Results for “Error Metrics” — Page 7

DOE OSTI2022

Energetic particle optimization of quasi-axisymmetric stellarator equilibria

Abstract An important goal of stellarator optimization is to achieve good confinement of energetic particles such as, in the case of a reactor, alphas created by deuterium–tritium fusion. In this work, a fixed-boundary stellarator equilibrium was re-optimized for energetic particle confinement via a two-step process: first, by minimizing deviations from quasi-axisymmetry (QA) on a single flux surface near the mid-radius, and secondly by maintaining this improved QA while minimizing the analytical quantity Γ C , which represents the angle between magnetic flux surfaces and contours of J | | , the second adiabatic invariant. This was performed multiple times, resulting in a group of equilibria with significantly reduced energetic particle losses, as evaluated by Monte Carlo simulations of alpha particles in scaled-up versions of the equilibria. This is the first time that energetic particle losses in a QA stellarator have successfully been reduced by optimizing Γ C . The relationship between energetic particle losses and metrics such as QA error ( E q a ) and Γ C in this set of equilibria were examined via statistical methods and a nearly linear relationship between volume-averaged Γ C and prompt particle losses was found.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Radar Super Resolution using a Deep Convolutional Neural Network

Super-resolution involves synthetically increasing the resolution of gridded data beyond its native resolution. Typically, this is done using interpolation schemes, which estimate sub-grid scale values from neighboring data, and perform the same operation everywhere regardless of the large-scale context, or by requiring a network of radars with overlapping fields of view. Recently, significant progress has been made in single image super resolution using convolutional neural networks. Conceptually, a neural network may be able to learn relations between large scale precipitation features and the associated sub-pixel scale variability and outperform interpolation schemes. Here, we use a deep convolutional neural network to artificially enhance the resolution of NEXRAD PPI scans. The model is trained on 6-months of reflectivity observations from the Langley Hill WA (KLGX) radar, and we find that it substantially outperforms common interpolation schemes for x4 and x8 resolution increases based on several objective error and perceptual quality metrics.

radar, machine learning, super resolution, Remote ↗

DOE OSTI2022

Development of advanced machine learning models for analysis of plutonium surrogate optical emission spectra

This work investigates and applies machine learning paradigms seldom seen in analytical spectroscopy for quantification of gallium in cerium matrices via processing of laser-plasma spectra. Ensemble regressions, support vector machine regressions, Gaussian kernel regressions, and artificial neural network techniques are trained and tested on cerium-gallium pellet spectra. A thorough hyperparameter optimization experiment is conducted initially to determine the best design features for each model. The optimized models are evaluated for sensitivity and precision using the limit of detection (LoD) and root mean-squared error of prediction (RMSEP) metrics, respectively. Gaussian kernel regression yields the superlative predictive model with an RMSEP of 0.33% and an LoD of 0.015% for quantification of Ga in a Ce matrix. This study concludes that these machine learning methods could yield robust prediction models for rapid quality control analysis of plutonium alloys.

Rao, Ashwin P. (ORCID:0000000319312568)↗

DOE OSTI2023

Evaluating E. coli genome‐scale metabolic model accuracy with high‐throughput mutant fitness data

Abstract The Escherichia coli genome‐scale metabolic model (GEM) is an exemplar systems biology model for the simulation of cellular metabolism. Experimental validation of model predictions is essential to pinpoint uncertainty and ensure continued development of accurate models. Here, we quantified the accuracy of four subsequent E. coli GEMs using published mutant fitness data across thousands of genes and 25 different carbon sources. This evaluation demonstrated the utility of the area under a precision–recall curve relative to alternative accuracy metrics. An analysis of errors in the latest (iML1515) model identified several vitamins/cofactors that are likely available to mutants despite being absent from the experimental growth medium and highlighted isoenzyme gene‐protein‐reaction mapping as a key source of inaccurate predictions. A machine learning approach further identified metabolic fluxes through hydrogen ion exchange and specific central metabolism branch points as important determinants of model accuracy. This work outlines improved practices for the assessment of GEM accuracy with high‐throughput mutant fitness data and highlights promising areas for future model refinement in E. coli and beyond.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Comparison of Machine Learning-Based Predictive Models of the Nutrient Loads Delivered from the Mississippi/Atchafalaya River Basin to the Gulf of Mexico

Predicting nutrient loads is essential to understanding and managing one of the environmental issues faced by the northern Gulf of Mexico hypoxic zone, which poses a severe threat to the Gulf’s healthy ecosystem and economy. The development of hypoxia in the Gulf of Mexico is strongly associated with the eutrophication process initiated by excessive nutrient loads. Due to the complexities in the excessive nutrient loads to the Gulf of Mexico, it is challenging to understand and predict the underlying temporal variation of nutrient loads. The study was aimed at identifying an optimal predictive machine learning model to capture and predict nonlinear behavior of the nutrient loads delivered from the Mississippi/Atchafalaya River Basin (MARB) to the Gulf of Mexico. For this purpose, monthly nutrient loads (N and P) in tons were collected from US Geological Survey (USGS) monitoring station 07373420 from 1980 to 2020. Machine learning models—including autoregressive integrated moving average (ARIMA), gaussian process regression (GPR), single-layer multilayer perceptron (MLP), and a long short-term memory (LSTM) with the single hidden layer—were developed to predict the monthly nutrient loads, and model performances were evaluated by standard assessment metrics—Root Mean Square Error (RMSE) and Correlation Coefficient (R). The residuals of predictive models were examined by the Durbin–Watson statistic. The results showed that MLP and LSTM persistently achieved better accuracy in predicting monthly TN and TP loads compared to GPR and ARIMA. In addition, GPR models achieved slightly better test RMSE score than ARIMA models while their correlation coefficients are much lower than ARIMA models. Moreover, MLP performed slightly better than LSTM in predicting monthly TP loads while LSTM slightly outperformed for TN loads. Furthermore, it was found that the optimizer and number of inputs didn’t show effects on the LSTM performance while they exhibited impacts on MLP outcomes. This study explores the capability of machine learning models to accurately predict nonlinearly fluctuating nutrient loads delivered to the Gulf of Mexico. Further efforts focus on improving the accuracy of forecasting using hybrid models which combine several machine learning models with superior predictive performance for nutrient fluxes throughout the MARB.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1985

Four applications of a software data collection and analysis methodology

The evaluation of software technologies suffers because of the lack of quantitative assessment of their effect on software development and modification. A seven-step data collection and analysis methodology couples software technology evaluation with software measurement. Four in-depth applications of the methodology are presented. The four studies represent each of the general categories of analyses on the software product and development process: blocked subject-project studies, replicated project studies, multi-project variation studies, and single project strategies. The four applications are in the areas of, respectively, software testing, cleanroom software development, characteristic software metric sets, and software error analysis.

Basili, Victor R.↗

NASA NTRS1993

Maximum-likelihood block detection of noncoherent continuous phase modulation

This paper examines maximum-likelihood block detection of uncoded full response CPM over an additive white Gaussian noise (AWGN) channel. Both the maximum-likelihood metrics and the bit error probability performances of the associated detection algorithms are considered. The special and popular case of minimum-shift-keying (MSK) corresponding to h = 0.5 and constant amplitude frequency pulse is treated separately. The many new receiver structures that result from this investigation can be compared to the traditional ones that have been used in the past both from the standpoint of simplicity of implementation and optimality of performance.

Simon, Marvin K.↗

NASA NTRS2012

Material Model Evaluation of a Composite Honeycomb Energy Absorber

A study was conducted to evaluate four different material models in predicting the dynamic crushing response of solid-element-based models of a composite honeycomb energy absorber, designated the Deployable Energy Absorber (DEA). Dynamic crush tests of three DEA components were simulated using the nonlinear, explicit transient dynamic code, LS-DYNA . In addition, a full-scale crash test of an MD-500 helicopter, retrofitted with DEA blocks, was simulated. The four material models used to represent the DEA included: *MAT_CRUSHABLE_FOAM (Mat 63), *MAT_HONEYCOMB (Mat 26), *MAT_SIMPLIFIED_RUBBER/FOAM (Mat 181), and *MAT_TRANSVERSELY_ANISOTROPIC_CRUSHABLE_FOAM (Mat 142). Test-analysis calibration metrics included simple percentage error comparisons of initial peak acceleration, sustained crush stress, and peak compaction acceleration of the DEA components. In addition, the Roadside Safety Verification and Validation Program (RSVVP) was used to assess similarities and differences between the experimental and analytical curves for the full-scale crash test.

Jackson, Karen E.↗

NASA NTRS2016

Uncertainty Assessment of the NASA Earth Exchange Global Daily Downscaled Climate Projections (NEX-GDDP) Dataset

The NASA Earth Exchange Global Daily Downscaled Projections (NEX-GDDP) dataset is comprised of downscaled climate projections that are derived from 21 General Circulation Model (GCM) runs conducted under the Coupled Model Intercomparison Project Phase 5 (CMIP5) and across two of the four greenhouse gas emissions scenarios (RCP4.5 and RCP8.5). Each of the climate projections includes daily maximum temperature, minimum temperature, and precipitation for the periods from 1950 through 2100 and the spatial resolution is 0.25 degrees (approximately 25 km x 25 km). The GDDP dataset has received warm welcome from the science community in conducting studies of climate change impacts at local to regional scales, but a comprehensive evaluation of its uncertainties is still missing. In this study, we apply the Perfect Model Experiment framework (Dixon et al. 2016) to quantify the key sources of uncertainties from the observational baseline dataset, the downscaling algorithm, and some intrinsic assumptions (e.g., the stationary assumption) inherent to the statistical downscaling techniques. We developed a set of metrics to evaluate downscaling errors resulted from bias-correction ("quantile-mapping"), spatial disaggregation, as well as the temporal-spatial non-stationarity of climate variability. Our results highlight the spatial disaggregation (or interpolation) errors, which dominate the overall uncertainties of the GDDP dataset, especially over heterogeneous and complex terrains (e.g., mountains and coastal area). In comparison, the temporal errors in the GDDP dataset tend to be more constrained. Our results also indicate that the downscaled daily precipitation also has relatively larger uncertainties than the temperature fields, reflecting the rather stochastic nature of precipitation in space. Therefore, our results provide insights in improving statistical downscaling algorithms and products in the future.

climate projection↗

NASA NTRS2016

Uncertainty Assessment of the NASA Earth Exchange Global Daily Downscaled Climate Projections (NEX-GDDP) Dataset

The NASA Earth Exchange Global Daily Downscaled Projections (NEX-GDDP) dataset is comprised of downscaled climate projections that are derived from 21 General Circulation Model (GCM) runs conducted under the Coupled Model Intercomparison Project Phase 5 (CMIP5) and across two of the four greenhouse gas emissions scenarios (RCP4.5 and RCP8.5). Each of the climate projections includes daily maximum temperature, minimum temperature, and precipitation for the periods from 1950 through 2100 and the spatial resolution is 0.25 degrees (approximately 25 km by 25 km). The GDDP dataset has received warm welcome from the science community in conducting studies of climate change impacts at local to regional scales, but a comprehensive evaluation of its uncertainties is still missing. In this study, we apply the Perfect Model Experiment framework (Dixon et al. 2016) to quantify the key sources of uncertainties from the observational baseline dataset, the downscaling algorithm, and some intrinsic assumptions (e.g., the stationary assumption) inherent to the statistical downscaling techniques. We developed a set of metrics to evaluate downscaling errors resulted from bias-correction ("quantile-mapping"), spatial disaggregation, as well as the temporal-spatial non-stationarity of climate variability. Our results highlight the spatial disaggregation (or interpolation) errors, which dominate the overall uncertainties of the GDDP dataset, especially over heterogeneous and complex terrains (e.g., mountains and coastal area). In comparison, the temporal errors in the GDDP dataset tend to be more constrained. Our results also indicate that the downscaled daily precipitation also has relatively larger uncertainties than the temperature fields, reflecting the rather stochastic nature of precipitation in space. Therefore, our results provide insights in improving statistical downscaling algorithms and products in the future.

general circulation model (GCM)↗

NASA NTRS2020

Q4 – A CubeSat Mission to Demonstrate Omnidirectional Optical Communications

We are proposing a technology demonstration mission for JPL’s Inter-Satellite Optical Communicator (ISOC). The ISOC has the potential to enable up to 1 Gbps data rates over a distance up to 200 km in free space. Key features of the ISOC include full sky coverage and the ability to maintain multiple links simultaneously. The Q4 mission consists of (4) 6U CubeSats furnished with ISOCs to demonstrate high data rate communications among the spacecraft. More specifically, we seek to demonstrate the omnidirectionality of the ISOC by providing simultaneous optical links between one spacecraft and the other three. Q4 will be a demonstrator for small spacecraft swarm capabilities. Following a proposed deployment from the ISS, the CubeSats will utilize their onboard thrusters to enter their desired orbit. The orbit consists of one “leader” spacecraft in a circular orbit with a 400 km LEO altitude and three “follower” spacecraft in slightly elliptical orbits rotating azimuthally about the leader. The main mission will consist of three consecutive phases: First, the spacecraft will demonstrate pointing, acquisition, and tracking using newly developed protocols. Next, link establishment and different channel access methods (CDMA and TDMA) will be tested. Finally, Delay Tolerant Network protocols will be implemented to allow fast data sharing among the spacecraft. The distance between the communicating spacecraft will be increased as the mission progresses to characterize the link quality as a function of distance. All communications over the course of the mission will be recorded and analyzed on the ground using bit error rate as a metric for success. The current design for each the four Q4 CubeSats contains an XACT advanced ADCS system for precision beam pointing. Other components currently under consideration include MiPS cold gas thrusters for orbital maneuvering and gimbaled eHaWK 84W solar arrays. In this paper we present design considerations for the Q4 CubeSats, link budget calculations, results from preliminary mission analysis, and expected results.

Velazco, Jose E↗

NASA NTRS2020

Structural Model Tuning Tool: User's Reference Manual

This report presents an efficient approach for tuning finite element models to match the measured ground vibration test and static test data. Frequencies, mode shapes, total weight, location of the center of gravity, and static deformation computed from the finite element model are matched to the measured data. The model tuning procedure used in this work is based on solving an optimization problem in which the errors for the considered metrics, between the finite element prediction and the measured data, are minimized. Analytical sensitivity values of performance indices are computed using the NASTRAN-generated sensitivity values together with the in-house computer codes, which allow for faster computational time and the use of gradient-based optimizers. The method is applied to the Aerostructures Test Wing IV model. The study shows that the military standard and the National Aeronautics and Space Administration standard for comparing analytical and experimental modal data are all satisfied. The final finite element model correlates well with the test data. The flutter speed decreases by 8.91 percent after model tuning compared with the original Aerostructures Test Wing IV design.

Chan-gi Pak↗

NASA NTRSDate not supplied

Effects of Communication Modality on Pilot-Controller Coordination during a Simulated m:N Operation

The last decade or so has seen growing interest in new control paradigms and concepts of operation for uncrewed aircraft systems (UAS) in which multiple aircraft are piloted remotely by a single or relatively small number of people. Referred to as “one-to-many” and “many-to- many” (alternatively, “multi-operator, multi-vehicle”)—and frequently expressed as the corresponding ratios, 1:N and m:N—such novel configurations of aircraft and the people who manage them are seen as critical to the path to future operations involving UAS. Examples of industry domains interested in these control paradigms are small package delivery services utilizing small UAS and passenger-carrying, short-range “Urban Air Mobility” (UAM) operations. Stakeholders in such operations have identified communication and coordination of flight activity with air traffic controllers (ATC) as a barrier to operations. In contrast to present-day flight operations, in which a pilot communicates with one ATC on one radio frequency for one aircraft, multi-vehicle operations potentially entail a significant increase in pilot task load for management of comms. New concepts, such as UAS Service Suppliers (USSs) and Providers of Services to UAM (PSUs), have been proposed to address the known bottleneck for Air Traffic Management (ATM) presented by multi-vehicle operations. While progress has been steadily made over years developing USSs and PSUs, it is generally expected that initial UAM operations will rely on traditional voice-over-radio communication with ATC for purposes of ATM. The current study was a human-in-the-loop simulation that had participants, each possessing a Private Pilot License, act as the ground-based pilot-in- command for multiple vehicles in a hypothetical UAM service in the San Francisco Bay Area. The experiment utilized a 2-by-3, within-subjects design in which the pilot’s Vehicle Load (4 vs. 12) and Comm System (Voice, Datalink, and a Hybrid) were manipulated. The task given to pilots was to use the Comm System to coordinate flight activity for all aircraft with appropriate controllers, having to obtain departure and arrival clearances at “vertiport” facilities and transition clearances for any intermediate airspaces along the route. Pilots were additionally responsible for compliance with vectoring instructions issued by ATC. Subjective workload questionnaires (NASA-TLX) were administered following each experimental trial. Screen recordings of the pilot’s Ground Control Station (GCS) and audio recordings of trials were subsequently coded to obtain performance metrics: response times and error rates. Presented in this paper are results related to pilot responses to vectoring instructions issued by ATC. Workload was found to be significantly higher in the 12-Vehicle condition compared to the 4-Vehicle condition, nearly maxing out the NASA-TLX overall workload scale. There was no significant difference made by the Comm System on workload ratings. Pilots’ response times to communications were fastest in the Voice condition, although overall “service time” for compliance was shorter in Datalink and Hybrid conditions in most cases. Errors by pilots were frequent in both Vehicle Load conditions, most perniciously when using the Voice system. The results of this study suggest tradeoffs in advantages and disadvantages of the three comm systems. Recommendations for communication system design are provided taking the tradeoffs into account.

Garrett G Sadler↗

NASA NTRSDate not supplied

Effects of Communication Modality on Pilot-Controller Coordination during a Simulated m:N Operation

The last decade or so has seen growing interest in new control paradigms and concepts of operation for uncrewed aircraft systems (UAS) in which multiple aircraft are piloted remotely by a single or relatively small number of people. Referred to as “one-to-many” and “many-to- many” (alternatively, “multi-operator, multi-vehicle”)—and frequently expressed as the corresponding ratios, 1:N and m:N—such novel configurations of aircraft and the people who manage them are seen as critical to the path to future operations involving UAS. Examples of industry domains interested in these control paradigms are small package delivery services utilizing small UAS and passenger-carrying, short-range “Urban Air Mobility” (UAM) operations. Stakeholders in such operations have identified communication and coordination of flight activity with air traffic controllers (ATC) as a barrier to operations. In contrast to present-day flight operations, in which a pilot communicates with one ATC on one radio frequency for one aircraft, multi-vehicle operations potentially entail a significant increase in pilot task load for management of comms. New concepts, such as UAS Service Suppliers (USSs) and Providers of Services to UAM (PSUs), have been proposed to address the known bottleneck for Air Traffic Management (ATM) presented by multi-vehicle operations. While progress has been steadily made over years developing USSs and PSUs, it is generally expected that initial UAM operations will rely on traditional voice-over-radio communication with ATC for purposes of ATM. The current study was a human-in-the-loop simulation that had participants, each possessing a Private Pilot License, act as the ground-based pilot-in- command for multiple vehicles in a hypothetical UAM service in the San Francisco Bay Area. The experiment utilized a 2-by-3, within-subjects design in which the pilot’s Vehicle Load (4 vs. 12) and Comm System (Voice, Datalink, and a Hybrid) were manipulated. The task given to pilots was to use the Comm System to coordinate flight activity for all aircraft with appropriate controllers, having to obtain departure and arrival clearances at “vertiport” facilities and transition clearances for any intermediate airspaces along the route. Pilots were additionally responsible for compliance with vectoring instructions issued by ATC. Subjective workload questionnaires (NASA-TLX) were administered following each experimental trial. Screen recordings of the pilot’s Ground Control Station (GCS) and audio recordings of trials were subsequently coded to obtain performance metrics: response times and error rates. Presented in this paper are results related to pilot responses to vectoring instructions issued by ATC. Workload was found to be significantly higher in the 12-Vehicle condition compared to the 4-Vehicle condition, nearly maxing out the NASA-TLX overall workload scale. There was no significant difference made by the Comm System on workload ratings. Pilots’ response times to communications were fastest in the Voice condition, although overall “service time” for compliance was shorter in Datalink and Hybrid conditions in most cases. Errors by pilots were frequent in both Vehicle Load conditions, most perniciously when using the Voice system. The results of this study suggest tradeoffs in advantages and disadvantages of the three comm systems. Recommendations for communication system design are provided taking the tradeoffs into account.

urban air mobility↗

NASA NTRS2024

Evaluation of Machine Learning and Deep Learning Algorithms for Fire Prediction in Southeast Asia

Vegetation fires are prevalent in South/Southeast Asian countries, making fire prediction crucial due to their potential environmental, economic, and social impacts. Accurate predictions of fires facilitate timely interventions, helping to mitigate uncontrolled fires that can lead to biodiversity loss and air quality issues. In this study, we utilize VIIRS satellite-derived fire data alongside six machine learning and deep learning models—Simple Persistence, Multi-Layer Perceptron (MLP), Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), CNN-LSTM, and ConvLSTM—to determine the most effective fire prediction model, using Root Mean Square Error (RMSE) as the metric. Our results indicate that the CNN model is the most reliable in regions with spatial dependencies, such as Brunei, Indonesia, Malaysia, the Philippines, Timor-Leste, and Thailand. Conversely, the ConvLSTM model excels in countries with complex spatiotemporal dynamics like Laos, Myanmar, and Vietnam. The CNN-LSTM hybrid model also performed well in Cambodia, suggesting a need for a balanced approach in areas requiring both spatial and temporal feature extraction. Furthermore, simpler models like Persistence and MLP showed limitations in capturing dynamic patterns and temporal dependencies. Our findings highlight the importance of evaluating models before implementing any decision support systems (DSS) in fire management. By tailoring models to specific regional fire data, we can enhance prediction accuracy and responsiveness, ultimately improving fire risk management in Southeast Asia and beyond.

Deep learning↗

DOE OSTI2020

Calibration of reactive burn and Jones-Wilkins-Lee parameters for simulations of a detonation-driven flow experiment with uncertainty quantification

Here, uncertainties in the explosive-specific parameters of the Jones-Wilkins-Lee (JWL) equation of state (EOS) are carefully considered in hydrodynamic simulations of an explosive experiment to minimize the error in the flow prediction. Experimental data of the leading shock position in the transverse direction over time serves as the prediction metric for quantifying simulation prediction error. The uncertainty quantification technique, global sensitivity analysis, is utilized to determine the JWL parameters to which the transverse shock propagation is most sensitive. A polynomial response surface (PRS) is constructed in the space of the most influential JWL parameters, and the point of minimum error between the experimental data and the PRS yields calibrated JWL parameters for the experimental flow. The simulation results following the parameter calibration show good agreement with the experimental data. It was found that two significant parameters, the heat release per unit mass of reactant Q and JWL model exponent R 1 are strongly related, which makes it difficult to identify accurate values.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Probabilistic Power Consumption Modeling for Commercial Buildings Using Logistic Regression Markov Chain

The total energy consumed by buildings takes up to 40% of U.S. energy use, in which a large portion is contributed by commercial buildings. Building performance optimization is desirable but requires accurate building models with uncertainties taken into account. This paper proposes a novel probabilistic modeling method using Logistic Regression Markov Chain (LRMC). The LRMC model enhances the performance of traditional Markov Chain (MC) models by adopting time-variant transition matrices calibrated using logistic regression with exogenous inputs. Compared with existing building models, the proposed model produces accurate multi-step modeling results with full probability distribution. The proposed probabilistic building model is tested using actual commercial building measurements and modeling performance is evaluated with two probabilisitc metrics. The results show that the LRMC model has higher accuracy than traditional MC model and Logistic Regression (LR) model in that it yields lower error scores under both evaluation metrics.

Building modeling↗

DOE OSTI2024

Benchmarking machine learning strategies for phase-field problems

Abstract We present a comprehensive benchmarking framework for evaluating machine-learning approaches applied to phase-field problems. This framework focuses on four key analysis areas crucial for assessing the performance of such approaches in a systematic and structured way. Firstly, interpolation tasks are examined to identify trends in prediction accuracy and accumulation of error over simulation time. Secondly, extrapolation tasks are also evaluated according to the same metrics. Thirdly, the relationship between model performance and data requirements is investigated to understand the impact on predictions and robustness of these approaches. Finally, systematic errors are analyzed to identify specific events or inadvertent rare events triggering high errors. Quantitative metrics evaluating the local and global description of the microstructure evolution, along with other scalar metrics representative of phase-field problems, are used across these four analysis areas. This benchmarking framework provides a path to evaluate the effectiveness and limitations of machine-learning strategies applied to phase-field problems, ultimately facilitating their practical application.

36 MATERIALS SCIENCE↗