An ensemble model for detection of Parkinson’s disease by comparing numerous machine learning models and XGBoost based on vocal features
An ensemble model for detection of Parkinson’s disease by comparing numerous machine learning models and XGBoost based on vocal features
- Research Article
3
- 10.1109/embc.2019.8857868
- Jul 1, 2019
- Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference
Cerebellar Ataxia (CA) is a neurological condition that leads to uncoordinated muscle movements, even affecting the production of speech. Effective biomarkers are necessary to produce an objective decision-making support tool for early diagnosis of CA in non-clinical environments. This paper investigates the reliability and effectiveness of vocal tract acoustic biomarkers for assessing CA speech. These features were tested on a database consisting of 52 clinically rated tongue-twister phrase 'British Constitution' and its 4 consonant-vowel (CV) excerpts /ti/, /ti/', /tu/, /tion/ acquired from 30 ataxic patients and 22 healthy controls. Such a marker could be applied to objectively assess the severity of CA from a simple speaking test, contributing to the possibility of being translated into a computer based automatic module to screen the disease from the speech. All the vocal tract features explored in this study were statistically significant using Kolmogorov-Smirnov test at 5% level in distinguishing healthy and CA speech. Several machine learning classifiers with 5-fold cross-validations were implemented on the vocal features. It was observed that the intensity ratios corresponding to the 4 C-V excerpts in CA group showed an increased variability and produced the best classification accuracy of 84.6% using KNN classifier. Results motivate the use of vocal tract features for monitoring CA speech.
- Research Article
27
- 10.1016/j.array.2021.100079
- Sep 1, 2021
- Array
This paper aims to employ Machine Learning (ML) classifying algorithms to predict whether the patient has Parkinson's Disease (PD) or not. Motor disorders mainly characterize PD, and consequently, a variety of data sets are recorded from the motor system. These data sets consist of either physical behaviors of patients or neuroimaging data captured from their brains. However, the disease mostly begins years before the motor symptoms. Consequently, non-motor symptoms have been studied more in the last decade. Since about 90% of patients experience vocal disorders in the early stages, these symptoms can be more useful for diagnosing the disease. We will review data sets developed for PD diagnosis and some machine learning classification models applied to these data sets. We will offer some models to accurately predict PD according to vocal symptoms characteristics provided in the UCI Machine Learning database, which suffers a low number of samples compared to features and being imbalanced. The results of comparative studies demonstrate that the proposed classic classification models can outperform various Deep learning methods that have been previously used in the literature. The accuracy of 97.22% was obtained by using Logistic Regression and Voting algorithms.
- Research Article
12
- 10.2196/42249
- Dec 19, 2022
- JMIR Formative Research
BackgroundElevated psychological distress has demonstrated impacts on individuals’ health. Reliable and efficient ways to detect distress are key to early intervention. Artificial intelligence has the potential to detect states of emotional distress in an accurate, efficient, and timely manner.ObjectiveThe aim of this study was to automatically classify short segments of speech obtained from callers to national suicide prevention helpline services according to high versus low psychological distress and using a range of vocal characteristics in combination with machine learning approaches.MethodsA total of 120 telephone call recordings were initially converted to 16-bit pulse code modulation format. Short variable-length segments of each call were rated on psychological distress using the distress thermometer by the responding counselor and a second team of psychologists (n=6) blinded to the initial ratings. Following this, 24 vocal characteristics were initially extracted from 40-ms speech frames nested within segments within calls. After highly correlated variables were eliminated, 19 remained. Of 19 vocal characteristics, 7 were identified and validated as predictors of psychological distress using a penalized generalized additive mixed effects regression model, accounting for nonlinearity, autocorrelation, and moderation by sex. Speech frames were then grouped using k-means clustering based on the selected vocal characteristics. Finally, component-wise gradient boosting incorporating these clusters was used to classify each speech frame according to high versus low psychological distress. Classification accuracy was confirmed via leave-one-caller-out cross-validation, ensuring that speech segments from individual callers were not used in both the training and test data.ResultsThe sample comprised 87 female and 33 male callers. From an initial pool of 19 characteristics, 7 vocal characteristics were identified. After grouping speech frames into 2 separate clusters (correlation with sex of caller, Cramer’s V =0.02), the component-wise gradient boosting algorithm successfully classified psychological distress to a high level of accuracy, with an area under the receiver operating characteristic curve of 97.39% (95% CI 96.20-98.45) and an area under the precision-recall curve of 97.52 (95% CI 95.71-99.12). Thus, 39,282 of 41,883 (93.39%) speech frames nested within 728 of 754 segments (96.6%) were classified as exhibiting low psychological distress, and 71455 of 75503 (94.64%) speech frames nested within 382 of 423 (90.3%) segments were classified as exhibiting high psychological distress. As the probability of high psychological distress increases, male callers spoke louder, with greater vowel articulation but with greater roughness (subharmonic depth). In contrast, female callers exhibited decreased vocal clarity (entropy), greater proportion of signal noise, higher frequencies, increased breathiness (spectral slope), and increased roughness of speech with increasing psychological distress. Individual caller random effects contributed 68% to risk reduction in the classification algorithm, followed by cluster configuration (23.4%), spectral slope (4.4%), and the 50th percentile frequency (4.2%).ConclusionsThe high level of accuracy achieved suggests possibilities for real-time detection of psychological distress in helpline settings and has potential uses in pre-emptive triage and evaluations of counseling outcomes.Trial RegistrationANZCTR ACTRN12622000486729; https://www.anzctr.org.au/ACTRN12622000486729.aspx
- Research Article
- 10.15680/ijirset.2021.1011128
- Nov 25, 2023
- International Journal of Innovative Research in Science,Engineering and Technology
Parkinson's disease (PD) is a neurodegenerative disorder that significantly impacts motor functions. Early and accurate detection of PD is crucial for effective treatment and management. This research explores the application of machine learning techniques to detect Parkinson's disease using vocal features from the UCI Parkinson's Disease Data Set. The study compares the performance of four machine learning models: Logistic Regression, Random Forest Classifier, Decision Tree Classifier, and Support Vector Machine (SVM). The dataset was split into training and testing sets, with each model evaluated based on accuracy and confusion matrix metrics. The Decision Tree Classifier and Random Forest Classifier achieved perfect accuracy on the training set, while the SVM model demonstrated the highest accuracy (89.74%) on the test set with a recall rate of 96.77%. These findings indicate that machine learning models, particularly SVM, can effectively contribute to the early detection of Parkinson's disease.
- Preprint Article
- 10.5194/egusphere-egu23-12566
- May 15, 2023
Since PM2.5 (particulate matter with an aerodynamic diameter of less than 2.5 µm) directly threatens public health, in order to take appropriate measures(prevention) in advance, the Korea Ministry of Environment(MOE) has been implementing PM10 forecast nationwide since February 2014. PM2.5 forecasts have been implemented nationwide since January 2015. The currently implemented PM forecast by the MOE subdivides the country into 19 regions, and forecasts the level of PM in 4 stages of “Good”, “Moderate”, “Unhealthy”, and “Very unhealthy”.Currently PM air quality forecasting system operated by the MOE is based on a numerical forecast model along with a weather and emission model. Numerical forecasting model has fundamental limitations such as the uncertainty of input data such as emissions and meteorological data, and the numerical model itself. Recently, many studies on predicting PM using artificial intelligence such as DNN, RNN, LSTM, and CNN have been conducted to overcome the limitations of numerical models.In this study, in order to improve the prediction performance of the numerical model, past observational data (air quality and meteorological data) and numerical forecasting model data (chemical transport model) are used as input data. The machine learning model consists of DNN and Seq2Seq, and predicts 3 days (D+0, D+1, D+2) using 6-hour and 1-hour average input data, respectively. The PM2.5 concentrations predicted by the machine learning model and the numerical model were compared with the PM2.5 measurements.The machine learning models were trained for input data from 2015 to 2020, and their PM forecasting performance was tested for 2021. Compared to the numerical model, the machine learning model tended to increase ACC and be similar or lower to FAR and POD.Time series trend was showed machine learning PM forecasting trend is more similar to PM measurements compared with numerical model. Especially, machine learning forecasting model can appropriately predict PM low and high concentrations that numerical model is used to overestimate.Machine learning forecasting model with DNN and Seq2Seq can found improvement of PM forecasting performance compared with numerical forecasting model. However, the machine learning model has limitations that the model can not consider external inflow effects.In order to overcome the drawback, the models should be updated and added some other machine learning module such as CNN with spatial features of PM concentrations.  Acknowledgements This study was supported in part by the ‘Experts Training Graduate Program for Particulate Matter Management’ from the Ministry of Environment, Korea and by a grant from the National Institute of Environmental Research (NIER), funded by the Ministry of Environment (ME) of the Republic of Korea (NIER-2022-04-02-068).  
- Book Chapter
- 10.1201/9781003190141-11
- Sep 20, 2022
Psychiatric diagnosises are is heavily prone to subjectivity bias from patients and clinicians. In the last few years there has been a growing effort in the development of objective markers in mental health. Vocal features appear as promising biomarkers for the detection of mental disorders and symptom severity assessment, with the advantages of scalability, cost-effectiveness, and non-invasiveness. Aims: This chapter aims Tto propose a framework for the detection of different mental disorders such as,– major depressive disorder (MDD), bipolar disorder, schizophrenia, and generalized anxiety disorder (GAD), by – using vocal acoustic analysis and machine learning models. Methods: In order to do so Wwe recorded interviews of 78 participants comprising of 66 psychiatric patients during medical visits, and 12 healthy controls. Patients belonged to four diagnostic groups, as follows: 28 patients with MDD; 20 patients with schizophrenia; 14 patients with bipolar disorder; 4 patients with GAD. Pre-processing and processing techniques were utilized for vocal features extraction. We tested the classification accuracy of several supervised machine learning models using the extracted vocal features. Results: The study found that random Forests with 300 trees achieved the greatest performance (75.27% for accuracy, 69.08% for kappa, 75.30% for sensitivity, and 93.80% for specificity) for the classification of the five categories (four disease groups and controls). The chapter ends with our finds, including the fact that Vvocal acoustic features appear to be promising biomarkers, with the advantages of being abundant, inexpensive, non-invasive and remotely performed. The results of this study are in line with previously written literature and supports the feasibility of vocal parameters screening and diagnosis in psychiatry.
- Research Article
- 10.1186/s12888-025-07635-0
- Nov 24, 2025
- BMC Psychiatry
BackgroundSuicidal ideation in depression is a critical predictor of suicide risk, yet its objective and early identification remains a significant challenge. Current machine learning models often fail to distinguish specific markers of suicidality from the general symptoms of severe depression. This study aimed to develop and validate a multimodal model, integrating vocal features and autobiographical memory, to specifically distinguish depressed patients with suicidal ideation from those without.MethodsThis study enrolled 88 patients with depression, who were divided into three groups based on depression severity and the presence of suicidal ideation: mild depression without suicidal ideation(mD-NSI), moderate depression with suicidal ideation(MD-SI), and severe depression with suicidal ideation(SD-SI). Methodologies included the Autobiographical Memory Test (AMT), clinical scales (BDI-II, OGMQ), and comprehensive vocal feature extraction. We used repeated measures analysis of variance (ANOVA) for group comparisons and developed machine learning models, primarily Random Forest, for various classification tasks.ResultsSignificant differences were found in autobiographical memory; patients with suicidal ideation demonstrated significant overgeneralization, retrieving fewer specific memories than those without. Acoustically, individuals with suicidal ideation exhibited distinct vocal patterns, including reduced prosodic variation and altered spectral energy, indicated by features like Mel-Frequency Cepstral Coefficients (MFCCs), spectral centroid, and zero-crossing rate. A Random Forest model achieved high accuracy (AUC up to 1.00) in classification. Crucially, model interpretability analysis (SHAP) revealed that the predictive importance of features shifted depending on the clinical comparison: autobiographical memory scores were key for distinguishing the initial presence of suicidal ideation, whereas depression severity scores became more prominent when differentiating between moderate and severe cases who were already suicidal.ConclusionThe integrated analysis of vocal features and autobiographical memory, validated through an interpretable machine learning model, offers a powerful and objective approach for predicting suicidal ideation in depression. This multimodal method not only effectively differentiates patients with and without suicidal ideation but also provides novel insights into the shifting cognitive and physiological markers of suicide risk. It represents a significant step towards developing precise, clinically applicable tools for early risk identification and timely intervention.Clinical trial numberNot applicable.Supplementary InformationThe online version contains supplementary material available at 10.1186/s12888-025-07635-0.
- Research Article
8
- 10.1016/j.jhydrol.2024.131418
- May 25, 2024
- Journal of Hydrology
Machine learning for faster estimates of groundwater response to artificial aquifer recharge
- Research Article
2
- 10.2196/67835
- Apr 16, 2025
- JMIR Formative Research
BackgroundThis research study aimed to detect the vocal features immersed in empathic counselor speech using samples of calls to a mental health helpline service.ObjectiveThis study aimed to produce an algorithm for the identification of empathy from these features, which could act as a training guide for counselors and conversational agents who need to transmit empathy in their vocals.MethodsTwo annotators with a psychology background and English heritage provided empathy ratings for 57 calls involving female counselors, as well as multiple short call segments within each of these calls. These ratings were found to be well-correlated between the 2 raters in a sample of 6 common calls. Using vocal feature extraction from call segments and statistical variable selection methods, such as L1 penalized LASSO (Least Absolute Shrinkage and Selection Operator) and forward selection, a total of 14 significant vocal features were associated with empathic speech. Generalized additive mixed models (GAMM), binary logistics regression with splines, and random forest models were used to obtain an algorithm that differentiated between high- and low-empathy call segments.ResultsThe binary logistics regression model reported higher predictive accuracies of empathy (area under the curve [AUC]=0.617, 95% CI 0.613‐0.622) compared to the GAMM (AUC=0.605, 95% CI 0.601‐0.609) and the random forest model (AUC=0.600, 95% CI 0.595‐0.604). This difference was statistically significant, as evidenced by the nonoverlapping 95% CIs obtained for AUC. The DeLong test further validated these results, showing a significant difference in the binary logistic model compared to the random forest (D=6.443, df=186283, P<.001) and GAMM (Z=5.846, P<.001). These findings confirm that the binary logistic regression model outperforms the other 2 models concerning predictive accuracy for empathy classification.ConclusionsThis study suggests that the identification of empathy from vocal features alone is challenging, and further research involving multimodal models (eg, models incorporating facial expression, words used, and vocal features) are encouraged for detecting empathy in the future. This study has several limitations, including a relatively small sample of calls and only 2 empathy raters. Future research should focus on accommodating multiple raters with varied backgrounds to explore these effects on perceptions of empathy. Additionally, considering counselor vocals from larger, more heterogeneous populations, including mixed-gender samples, will allow an exploration of the factors influencing the level of empathy projected in counselor voices more generally.
- Preprint Article
- 10.5194/egusphere-egu24-11880
- Nov 27, 2024
Machine learning (ML) models have become popular in the Earth Sciences for improving predictions based on observations. Beyond pure prediction, though, ML has a large potential to create surrogates that emulate complex numerical simulation models, considerably reducing run time, hence facilitating their analysis.The behaviour of eco-geomorphological systems is often examined using minimal models, simple equation-based expressions derived from expert knowledge. From them, one can identify complex system characteristics such as equilibria, tipping points, and transients. However, model formulation is largely subjective, thus disputable. Here, we propose an alternative approach where a ML surrogate of a high-fidelity numerical model is used instead, conserving suitability for analysis while incorporating the higher-order physics of its parent model. The complexities of developing such an ML surrogate for understanding the co-evolution of vegetation, hydrology, and geomorphology on a geological time scale are presented, highlighting the potential of this approach to capture novel, data-driven scientific insights.To obtain the surrogate, the ML models were trained on a data set simulating a coupled hydrological-vegetation-soil system. The rate of change of the two variables describing the system, soil depth and biomass, was used as output, taking their value at the previous time step and the pre-defined grazing pressure as inputs. Two popular ML methods, random forest (RF) and fully connected neural network (NN), were used. As proof of concept and to configure the model setup, we first trained the ML models on the output of the minimal model described in [1], comparing the ML responses at gridded inputs with the derivative values predicted by the minimal model. While RF required less tuning to achieve competitive results, a relative root mean squared error (rRMSE) of 5.8% and 0.04% for biomass and soil depth respectively, NN produced better-behaved outcome, reaching a rRMSE of 2.2% and 0.01%. Using the same setup, the ML surrogates were trained on a high-resolution numerical model describing the same system. The study of the response from this surrogate provided a more accurate description of the dynamics and equilibria of the hillslope ecosystem, depicting, for example, a much more complex process of hillslope desertification than captured by the minimal model.It is thus concluded that the use of ML models instead of expert-based minimal models may lead to considerably different findings, where ML models have the advantage that they directly rely on system functioning embedded in their parent numerical simulation model.
- Research Article
7
- 10.3389/fpsyt.2023.1079448
- Jul 20, 2023
- Frontiers in Psychiatry
Vocal features have been exploited to distinguish depression from healthy controls. While there have been some claims for success, the degree to which changes in vocal features are specific to depression has not been systematically studied. Hence, we examined the performances of vocal features in differentiating depression from bipolar disorder (BD), schizophrenia and healthy controls, as well as pairwise classifications for the three disorders. We sampled 32 bipolar disorder patients, 106 depression patients, 114 healthy controls, and 20 schizophrenia patients. We extracted i-vectors from Mel-frequency cepstrum coefficients (MFCCs), and built logistic regression models with ridge regularization and 5-fold cross-validation on the training set, then applied models to the test set. There were seven classification tasks: any disorder versus healthy controls; depression versus healthy controls; BD versus healthy controls; schizophrenia versus healthy controls; depression versus BD; depression versus schizophrenia; BD versus schizophrenia. The area under curve (AUC) score for classifying depression and bipolar disorder was 0.5 (F-score = 0.44). For other comparisons, the AUC scores ranged from 0.75 to 0.92, and the F-scores ranged from 0.73 to 0.91. The model performance (AUC) of classifying depression and bipolar disorder was significantly worse than that of classifying bipolar disorder and schizophrenia (corrected p < 0.05). While there were no significant differences in the remaining pairwise comparisons of the 7 classification tasks. Vocal features showed discriminatory potential in classifying depression and the healthy controls, as well as between depression and other mental disorders. Future research should systematically examine the mechanisms of voice features in distinguishing depression with other mental disorders and develop more sophisticated machine learning models so that voice can assist clinical diagnosis better.
- Research Article
35
- 10.1371/journal.pone.0253988
- Jul 14, 2021
- PLOS ONE
Due to difficulty in early diagnosis of Alzheimer’s disease (AD) related to cost and differentiated capability, it is necessary to identify low-cost, accessible, and reliable tools for identifying AD risk in the preclinical stage. We hypothesized that cognitive ability, as expressed in the vocal features in daily conversation, is associated with AD progression. Thus, we have developed a novel machine learning prediction model to identify AD risk by using the rich voice data collected from daily conversations, and evaluated its predictive performance in comparison with a classification method based on the Japanese version of the Telephone Interview for Cognitive Status (TICS-J). We used 1,465 audio data files from 99 Healthy controls (HC) and 151 audio data files recorded from 24 AD patients derived from a dementia prevention program conducted by Hachioji City, Tokyo, between March and May 2020. After extracting vocal features from each audio file, we developed machine-learning models based on extreme gradient boosting (XGBoost), random forest (RF), and logistic regression (LR), using each audio file as one observation. We evaluated the predictive performance of the developed models by describing the receiver operating characteristic (ROC) curve, calculating the areas under the curve (AUCs), sensitivity, and specificity. Further, we conducted classifications by considering each participant as one observation, computing the average of their audio files’ predictive value, and making comparisons with the predictive performance of the TICS-J based questionnaire. Of 1,616 audio files in total, 1,308 (81.0%) were randomly allocated to the training data and 308 (19.1%) to the validation data. For audio file-based prediction, the AUCs for XGboost, RF, and LR were 0.863 (95% confidence interval [CI]: 0.794–0.931), 0.882 (95% CI: 0.840–0.924), and 0.893 (95%CI: 0.832–0.954), respectively. For participant-based prediction, the AUC for XGboost, RF, LR, and TICS-J were 1.000 (95%CI: 1.000–1.000), 1.000 (95%CI: 1.000–1.000), 0.972 (95%CI: 0.918–1.000) and 0.917 (95%CI: 0.918–1.000), respectively. There was difference in predictive accuracy of XGBoost and TICS-J with almost approached significance (p = 0.065). Our novel prediction model using the vocal features of daily conversations demonstrated the potential to be useful for the AD risk assessment.
- Research Article
2
- 10.3390/ma18153718
- Aug 7, 2025
- Materials (Basel, Switzerland)
The growing demand for innovation and the use of diverse materials in cementitious composites necessitate predictive models that account for material variability. Numerical, code-based, and machine learning (ML) models have been developed to predict various concrete properties. However, their accuracy is significantly influenced by factors such as mix design, composition, intrinsic properties, and external conditions. Developing robust models that integrate these variables is essential for improving predictive accuracy and optimizing material performance. This paper presents a comprehensive review of numerical, code-based, and ML modelling techniques for predicting both fresh and long-term concrete properties. Since both numerical and ML models rely on experimental data-either to determine coefficients in numerical approaches or to train ML models-data gathering, preprocessing, and handling are crucial for model performance. Previous studies indicated that data variability significantly impacts accuracy, emphasizing the importance of effective preprocessing. While larger datasets generally improve reliability, some models achieve high accuracy even with very limited data. This review not only demonstrates the superior performance of ML models over traditional numerical approaches but also highlights the relative effectiveness of different ML algorithms based on reported accuracy metrics. ML-based approaches, including both ensemble and non-ensemble models, have exhibited strong predictive capabilities across a wide range of concrete property categories. In contrast, traditional numerical models often yield lower accuracy, although modified versions that incorporate additional parameters have shown improved performance. Furthermore, the integration of optimization algorithms and interpretability tools enhances both predictive reliability and model transparency-critical aspects that are often overlooked.
- Research Article
21
- 10.3390/en14237970
- Nov 29, 2021
- Energies
Solar radiation prediction is an important process in ensuring optimal exploitation of solar energy power. Numerous models have been applied to this problem, such as numerical weather prediction models and artificial intelligence models. However, well-designed hybridization approaches that combine numerical models with artificial intelligence models to yield a more powerful model can provide a significant improvement in prediction accuracy. In this paper, novel hybrid machine learning approaches that exploit auxiliary numerical data are proposed. The proposed hybrid methods invoke different machine learning paradigms, including feature selection, classification, and regression. Additionally, numerical weather prediction (NWP) models are used in the proposed hybrid models. Feature selection is used for feature space dimension reduction to reduce the large number of recorded parameters that affect estimation and prediction processes. The rough set theory is applied for attribute reduction and the dependency degree is used as a fitness function. The effect of the attribute reduction process is investigated using thirty different classification and prediction models in addition to the proposed hybrid model. Then, different machine learning models are constructed based on classification and regression techniques to predict solar radiation. Moreover, other hybrid prediction models are formulated to use the output of the numerical model of Weather Research and Forecasting (WRF) as learning elements in order to improve the prediction accuracy. The proposed methodologies are evaluated using a data set that is collected from different regions in Saudi Arabia. The feature-reduction has achieved higher classification rates up to 8.5% for the best classifiers and up to 15% for other classifiers, for the different data collection regions. Additionally, in the regression, it achieved improvements of average root mean square error up to 5.6% and in mean absolute error values up to 8.3%. The hybrid models could reduce the root mean square errors by 70.2% and 4.3% than the numerical and machine learning models, respectively, when these models are applied to some dataset. For some reduced feature data, the hybrid models could reduce the root mean square errors by 47.3% and 14.4% than the numerical and machine learning models, respectively.
- Research Article
30
- 10.3390/w14152307
- Jul 25, 2022
- Water
This paper presents a review of papers specifically focused on the use of both numerical and machine learning methods for groundwater level modelling. In the reviewed papers, machine learning models (also called data-driven models) are used to improve the prediction or speed process of existing numerical modelling. When long runtimes inhibit the use of numerical models, machine learning models can be a valid alternative, capable of reducing the time for model development and calibration without sacrificing accuracy of detail in groundwater level forecasting. The results of this review highlight that machine learning models do not offer a complete representation of the physical system, such as flux estimates or total water balance and, thus, cannot be used to substitute numerical models in large study areas; however, they are affordable tools to improve predictions at specific observation wells. Numerical and machine learning models can be successfully used as complementary to each other as a powerful groundwater management tool. The machine learning techniques can be used to improve calibration of numerical models, whereas results of numerical models allow us to understand the physical system and select proper input variables for machine learning models. Machine learning models can be integrated in decision-making processes when rapid and effective solutions for groundwater management need to be considered. Finally, machine learning models are computationally efficient tools to correct head error prediction of numerical models.
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