct Broadcast BRDF/albedo algorithm, and shows that these products agree well with ground-based albedo measurements during the more difficult periods of vegetation dormancy and snow cover. Cropland, grassland, deciduous and coniferous forests are considered. Using an integrated validation strategy, analyses of the representativeness of the surface heterogeneity under both dormant and snow-covered situations are performed to decide whether direct comparisons between ground measurements and 500-m satellite observations can be made or whether finer spatial resolution airborne or spaceborne data are required to scale the results at each location. Landsat Enhanced Thematic Mapper Plus (ETM +) data are used to generate finer scale representations of albedo at each location to fully link ground data with satellite data. In general, results indicate the root mean square errors (RMSEs) are less than 0.030 over spatially representative sites of agriculture/grassland during the dormant periods and less than 0.050 during the snow-covered periods for MCD43A albedo products. For forest, the RMSEs are less than 0.020 during the dormant period and 0.025 during the snow-covered periods. However, a daily retrieval strategy is necessary to capture ephemeral snow events or rapidly changing situations such as the spring snow melt.

MODIS↗

DOE OSTI2024

A dynamic solvent chamber propagation estimation framework using RNN for warm solvent injection in heterogeneous reservoirs

Warm solvent injection (WSI), injecting low-temperature solvent into formations to reduce the viscosity of heavy oil, is a clean technology for heavy oil production through reducing greenhouse gas emissions and water usage. The success of WSI operation depends on the uniform development and propagation of solvent chambers in reservoirs. However, reservoir heterogeneity stemming from shale barriers plays a detrimental role in the conformance of solvent chamber development and oil production rate. In this work, we developed a novel recurrent neural network (RNN)-based framework with the capability of efficiently tracking and estimating the solvent chamber positions in heterogeneous reservoirs based on only production time-series data. The developed estimation model utilizes the “sequence-to-sequence" mapping methodology to correlate observed production time-series sequence and solvent chamber edge sequence via a long short-term memory (LSTM) algorithm. The trained RNN models exhibit high accuracy, evidenced by the predicted dynamic solvent chamber locations match the corresponding true locations from numerical simulation, with a high coefficient of determination (R 2 ) and a low mean squared error. Specifically, the achieved R 2 values exceed 0.98 on both the training and testing data. The developed RNN-based workflow was tested via several cases from both regularly- and irregularly-shaped shale barriers, and the results were promising. The predicted solvent chambers showed strong agreement with those obtained from numerical simulations. The major benefits of this workflow include reducing computational time and saving overall monitoring and tracking costs for conventional techniques. In conclusion, the present work would provide a good demonstration of the capability of practical integration of machine learning methods in solving engineering problems.

58 GEOSCIENCES↗

NASA NTRS2021

Characterizing Deformable Mirrors for the MagAO-X Instrument

The MagAO-X instrument is a new extreme adaptive optics system for high-contrast imaging at visibleand near-infrared wavelengths on the Magellan Clay Telescope. A central component of this system is a 2040-actuatormicroelectromechanical deformable mirror (DM) from Boston Micromachines Corp. that operates at 3.63 kHz forhigh-order wavefront control (the tweeter). Two additional DMs from ALPAO perform the low-order (the woofer)and non-common-path science-arm wavefront correction (the NCPC DM). Prior to integration with the instrument, wecharacterized these devices using a Zygo Verifire Interferometer to measure each DM surface. We present the resultsof the characterization effort here, demonstrating the ability to drive tweeter to a flat of 6.9 nm RMS surface (and 0.56nm RMS surface within its control bandwidth), the woofer to 2.2 nm root mean square (RMS) surface, and the NCPCDM to 2.1 nm RMS surface over the MagAO-X beam footprint on each device. Using focus-diversity phase retrievalon the MagAO-X science cameras to estimate the internal instrument wavefront error (WFE), we further show that theintegrated DMs correct the instrument WFE to 18.7 nm RMS, which, combined with a 11.7% pupil amplitude RMS,produces a Strehl ratio of 0.94 at H↵

Kyle Van Gorkom↗

NASA NTRS1994

Correlated environmental corrections in TOPEX/POSEIDON, with a note on ionospheric accuracy

Estimates of the effectiveness of an altimetric correction, and interpretation of sea level variability as a response to atmospheric forcing, both depend upon assuming that residual errors in altimetric corrections are uncorrelated among themselves and with residual sea level, or knowing the correlations. Not surprisingly, many corrections are highly correlated since they involve atmospheric properties and the ocean surface's response to them. The full corrections (including their geographically varying time mean values), show correlations between electromagnetic bias (mostly the height of wind waves) and either atmospheric pressure or water vapor of -40%, and between atmospheric pressure and water vapor of 28%. In the more commonly used collinear differences (after removal of the geographically varying time mean), atmospheric pressure and wave height show a -30% correlation, atmospheric pressure and water vapor a -10% correlation, both pressure and water vapor a 7% correlation with residual sea level, and a bit surprisingly, ionospheric electron content and wave height a 15% correlation. Only the ocean tide is totally uncorrelated with other corrections or residual sea level. The effectiveness of three ionospheric corrections (TOPEX dual-frequency, a smoothed version of the TOPEX dual-frequency, and Doppler orbitography and radiopositioning integrated by satellite (DORIS) is also evaluated in terms of their reduction in variance of residual sea level. Smooth (90-200 km along-track) versions of the dual-frequency altimeter ionosphere perform best both globally and within 20 deg in latitude from the equator. The noise variance in the 1/s TOPEX inospheric samples is approximately (11 mm) squared, about the same as noise in the DORIS-based correction; however, the latter has its error over scales of order 10(exp 3) km. Within 20 deg of the equator, the DORIS-based correction adds (14 mm) squared to the residual sea level variance.

Zlotnicki, V.↗

DOE OSTI2025

Temporal Forecasting of Distributed Temperature Sensing in a Thermal Hydraulic System With Machine Learning and Statistical Models

We benchmark performance of long-short term memory (LSTM) network machine learning model and autoregressive integrated moving average (ARIMA) statistical model in temporal forecasting of distributed temperature sensing (DTS). Data in this study consists of fluid temperature transient measured with two co-located Rayleigh scattering fiber optic sensors (FOS) in a forced convection mixing zone of a thermal tee. We treat each gauge of a FOS as an independent temperature sensor. We first study prediction of DTS time series using Vanilla LSTM and ARIMA models trained on prior history of the same FOS that is used for testing. The results yield maximum absolute percentage error (MaxAPE) and root mean squared percentage error (RMSPE) of 1.58% and 0.06% for ARIMA, and 3.14% and 0.44% for LSTM, respectively. Next, we investigate zero-shot forecasting (ZSF) with LSTM and ARIMA trained on history of the co-located FOS only, which is advantageous when limited training data is available. The ZSF MaxAPE and RMSPE values for ARIMA are comparable to those of the Vanilla use case, while the error values for LSTM increase. We show that in ZSF, performance of LSTM network can be improved by training on most correlated gauges between the two FOS, which are identified by calculating the Pearson correlation coefficient. The improved ZSF MaxAPE and RMSPE for LSTM are 4.4% and 0.33%, respectively. Performance of ZSF LSTM can be further enhanced through transfer learning (TL), where LSTM is re-trained on a subset of the FOS that is the target of forecasting. We show that LSTM pre-trained on correlated dataset and re-trained on 30% of testing target dataset achieves MaxAPE and RMSPE values of 2.32% and 0.28%, respectively.

ARIMA↗

NASA NTRS1981

Model error estimation for large flexible spacecraft

The basic model obtained for spacecraft control system design applications is used to develop the control and estimation algorithms which constitute integral elements of the control system. The performance of this system is limited on account of modeling errors. The presence of such errors is inevitable in connection with truncated dynamics, parameter uncertainties, neglected nonlinearities, and external disturbances. In many cases, an approximate knowledge of the model errors can only be established by means of an estimation procedure. The present investigation has the objective to outline an approach to estimate errors inherent in a reduced-order model and to illustrate its application to modeling problems arising in spacecraft control system design. The considered procedure makes use of the principle of least-squares. In the discussed application this principle is employed to minimize a quadratic functional of the model errors.

Rodriguez, G.↗

DOE OSTI2025

Virtual sensing-enabled digital twin framework for real-time monitoring of nuclear systems leveraging deep neural operators

Abstract Real-time monitoring is a foundation of nuclear digital twin technology, crucial for detecting material degradation and maintaining nuclear system integrity. Traditional physical sensor systems face limitations, particularly in measuring critical parameters in hard-to-reach or harsh environments, often resulting in incomplete data coverage. Machine learning-driven virtual sensors offer a transformative solution by complementing physical sensors in monitoring critical degradation indicators. This paper introduces the use of Deep Operator Networks (DeepONet) to predict key thermal-hydraulic parameters in the hot leg of pressurized water reactor. DeepONet acts as a virtual sensor, mapping operational inputs to spatially distributed system behaviors without requiring frequent retraining. Our results show that DeepONet achieves low mean squared and Relative L2 error, making predictions 1400 times faster than traditional CFD simulations . These characteristics enable DeepONet to function as a real-time virtual sensor, synchronizing with the physical system to track degradation conditions and provide insights within the digital twin framework for nuclear systems.

Hossain, Raisa↗

NASA NTRS1992

Airborne gamma radiation measurements of soil moisture during FIFE: Activities and results

Soil moisture measurements were obtained during the summer of 1987 and 1989 near Manhattan, Kansas, using the National Weather Service (NWS) airborne gamma radiation system. A network of 24 flight lines were established over the research area. Airborne surveys were flown daily during two intensive field campaigns. The data collected was sufficient to modify the NWS standard operational method for estimating soil moisture for the Field Experiment (FIFE) flight lines. The average root mean square error of the soil moisture estimates for shorter FIFE flight lines was found to be 2.5 percent, compared with a reported value of 3.9 percent for NWS flight lines. Techniques were developed to compute soil moisture estimates for portions of the flight lines. Results of comparisons of the airborne gamma radiation soil moisture estimates with those obtained using the NASA Pushbroom Microwave Radiation (PBMR) system and hydrological model are presented. The airborne soil moisture measurements, and real averages computed using all remotely sensed and ground data, have been in support of the research of the many FIFE investigators whose overall goal was the upscale integration of models and the application of satellite remote sensing.

Peck, Eugene L.↗

NASA NTRS1986

Static shape control for flexible structures

An integrated methodology is described for defining static shape control laws for large flexible structures. The techniques include modeling, identifying and estimating the control laws of distributed systems characterized in terms of infinite dimensional state and parameter spaces. The models are expressed as interconnected elliptic partial differential equations governing a range of static loads, with the capability of analyzing electromagnetic fields around antenna systems. A second-order analysis is carried out for statistical errors, and model parameters are determined by maximizing an appropriate defined likelihood functional which adjusts the model to observational data. The parameter estimates are derived from the conditional mean of the observational data, resulting in a least squares superposition of shape functions obtained from the structural model.

Rodriguez, G.↗

DOE OSTI2026

Data for Soil Oxygen Dynamics: A Key Mediator of Tile Drainage Impacts on Coupled Hydrological, Biogeochemical, and Crop Systems

Tile drainage removes excess water and is an essential, widely adopted management practice to enhance crop productivity in the US Midwest and throughout the world. Tile drainage has been shown to significantly change hydrological and biogeochemical cycles by lowering the water table and reducing the residence time of soil water, although examining the complex interactions and feedbacks in an integrated hydrology–biogeochemistry–crop system remains elusive. Oxygen dynamics are critical to unraveling these interactions and have been ignored or oversimplified in existing models. Understanding these impacts is essential, particularly so because tile drainage has been highlighted as an adaptation under projected wetter springs and drier summers in the changing climate in the US Midwest. We used the ecosys model that uniquely incorporates first-principle soil oxygen dynamics and crop oxygen uptake mechanisms to quantify the impacts of tile drainage on hydrological and biogeochemical cycles and crop growth in corn–soybean rotation fields. The model was validated with data from a multi-treatment, multi-year experiment in Washington, IA. The relative root mean square error (rRMSE) for the corn and soybean yield in validation is 5.66 % and 12.57 %, respectively. The Pearson coefficient (r) of the monthly tile flow during the growing season is 0.78. Plant oxygen stress turns out as an emergent property of the equilibrium between the soil oxygen supply and biological demand. The impact of tile drainage on the system is achieved through a series of coupled feedback mechanisms. The model results show that tile drainage reduces the soil water content and enhances soil oxygenation. It additionally increases the subsurface discharge and elevates inorganic nitrogen leaching, with seasonal variations influenced by climate and crop phenology. The improved aerobic condition alleviates crop oxygen stress during wet springs, thereby promoting crop root growth during the early growth stage. The development of greater root density, in turn, mitigates water stress during dry summers, leading to an overall increase in the crop yield by ∼6 %. These functions indicate the potential of tile drainage in bolstering crop resilience to climate change and the use of this modeling tool for large-scale assessments of tile drainage. The model reveals the underlying causal mechanisms that drive the agroecosystem response to drainage on the coupled hydrology, biogeochemistry, and crop system dynamics.

Modeling↗

DOE OSTI2025

Soil oxygen dynamics: a key mediator of tile drainage impacts on coupled hydrological, biogeochemical, and crop systems

60 APPLIED LIFE SCIENCES↗

DOE OSTI2025

Coupled Induction Machine and HVAC Models for Simulating HVAC Performance Considering Grid Dynamics in Buildings

This paper presents the development of novel models that integrate induction machines with HVAC equipment, such as pumps, heat pumps, and chillers, to analyze the impact of electrical parameters on the operational performance of thermo-fluid systems. The proposed model employs a coupling technique that captures the dynamic interactions between induction machines and HVAC systems. By integrating electrical, thermal, and mechanical dynamics, the models provide a comprehensive framework for simulating real-world scenarios, including interactions with the electrical grid. This achievement was made possible through the development of a Computationally Efficient and Accurate Induction Machine (CEAIM) model. Implemented using the equation-based Modelica language, the CEAIM model has been validated against experimental results, manufacturer data sheets, and various operating conditions. Its performance has been compared with existing induction machine models in the Modelica Standard Library (MSL), demonstrating superior accuracy and computational efficiency. The CEAIM model predicts torque, speed, and power consumption with a coefficient of determination (R 2 ) ranging from 0.98 to 1 and a coefficient of variation of root mean square error (CVRMSE) between 0.27% and 6.67%. Additionally, CEAIM scales more efficiently than conventional MSL models, with a slower computational growth rate in large-scale simulations. After thorough validation of the CEAIM model, it was coupled with HVAC equipment as this approach provides a detailed multi-dimensional view of capturing electrical transients and mechanical performance. To support this, a case study was conducted to showcase its capabilities.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2009

Identifying Optimal Temporal Scale for the Correlation of AOD and Ground Measurements of PM2.5 to Improve the Model Performance in a Real-time Air Quality Estimation System

Aerosol optical depth (AOD), an indirect estimate of particle matter using satellite observations, has shown great promise in improving estimates of PM 2.5 air quality surface. Currently, few studies have been conducted to explore the optimal way to apply AOD data to improve the model accuracy of PM 2.5 surface estimation in a real-time air quality system. We believe that two major aspects may be worthy of consideration in that area: 1) the approach to integrate satellite measurements with ground measurements in the pollution estimation, and 2) identification of an optimal temporal scale to calculate the correlation of AOD and ground measurements. This paper is focused on the second aspect on the identifying the optimal temporal scale to correlate AOD with PM2.5. Five following different temporal scales were chosen to evaluate their impact on the model performance: 1) within the last 3 days, 2) within the last 10 days, 3) within the last 30 days, 4) within the last 90 days, and 5) the time period with the highest correlation in a year. The model performance is evaluated for its accuracy, bias, and errors based on the following selected statistics: the Mean Bias, the Normalized Mean Bias, the Root Mean Square Error, Normalized Mean Error, and the Index of Agreement. This research shows that the model with the temporal scale of within the last 30 days displays the best model performance in this study area using 2004 and 2005 data sets.

Li, Hui↗