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DOE OSTI2026

Leveraging large language models to address data scarcity in machine learning for graphene synthesis

Machine learning in experimental materials science faces significant challenges due to the scarcity of data, which are costly and time-consuming to generate, particularly when relying on in-house experiments. Literature data mining offers a potential solution but introduces issues like mixed data quality, inconsistent formats, and non-uniform reporting of synthesis parameters, resulting in partially missing and heterogeneous features across the dataset. Here, we propose data imputation and feature engineering methods that employ pre-trained large language models (LLMs) to enhance machine learning performance on scarce, heterogeneous datasets, demonstrated on graphene CVD synthesis data and the ML-HydPARK hydrogen storage dataset. GPT models perform data imputation via tailored prompting and semantic normalization of inconsistently reported features through embeddings, for example, to harmonize the complex nomenclature of CVD substrates. Beyond yielding more diverse and richer feature representations than traditional methods such as K-nearest neighbors (KNN) and Multivariate Imputation by Chained Equations (MICE), LLM-based data imputation is evaluated against dataset characteristics and prompting strategies. We vary the level of autonomy granted to the LLM, from generic prompting that leverages pre-trained knowledge for autonomous data generation to data-informed prompting that constrains outputs using target-specific information, and demonstrate which level of autonomy yields superior imputation performance across datasets and feature types. The proposed data engineering methods markedly improve downstream performance; for example, in graphene layer number classification using a support vector machine (SVM), binary accuracy increases from 39% to 65% and ternary accuracy from 52% to 72%. Fine-tuning experiments on both datasets show that combining our proposed LLM-based data imputation and feature encoding methods with numerical machine learning predictors outperforms standalone fine-tuned LLM predictors in data-scarce settings. The proposed strategies emphasize data enhancement techniques rather than refining learning architectures or regularizing loss functions, offering a broadly applicable framework for improving machine learning performance on scarce, inhomogeneous datasets.

Chemical vapor deposition↗

DOE OSTI2023

Applying NIR and MIR spectroscopy for C and soil property prediction in northern cold-region ecosystems. Which approach works better?

Here, developing reliable predictions of soil attributes is necessary to understand northern cold-region climate-soil feedback. Calibration models using near-infrared (NIR) and mid-infrared (MIR) spectroscopy were developed to predict eight commonly measured soil properties for 119 soil samples representing a range of vegetation types, parent materials, and soil types spanning >23° of latitude from southeast Alaska to the Canadian high Arctic. In order to obtain a more accurate prediction, this study compared the performance of linear and non-linear calibration techniques, including lasso regression (Lasso), support vector machine (SVM), random forest (RF) and classic partial least squares (PLS) to predict different soil properties of these soils. Comparing the four models, we noticed that their performance was quite similar for MIR overall, while NIR achieved better results with a PLS model for our dataset. PLS coupled with MIR showed a better performance for soil parameters, such as total organic carbon (TOC), total nitrogen (TN), cation exchange capacity (CEC) and clay (R-squared of 0.9, 0.81, 0.80, and 0.84) when compared with NIR (R-squared of 0.85, 0.72, 0.81 and 0.68). However, using either MIR or NIR spectroscopy, PLS predictions for bulk density (BD) and sand content were not accurate. The variable importance analysis based on the PLS model successfully estimated the relative contribution of wavelengths influencing soil property predictions most. Overall, TOC, TN, CEC and clay mineral predictions are closely related to the occurrence of specific spectral bands in the MIR region. For example, wavelengths at 2978 and 1761 cm -1 for TOC and TN, as well as at 3064 cm -1 for CEC, were selected as the most influential predictor variables. We demonstrated that MIR spectroscopy is a powerful tool for more extensive monitoring in soils of the northern cold climate region; however, NIR could be utilized for rapid estimates when the highest accuracy is not essential.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

End-To-End Decentralized Transmission Line Protection in IBR-Dominated Weak Grids Using Interpretable Data-Driven Methods

Traditional transmission line protection relies on predictable synchronous-based fault signatures, which frequently fail under the non-standard, current-limited fault characteristics of Inverter-Based Resources (IBRs). This study investigates how to achieve secure, communication-free fault isolation in IBR-dominated weak grids without relying on opaque, computationally heavy "black-box" machine learning algorithms. To address this, we propose a novel, standalone, and inherently interpretable data-driven protection framework. Unlike centralized methods requiring multi-terminal communication, this decentralized approach relies solely on local measurements using a hierarchical linear-kernel Support Vector Machine (SVM). The methodology decomposes the protection task into four sequential stages that mimic traditional protection elements: fault detection and fault direction identification, fault type classification, zone classification, and location estimation. This multi-stage architecture allows for specialized feature engineering at each stage, combining high computational efficiency with logic traceability. The framework's end-to-end performance was validated via C-code and PSCAD/EMTDC co-simulation, utilizing a real-world utility network and an OEM black-box IBR model. The proposed relay achieves 97.2% overall accuracy and provides a reliable trip decision within a 2.5-cycle window. The results confirm 100% accuracy in fundamental fault detection, reliable zone selectivity across low to moderate fault resistances, and robust security against non-fault transients, proving its immediate viability for integration into commercial numerical relays.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Machine learning models for estimating contamination across different curbside collection strategies

Contaminated recyclables, which are frequently discarded as waste, pose a significant challenge to the implementation of a circular economy. These contaminated recyclables impede the circulation of resources, resulting in higher processing costs at material recovery facilities (MRFs). Over the past few decades, machine learning (ML) models such as linear regression (LR), support vector machine (SVM), and random forest (RF) have evolved to provide new methods for predicting inbound contamination rates in addition to traditional statistical models. In this study, we applied ML models to predict inbound contamination rates using demographic features from 15 counties in the U.S. with different curbside collection strategies. In general, we found that ML models outperformed linear mixed models. Specifically, SVM models had the highest performance (R 2 = 0.75; mean absolute error (MAE) = 0.06), which may be due to their ability to model nonlinear relationships between features and inbound contamination rates. Further, the key predictor was population, with poverty rate being positively correlated and median age negatively correlated with inbound contamination rates. To improve the management of contamination and enhance the implementation of a circular economy, better models are needed to understand and estimate inbound contamination rates as well as identify critical factors in the present and future.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Predicting melt pool depth and grain length using multiple signatures from in-situ single camera two-wavelength imaging pyrometry for laser powder bed fusion

In laser powder bed fusion (LPBF), the in-situ process signatures are known to have a direct correlation with the microstructural properties of the solidified melt pool (MP). It is known that the MP cooling and heating rates, and laser processing parameters can critically determine the grain structure and thereby affect the part properties. The objective of this work is to study the feasibility of using in-process, high-speed imaging pyrometry for evaluating the solidified MP properties “below” the surface, such as depth and microstructural properties. To accomplish this, we employ an in-house single camera-based two-wavelength imaging pyrometry (STWIP) system for monitoring the printing of single-scan tracks with Inconel 718 on a commercial LPBF printer (EOS M290). Further, the lab designed STWIP system is a coaxial high-speed (>10,000 fps) imaging system capable of monitoring MP temperature, morphology, and intensity profiles. The temperature measurements from STWIP are emissivity independent. The STWIP measured MP signatures of the printed tracks are correlated with the ex-situ microscopy characterized MP depth and the average grain lengths. From the data analysis, using support vector machine (SVM)-based regression models, we found that the MP temperature signatures are crucial for an accurate prediction of MP depth and the grain length, thus validating the novelty and necessity of the developed in-situ monitoring methods and analysis.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Predicting measures of soil health using the microbiome and supervised machine learning

Soil health encompasses a range of biological, chemical, and physical soil properties that sustain the commercial and ecological value of agroecosystems. Monitoring soil health requires a comprehensive set of diagnostics that can be cost-prohibitive for routine analyses. The soil microbiome provides a rich source of information about soil properties, which can be assayed in a high-throughput, cost-effective way. We evaluated the accuracy of random forest (RF) and support vector machine (SVM) regression and classification models in predicting 12 measures of soil health, tillage status, and soil texture from 16S rRNA gene amplicon data with an operationally relevant sample set. We validated the efficacy of the best performing models against independent datasets and also tested best practices for processing microbiome data for use in machine learning. Soil health metrics could be predicted from microbiome data with the best models achieving a Kappa value of ~0.65, for categorical assessments, and a R2 value of ~0.8, for numerical scores. Biological health ratings were better predicted than chemical or physical ratings. Validation with independent datasets revealed that models had general predictive value for soil properties, including yield. The ecological profiles of several taxa important for model accuracy matched the observed relationships with soil health, including Pyrinomonadaceae, Nitrososphaeraceae, and Candidatus Udeaobacter. Models trained at the highest taxonomic resolution proved most accurate, with losses in accuracy resulting from rarefying, sparsity filtering, and aggregating at higher taxonomic ranks. Furthermore, our study provides the groundwork for developing scalable technology to use microbiome-based diagnostics for the assessment of soil health.

16S rRNA gene↗

DOE OSTI2020

A Remote Sensing Technique to Upscale Methane Emission Flux in a Subtropical Peatland

Abstract Quantification of methane (CH 4 ) gas emission from peat is critical to understand CH 4 budget from natural wetlands under a climate warming scenario. Previous studies have focused on prediction and mapping of CH 4 emission flux using process‐based models, while application of statistical‐empirical models for upscaling spatially sparse in situ measurements is scarce. In this study, we developed an empirical remote sensing upscaling approach to estimate CH 4 emission flux in the Everglades using limited in situ point‐based CH 4 emission flux measurements and Landsat data during 2013–2018. We spatially and temporally linked in situ data with Landsat surface reflectance based on temporally composite data sets and developed an object‐based machine learning framework to model and map CH 4 emission flux. An ensemble analysis of two machine learning models, k ‐Nearest Neighbor ( k ‐NN) and Support Vector Machine (SVM), shows that the upscaling approach is promising for predicting CH 4 emission flux with a R 2 of 0.65 and 0.87 based on a fivefold cross‐validation for a dry season and wet season estimation, respectively. We generated emission flux map products that successfully revealed the spatial and temporal heterogeneity of CH 4 emission within the dominant freshwater marsh ecosystem in the Everglades. We conclude that Landsat is promising for upscaling and monitoring CH 4 emission flux and reducing the uncertainty in emission estimates from wetlands.

Zhang, Caiyun↗

DOE OSTI2021

Deep Learning Estimation of Daily Ground–Level NO 2 Concentrations from Remote Sensing Data

The limited number of nitrogen dioxide (NO 2 ) surface measurements calls for the development of highly accurate approaches to estimating surface NO 2 concentrations. In this study, we leverage a new satellite instrument, the TROPOspheric Monitoring Instrument (TROPOMI), along with other predictor variables, to estimate daily surface NO 2 concentrations over Texas in 2019. We use the deep convolutional neural network (Deep-CNN), an advanced deep learning algorithm, to obtain estimates and achieve a correlation coefficient (R) of 0.91, an index of agreement (IOA) of 0.95, and a mean absolute bias (MAB) of 1.75 ppb in surface NO 2 estimation. Additionally, we leverage a novel approach, SHapley Additive exPlanations (SHAP), to describe how Deep-CNN understands each predictor variable. The SHAP results show that the Deep-CNN model has an advanced understanding of the dataset, revealing that TROPOMI closely captures levels of NO 2 . In addition, we show the superiority of our Deep-CNN model at estimating surface NO 2 over other well-known machine learning and regression models in the field, including the support vector machines (SVM), random forest (RF), and multiple linear regression (MLR). Although SVM and RF show strong capabilities at estimating surface NO 2 concentrations, their accuracy is inferior to that of the Deep-CNN model, ranking second and third in model accuracy in this study. The MLR, however, shows a poor ability at NO 2 estimation and ranks last among all models. Furthermore, testing the impact of sample size on model performance, we also show that, compared to other models, Deep-CNN needs more samples to trigger its strength at surface NO 2 estimation.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Fusion of Multiple Models for Improving Gross Primary Production Estimation With Eddy Covariance Data Based on Machine Learning

Abstract Terrestrial gross primary production (GPP) represents the magnitude of CO 2 uptake through vegetation photosynthesis, and is a key variable for carbon cycles between the biosphere and atmosphere. Light use efficiency (LUE) models have been widely used to estimate GPP for its physiological mechanisms and availability of data acquisition and implementation, yet each individual GPP model has exhibited large uncertainties due to input errors and model structure, and further studies of systematic validation, comparison, and fusion of those models with eddy covariance (EC) site data across diverse ecosystem types are still needed in order to further improve GPP estimation. We here compared and fused five GPP models (VPM, EC‐LUE, GOL‐PEM, CHJ, and C‐Fix) across eight ecosystems based on FLUXNET2015 data set using the ensemble methods of Bayesian Model Averaging (BMA), Support Vector Machine (SVM), and Random Forest (RF) separately. Our results showed that for individual models, EC‐LUE gave a better performance to capture interannual variability of GPP than other models, followed by VPM and GLO‐PEM, while CHJ and C‐Fix were more limited in their estimation performance. We found RF and SVM were superior to BMA on merging individual models at various plant functional types (PFTs) and at the scale of individual sites. On the basis of individual models, the fusion methods of BMA, SVM, and RF were examined by a five‐fold cross validation for each ecosystem type, and each method successfully improved the average accuracy of estimation by 8%, 18%, and 19%, respectively.

Environmental Sciences & Ecology↗

DOE OSTI2023

High–Resolution Maps of Near–Surface Permafrost for Three Watersheds on the Seward Peninsula, Alaska Derived From Machine Learning

Permafrost soils are a critical component of the global carbon cycle and are locally important because they regulate the hydrologic flux from uplands to rivers. Furthermore, degradation of permafrost soils causes land surface subsidence, damaging infrastructure that is crucial for local communities. Regional and hemispherical maps of permafrost are too coarse to resolve distributions at a scale relevant to assessments of infrastructure stability or to illuminate geomorphic impacts of permafrost thaw. Here we train machine learning models to generate meter–scale maps of near–surface permafrost for three watersheds in the discontinuous permafrost region. The models were trained using ground truth determinations of near–surface permafrost presence from measurements of soil temperature and electrical resistivity. We trained three classifiers: extremely randomized trees (ERTr), support vector machines (SVM), and an artificial neural network (ANN). Model uncertainty was determined using k–fold cross validation, and the modeled extents of near–surface permafrost were compared to the observed extents at each site. At–a–site near–surface permafrost distributions predicted by the ERTr produced the highest accuracy (70%–90%). However, the transferability of the ERTr to the sites outside of the training data set was poor, with accuracies ranging from 50% to 77%. The SVM and ANN models had lower accuracies for at–a–site prediction (70%–83%), yet they had greater accuracy when transferred to the non–training site (62%–78%). These models demonstrate the potential for integrating high–resolution spatial data and machine learning models to develop maps of near–surface permafrost extent at resolutions fine enough to assess infrastructure vulnerability and landscape morphology influenced by permafrost thaw.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

QUBO formulations for training machine learning models

Abstract Training machine learning models on classical computers is usually a time and compute intensive process. With Moore’s law nearing its inevitable end and an ever-increasing demand for large-scale data analysis using machine learning, we must leverage non-conventional computing paradigms like quantum computing to train machine learning models efficiently. Adiabatic quantum computers can approximately solve NP-hard problems, such as the quadratic unconstrained binary optimization (QUBO), faster than classical computers. Since many machine learning problems are also NP-hard, we believe adiabatic quantum computers might be instrumental in training machine learning models efficiently in the post Moore’s law era. In order to solve problems on adiabatic quantum computers, they must be formulated as QUBO problems, which is very challenging. In this paper, we formulate the training problems of three machine learning models—linear regression, support vector machine (SVM) and balanced k-means clustering—as QUBO problems, making them conducive to be trained on adiabatic quantum computers. We also analyze the computational complexities of our formulations and compare them to corresponding state-of-the-art classical approaches. We show that the time and space complexities of our formulations are better (in case of SVM and balanced k-means clustering) or equivalent (in case of linear regression) to their classical counterparts.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Machine learning for design principles for single atom catalysts towards electrochemical reactions

Machine learning (ML) integrated density functional theory (DFT) calculations have recently been used to accelerate the design and discovery of heterogeneous catalysts such as single atom catalysts (SACs) through the establishment of deep structure–activity relationships. Here, this review provides recent progress in the ML-aided rational design of heterogeneous catalysts with the focus on SACs in terms of structure–activity relationships, feature importance analysis, high-throughput screening, stability, and metal–support interactions for electrochemistry. Support vector machine (SVM), random forest regression (RFR), and deep neural networks (DNN) along with atomic properties are mainly used for the design of SACs. The ML results have shown that the number of electrons in the d orbital, oxide formation enthalpy, ionization energy, Bader charge, d-band center, and enthalpy of vaporization are mainly the most important parameters for the defining of the structure–activity relationships for electrochemistry. However, the black-box nature of ML techniques occasionally makes a physical interpretation of descriptors, such as the Bader charge, d-band center, and enthalpy of vaporization, non-trivial. At the current stage, ML application is limited by the lack of a large and high-quality database. Future prospects for the development of a large database and a generalized ML algorithm for SAC design are discussed to give insights for further studies in this field.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Open-circuit submodule fault diagnosis in MMCs using support vector machines

Series connection of semiconductor submodules (SM) in a modular multilevel converter (MMC) makes the MMC prone to open-circuit (OC) IGBT failures inside SMs. If left undetected, these faults degrade the operation of the MMC and lead to its instability. This article proposes a method to detect, localise, and classify single OC SM faults in an MMC using support vector machines (SVM) trained with data obtained from the capacitor voltage balancing block of the MMC control system. The proposed method relies on data extracted from the sorted capacitor voltage arrays of the upper and lower phase arms. Therefore, it does not require extra measurements and hardware. Additionally, it offers a fixed time for detecting and localising OC SM faults. This method is easy to implement as SVM has a simple decision function. Time-domain simulation case studies are performed on a three-phase nine-level MMC to evaluate the performance of the proposed method.

42 ENGINEERING↗

DOE OSTI2024

Data Science Shows that Entropy Correlates with Accelerated Zeolite Crystallization in Monte Carlo Simulations

We have performed a data science study of Monte Carlo simulation trajectories to understand factors that can accelerate formation of zeolite nanoporous crystals, a process that can take days or even weeks. In previous work, Monte Carlo simulations predicted and experiments confirmed that using a secondary organic structure-directing agent (OSDA) accelerates crystallization of all-silica LTA zeolite, with experiments finding a three-fold speedup [PCCP 24, 142-148 (2022)]. However, it remains unclear what physical factors cause the speed-up. Here, we apply data science to analyze the simulation trajectories to discover what drives accelerated zeolite crystallization in Monte Carlo going from a one-OSDA synthesis (1OSDA) to a two-OSDA version (2OSDA). We encoded simulation snapshots using the Smooth Overlap of Atomic Positions approach, which represents all 2- and 3-body correlations within a given cutoff distance. Principal component analyses failed to discriminate datasets of structures from 1OSDA and 2OSDA simulations, while the Support Vector Machine (SVM) approach succeeded at classifying such structures with an area-under-curve (AUC) score of 0.99 (where AUC = 1 is a perfect classification) with all 3-body correlations, and as high as 0.94 with only 2-body correlations. SVM decision functions reveal relatively broad / narrow histograms for 1OSDA / 2OSDA datasets, suggesting that the two simulations differ strongly in information heterogeneity. Informed by these results, we performed pair (2-body) entropy calculations during crystallization, resulting in entropy differences that semi-quantitatively account for the speedup observed in the previous Monte Carlo simulations. We conclude that altering synthesis conditions in ways that substantially changes the entropy of labile silica networks may accelerate zeolite crystallization, and we discuss possible approaches for achieving such acceleration.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2025

Reinforcement Learning for Anomaly Detection in Nuclear Power Plant Operation and Maintenance

In nuclear power plants (NPPs), timely identification of sensor and human errors is critical to ensure safe and efficient plant operations. Anomaly detection models can be employed for this task. However, traditional anomaly detection approaches may have high dependency on labeled datasets and struggle with adaptability in complex, dynamic environments. Reinforcement learning (RL) has demonstrated significant potential in fault diagnosis and anomaly detection; however, its application to anomaly detection in NPPs remains a relatively underexplored research direction. Hence, to address this gap, in this study, we present a novel physics-informed reinforcement learning model, PIRL-AD: Physics-Informed Reinforcement Learning for Anomaly Detection, that integrates domain knowledge from calorimetric equations into the RL framework for enhanced sensor and human error anomaly detection. We evaluate the performance of PIRL-AD against a non-physics informed RL benchmark and a support vector machine (SVM) on data collected from a forced flow loop testbed. Experimental results suggest that PIRL-AD outperforms other baselines on a range of anomalous datasets that include both sensor and human-induced anomalies across key performance metrics, statistically outperforming the RL and SVM benchmarks with respect to geometric mean (respectively, 92.96% vs. 91.06% vs. 83.01%) and F1-score (respectively, 89.23% vs. 86.98% vs. 77.01%). Furthermore, the findings suggest the potential of physics-integrated reinforcement learning models for enhanced anomaly detection performance in NPPs.

Reinforcement learning↗

DOE OSTI2022

Application of machine learning approaches in the analysis of mass absorption cross-section of black carbon aerosols: Aerosol composition dependencies and sensitivity analyses

Physics-based models typically require an in-depth understanding of a phenomenon and assumptions of the underlying process(es), which are often hard to obtain in practice, whereas data-driven machine learning models learn the structure and patterns in the training data without any prior theoretical assumptions and then use inference to develop useful predictions. A novel machine learning-based algorithm has been previously developed for the prediction of black carbon mass absorption cross-section (MAC BC ) and applied to a variety of different atmospheric environments. In contrast to light scattering theories which require assumptions about the underlying physics, this algorithm uses time-series data of aerosol properties to estimate the temporally-varying MAC BC at 870 nm. Here, we analyze our algorithm and discuss the influence of aerosol optical properties (such as Ångström exponents and single scattering albedo) and chemical composition on the model outputs and the associated accuracy. Additionally, we conduct sensitivity analyses on our models to understand how the predictions change in response to different sets of input variables. Our support vector machine (SVM) for regression model is the least sensitive to variations in the input variables, although all models tend to exhibit a degradation to their accuracy when scattering Ångström exponents are less than one.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Shifts in hydroclimatology of US megaregions in response to climate change

Most of the population and economic growth in the United States occurs in megaregions as the clustered metropolitan areas, whereas climate change may amplify negative impacts on water and natural resources. This study assesses shifts in regional hydroclimatology of fourteen US megaregions in response to climate change over the 21st century. Hydroclimatic projections were simulated using the Variable Infiltration Capacity (VIC) model driven by three downscaled climate models from the Multivariate Adaptive Constructed Analogs (MACA) dataset to cover driest to wettest future conditions in the conterminous United States (CONUS). Shifts in the regional hydroclimatolgy and basin characteristics of US megaregions were represented as a combination of changes in the aridity and evaporative indices using the Budyko framework and Fu's equation. Changes in the climate types of US megaregions were estimated using the Fine Gaussian Support Vector Machine (SVM) method. The results indicate that Los Angeles, San Diego, and San Francisco are more likely to experience less arid conditions with some shifts from Continental to Temperate climate type while the hydroclimatology of Houston may become drier with some shifts from Temperate to Continental climate type. Additionally, water yield is likely to decrease in Seattle. Change in the hydroclimatology of Denver and Phoenix highly depends on the selected climate model. However, the basin characteristics of Phoenix have the highest sensitivity to climate change. Overall, the hydroclimatic conditions of Los Angeles, San Diego, Phoenix, Denver, and Houston have the highest sensitivity to climate change. Understanding of future shifts in hydroclimatology of megaregions can help decision-makers to attenuate negative consequences by implementing appropriate adaptation strategies, particularly in the water-scare megaregions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Classification of four-qubit entangled states via machine learning

We apply the support vector machine (SVM) algorithm to derive a set of entanglement witnesses (EW) to identify entanglement patterns in families of four-qubit states. The effectiveness of SVM for practical EW implementations stems from the coarse-grained description of families of equivalent entangled quantum states. The equivalence criteria in our work is based on the stochastic local operations and classical communication classification and the description of the four-qubit entangled Werner states. We numerically verify that the SVM approach provides an effective tool to address the entanglement witness problem when the coarse-grained description of a given family state is available. Here, we also discuss and demonstrate the efficiency of nonlinear kernel SVM methods as applied to four-qubit entangled state classification.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗