Gaussian Process Regression Model Research Articles

A Gaussian Process Regression and Wavelet Transform Time Series approaches to modeling Influenza A.

The global spread of Influenza A viruses is worsening economic and social challenges. Various mechanistic models have been developed to understand the virus's spread and evaluate intervention effectiveness. This study aimed to model the temporal dynamics of Influenza A using Gaussian Process Regression (GPR) and wavelet transform approaches. The study employed Continuous Wavelet Transform (CWT), Discrete Wavelet Transform (DWT) and Wavelet Power Spectrum to analyze time-series data from 2009 to 2023. The GPR model, known for its non-parametric Bayesian nature, effectively captured non-linear trends in the Influenza A data, while wavelet transforms provided insights into frequency and time-localized characteristics. The integration of GPR with DWT denoising techniques demonstrated superior performance in forecasting Influenza A cases compared to traditional models like Auto Regressive Integrated Moving Averages (ARIMA) and Exponential Smoothing (ETS) using Holt-Winter method. The study identified significant anomalies in Influenza A cases, corresponding to known pandemic events and seasonal variations. These findings highlight the effectiveness of combining wavelet transform analysis with GPR in understanding and predicting infectious disease patterns, offering valuable insights for public health planning and intervention strategies. The research recommends extending this approach to other respiratory viruses to assess its broader applicability.

Evaluation of the Changes in the Strength of Clay Reinforced with Basalt Fiber Using Artificial Neural Network Model

In this research, the impact of basalt fiber reinforcement on the unconfined compressive strength of clay soils was experimentally analyzed, and the collected data were utilized in an artificial neural network (ANN) to predict the unconfined compressive strength based on the basalt fiber reinforcement ratio and length. For this purpose, two different lengths of basalt fiber (6 mm and 12 mm) were added to unreinforced bentonite clay at ratios of 0%, 1%, 2%, 3%, 4%, and 5%, and unconfined compressive tests were performed on the prepared reinforced clay samples to determine the unconfined compressive strength (qu) values. The evaluation of the obtained experimental results was carried out by creating ANN models. To validate the prediction capabilities of the ANN, a comparative analysis was performed using linear regression, support vector machines, and Gaussian process regression models. Ultimately, a five-fold cross-validation technique was employed to objectively evaluate the overall performance of the model. The evaluations revealed that the ANN model predictions using data obtained from experimental studies showed the highest accuracy and were in close agreement with the experimental results.

Data-Driven Surrogate Modeling with Microstructure-Sensitivity of Viscoplastic Creep in Grade 91 Steel

AbstractTo support the development of advanced steel alloys tailored to withstand extreme conditions, it is imperative to account for the mechanical performance of components, while considering the influence of local microstructure on the macroscopic response. To this end, this study focuses on the development of microstructure-sensitive constitutive models for the mechanical response of Grade 91 steel exposed to extreme thermo-mechanical environments. Polynomial chaos expansion (PCE) surrogates are used to emulate high-fidelity polycrystal simulations of the viscoplastic response of Grade 91 steel as a function of the microstructure fingerprint (e.g., dislocations and precipitates). To cover a wide temperature–stress domain, two separate PCE surrogates—one that captures softening and the other that captures hardening behavior—are combined using another (sparse) Gaussian process regression model. The resulting constitutive creep surrogate model is integrated within the MOOSE finite element framework to simulate the intricate effects of microstructure, in particular MX-phase precipitates, on a component with a graded microstructure. Surrogate sensitivity analysis is applied to quantify the relevant impact of spatially varying microstructure on the creep response in a test-case involving a Grade 91 alloy with a prototypical weld.

The Use of Machine Learning Models and SHAP Interaction Values to Predict the Soil Swelling Index

Predicting the soil swelling index (CS) is crucial for geotechnical engineer to ensure the stability of civil engineering conceptions. Recently, ML models has sparked great interest from researchers in predicting the soil swelling index. However, due to the black-box nature of ML models, their prediction capabilities are still uninterpretable. This study aims to predict the soil swelling index using ML algorithms and interpret predictions. First, it employs the prediction capability of the Gaussian process regression (GPR) algorithm and compares it to the artificial neural network (ANN) for prediction the soil swelling index. Second, the SHAP algorithm as one recent explainable artificial intelligence (XAI) models is applied to interpret the predictions of the complex GPR and ANN models. The compiled experimental database covers 362 clayey samples gathered from different sites located in Northern Algeria. The modeling involved six input features, including the liquid limit (LL), plastic limit (PL), plasticity index (PI), water content (ωn), dry density (γd), and void ratio (e) to predict the soil swelling index. The findings based on statistical metrics showed a good performance of GPR with R2 = 0.78 and of ANN with R2 = 0.79. Comparative study based on Wilcoxon signed- rank test and sign test indicated that the ANN outperform better than GPR. Based on the interpretations obtained by SHAP algorithm, it is observed that the liquid limit (LL) and plastic limit (PL) are the two main input features that influence the CS, indicating, the higher content of LL and PL increase the model's output.

Machine learning-based optimization of photogrammetric JRC accuracy

To improve the accuracy of photogrammetric joint roughness coefficient (JRC) estimation, this study proposes two optimization models based on ground sample distance (GSD), point density, and the root mean square error (RMSE) of checkpoints. First, an algorithm that automatically generates spatial positions for equipment based on the convergence strategy was developed, using principles of Structure from Motion and Multi-View Stereo (SfM-MVS) and the shooting parameter selection algorithm (SPSA). Second, a portable positioning plate containing ground control points and checkpoints was designed based on optical principles, and a moving camera capture strategy guided by SPSA was proposed. Combining SPSA, portable positioning plate, and moving camera capture strategy, a photogrammetric experiment for small-scale rock samples in the field was conducted, collecting 48 datasets with different shooting parameters. Subsequently, a dataset incorporating GSD, point density, RMSE, and three JRC estimation metrics was established, revealing their correlations and sensitivities. Using seven machine learning algorithms, optimization models for photogrammetric JRC accuracy were developed, with Linear Multidimensional Regression and Gaussian Process Regression models improving JRC accuracy by an average of 85.73%. Finally, the applicability and limitations of the newly proposed method were further discussed.

Trajectory tracking for autonomous surface ships using Gaussian process regression and model predictive control with BVS strategy

Autonomous navigation is critical to the development of next-generation shipping systems. The proposal of intelligent ships enables innovation in the shipping and shipbuilding industry and increases the safety and efficiency of ship operations. Autonomous control of surface ships to follow a prescribed trajectory is critical in a variety of maritime applications. This paper proposes a trajectory tracking control strategy for autonomous surface ships that combines nonparametric modelling using Gaussian Process Regression (GPR) with the Model Predictive Control (MPC) framework. A Bézier curve-based Virtual Ship(BVS) guidance strategy is proposed to convert dynamic trajectory points into reference heading angles and speeds, such that the trajectory tracking problem can be decomposed into heading control and speed control problems. Gaussian process regression is utilised to identify the correlation between propeller revolution speed and ship speed, as well as the correlation between rudder angle and heading angle based on experimental data. Two GPR models are therefore constructed as the prediction models for designing MPC controllers for heading control and speed control, respectively. Nonlinear optimisation algorithms are utilised to search for optimal control commands in each sampling interval to solve the optimisation problem in MPC with GPR models and input constraints. Simulations are carried out to evaluate the effectiveness of the proposed method.

Hybrid real-time wave forecasting model combining Gaussian process regression and neural networks

To safely and effectively conduct offshore operations, a real-time wave forecast model that can accurately and rapidly forecast waves hours or days in advance is highly valuable. Recent studies have investigated models with neural networks (NNs) and have demonstrated their advantages in terms of forecasting speed and accuracy. However, NNs are limited by their requirement for a large training dataset, which can hinder the construction of the model if sufficient training data are unavailable. Therefore, this study constructed a hybrid real-time wave forecast model by combining an NN model and Gaussian process regression (GPR) model. The objective was to obtain reasonably accurate forecasts that were more accurate than those from individual NN models even when sufficient training data for the NN model was unavailable. To derive an optimal prediction, the values predicted by the NN and GPR models were combined by utilizing the standard deviation of the latter and considering the accuracy of each model. Consequently, predictions that were more accurate compared to those of the individual models for an entire year were obtained. This improvement was particularly significant for predicting relatively large wave heights, as indicated by the daily maximum wave heights. Additionally, various accuracy evaluation metrics demonstrated that despite using a small training dataset, the optimal prediction of the hybrid model was still superior to those of the individual models for predicting the daily maximum wave heights.

Gaussian process regression as a powerful tool for analysing time series in environmental geochemistry

Monitoring programs require more advanced data management for the registered time series. Classical temporal series decomposition cannot fulfil current needs regarding adequate data representation, optimization of the spatial-temporal sampling resolution and predictive power. In the manuscript at hand, we will demonstrate that Gaussian process regression (GPR) models are a vital machine-learning tool to interpret temporal series, improving understanding of geochemical cycles, providing input data for geochemical models and acting as a guide for future decisions in environmental monitoring. Firstly, we explore the impacts of sampling frequency in the GPR performance for temporal series with variable lengths and sampled frequencies of water discharges. On a second approach, we present the strengths and weaknesses between classical decomposition of temporal series and GPR results for a case study: a 14-year record of water discharge, suspended particulate matter and antimony concentrations in the Garonne River. Our results suggest that (i) even short temporal series with low sampling resolution can be accurately characterized by GPR when presenting well defined seasonal patterns, and (ii) GPR provides more detailed and robust support than classical statistics to identify processes responsible for multi-scale geochemical signals. This work provides a reference for researchers, engineers, and stakeholders for more reliable monitoring, understanding, and managing aquatic ecosystems.

Circular rubber aggregate CFST stub columns under axial compression: prediction and reliability analysis

Extensive studies support using steel tubes to enhance the structural integrity of rubber aggregate concrete (RBAC), namely RBAC-filled steel tubes (RCFST). However, current design codes for assessing the axial compressive behaviour of circular stub RCFST (CS-RCFST) columns are limited. Furthermore, there is a scarcity of studies focused on ensuring the structural safety of these columns. Based on an extensive experimental database comprising 145 columns, this study explores machine learning (ML) capabilities for predicting the axial strength of CS-RCFST columns, using six typical machine-learning models, i.e., symbolic regression (SR), XGBoost, CatBoost, random forest, LightGBM, and Gaussian process regression models. The hyperparameter tuning of the introduced ML models is performed using the Bayesian Optimization technique. The comparison results show that the CatBoost model is the most reliable and accurate ML model (R2 = 0.999 and 0.993 for the training and testing sets, respectively). In addition, a simple and practical design expression for CS-RCFST columns has been developed with acceptable accuracy based on the SR model (an average test-to-prediction ratio of 0.99 and CoV of 0.132). Meanwhile, the axial strength predicted by ML models was compared with two prominent practice codes (i.e., AISC360 and EC4). The comparison results indicated that the ML models could introduce a highly reliable and accurate approach over current design standards for strength prediction. Furthermore, a reliability analysis is conducted on two different ML models to evaluate the reliability of utilising ML models in practical design applications. This assessment involves identifying the statistical properties associated with the compressive strength of RBAC, as well as introducing the required resistance design factors aligned with the target reliability recommended by code standards.

Stacking BSRG-PLS: A physical and data-driven real-time stability safety analysis of arch dams during operation

Anti-sliding stability is the foundation for the normal operation of arch dams. In recent years, extreme weather has occurred frequently. It is important to grasp the anti-slide stability of arch dam (ASSAD) under complex load conditions in time. Currently, the ASSAD safety factor is primarily analyzed through the finite element method (FEM), which are time-consuming, labor-intensive, and lack timeliness. To address this, this paper proposes a real-time ASSAD analysis method during operation based on the Stacking BSRG-PLS model, which integrates a Bidirectional long short-term memory network, Residual neural network, Support vector machine, Gaussian process regression model and Partial Least Squares regression method. Firstly, based on the Stacking BSRG-PLS model and measured temperature combing with FEM, the transient temperature field of arch dam is established. Subsequently, a sample dataset containing the load data and the corresponding ASSAD safety factors calculated by FEM is constructed. Whereafter, using the Stacking BSRG-PLS model again, the real-time ASSAD safety factor is obtained based on the sample dataset. Case studies indicate that this method is effective and feasible, and has high analysis precision. It provides an effective way to quickly evaluate the ASSAD safety based on the measured data.

A machine-learned kinetic energy model for light weight metals and compounds of group III-V elements

Abstract We present a machine-learned (ML) model of kinetic energy for orbital-free density functional theory (OF-DFT) suitable for bulk light weight metals and compounds made of group III–V elements. The functional is machine-learned with Gaussian process regression (GPR) from data computed with Kohn-Sham DFT with plane wave bases and local pseudopotentials. The dataset includes multiple phases of unary, binary, and ternary compounds containing Li, Al, Mg, Si, As, Ga, Sb, Na, Sn, P, and In. A total of 433 materials were used for training, and 18 strained structures were used for each material. Averaged (over the unit cell) kinetic energy density is fitted as a function of averaged terms of the 4th order gradient expansion and the product of the density and effective potential. The kinetic energy predicted by the model allows reproducing energy-volume curves around equilibrium geometry with good accuracy. We show that the GPR model beats linear and polynomial regressions. We also find that unary compounds sample a wider region of the descriptor space than binary and ternary compounds, and it is therefore important to include them in the training set; a GPR model trained on a small number of unary compounds is able to extrapolate relatively well to binary and ternary compounds but not vice versa.

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution.Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O(nlogn) instead of the typical O(n3) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

Optimization of Linear Loading Strategy for Fuel Cell Initiation Based on Gaussian Process Regression Model

Optimization of Linear Loading Strategy for Fuel Cell Initiation Based on Gaussian Process Regression Model

Machine Learning Model Trained with Finite Element Modeling Can Predict the Risk of Osteoarthritis: Data from the Osteoarthritis Initiative

Objective: Despite long simulation times, recently developed finite element analysis (FEA) models of knee joints have demonstrated their suitability for predicting individual risk of onset and progression of knee osteoarthritis. Therefore, the objective of this study was to assess the feasibility of machine learning (ML) to replicate outcomes obtained from FEA when simulating mechanical responses and predicting cartilage degeneration within the knee joint.Design: Two ML models based on the Gaussian Process Regression (GPR) algorithms were developed. The first model (GPR1) utilized age, weight, and anatomical joint dimensions as predictor variables to predict tissue mechanical responses and cartilage degeneration based on FEA data. The second model (GPR2) utilized age, weight, height, and gender to predict anatomical joint dimensions, which were then used as inputs in the GPR1 model. Finally, the GPR1 and combined GPR1+GPR2 models were used to investigate the importance of clinical imaging when making personalized predictions for knees from healthy subjects with no history of knee injuries.Results: In the GPR1 model, R2 of 0.9 was exceeded for most of the predicted mechanical parameters. The GPR2 model was able to predict knee shape with R2 of 0.67–0.9. Both GPR1 and combined GPR1+GPR2 models offered equally good performances (AUC = 0.73–0.74) in classifying patients at high risk for the onset and development of knee osteoarthritis.Conclusions: In the future, real-time and easy-to-use GPR models may provide a rapid technology to evaluate mechanical responses within the knee for researchers or clinicians who have no former knowledge of FEA.

Hyperspectral indices data fusion-based machine learning enhanced by MRMR algorithm for estimating maize chlorophyll content.

Accurate estimation of chlorophyll is essential for monitoring maize health and growth, for which hyperspectral imaging provides rich data. In this context, this paper presents an innovative method to estimate maize chlorophyll by combining hyperspectral indices and advanced machine learning models. The methodology of this study focuses on the development of machine learning models using proprietary hyperspectral indices to estimate corn chlorophyll content. Six advanced machine learning models were used, including robust linear stepwise regression, support vector machines (SVM), fine Gaussian SVM, Matern 5/2 Gaussian stepwise regression, and three-layer neural network. The MRMR algorithm was integrated into the process to improve feature selection by identifying the most informative spectral bands, thereby reducing data redundancy and improving model performance. The results showed significant differences in the performance of the six machine learning models applied to chlorophyll estimation. Among the models, the Matern 5/2 Gaussian process regression model showed the highest prediction accuracy. The model achieved R2 = 0.71 for the training set, RMSE = 338.46 µg/g and MAE = 264.30 µg/g. In the case of the validation set, the Matern 5/2 Gaussian process regression model further improved its performance, reaching R2 =0.79, RMSE=296.37 µg/g, MAE=237.12 µg/g. These metrics show that Matern's 5/2 Gaussian process regression model combined with the MRMR algorithm to select optimal traits is highly effective in predicting corn chlorophyll content. This research has important implications for precision agriculture, particularly for real-time monitoring and management of crop health. Accurate estimation of chlorophyll allows farmers to take timely and targeted action.

Research on Stock Price Prediction Model Based on Sentiment Factor and Multi-Core Bagging Algorithm

Stock price prediction model is one of the key research points in the quantitative financial field. With the rapid development of data acquisition and storage technology, the data of emotional factors based on nonlinear structure is increasing. How to combine this part of information with common European technology factors to increase the ability of the model is a problem that needs to be solved. Based on this, this paper proposes a method of uncertainty quantification that combines European-and non-European data. Specifically, on the one hand, the Gaussian process regression model is used to capture the unknown relationship between predictive variables and price; on the other hand, the multi-kernel learning technology based on European and non- European kernel functions is used to combine the effective information of European and non- European predictive variables. Moreover, the proposed method can weigh the bias of the prediction model against the variance by using the Bagging algorithm. The simulated data analysis shows that the proposed method not only improves the prediction performance of the European Gaussian process, but also works in the presence of irrelevant predictive variables. Finally, the actual data analysis shows that the proposed method has achieved good prediction results in the task of predicting the rise and fall of stock prices.

Machine learning based prediction for bulk porosity and static elastic modulus of Yungang Grottoes sandstone

In this work, four mainstream machine learning (ML) techniques are used to evaluate the bulk porosity and static elastic modulus of weathered Yungang Grottoes sandstone. Datasets are gathered from the experiments, which includes 432 groups effective experimental data including 8 inputs features. bulk porosity and static elastic modulus were considered as outputs to determine the weathering degrees of Yungang Grottoes sandstone. The 4 performance criteria were used to evaluate the ML models. Results demonstrate that the Artificial Neural Network (ANN) is the best-fitted models for estimating the bulk porosity and static elastic modulus compared to Multiple Linear Regression (MLR), Support Vector Regression (SVR), Gaussian Process Regression (GPR). The accuracy of the trained model for static elastic modulus is slightly higher than that of bulk porosity. The GPR and ANN model can accurately predict the bulk porosity and static elastic modulus in training stages. The ANN with multi-hidden layers developed is competent with high degree of precision and generalization ability for bulk porosity and static elastic modulus compared to other selected regression-based ML models (MLR, SVR, and GPR). The coefficient of determinations of ANN in the range of (0.9537–0.9641) during the testing stages is more stable and higher than that of (0.8883–0.9453) other built ML models. The prediction efficiency of pretrained ANN model was well adjusted for the actual and forecast datasets at the training and testing stages, and the error range was no more than 0.7% and 0.15 GPa at both stages of prediction for bulk porosity and static elastic modulus respectively. And the ANN based static elastic modulus prediction model’s error proportions significantly decreased and were confined to a modest range between + 10% and − 10%. The proposed surrogate models are valid for the bulk porosity ranging from 7 to 14% and the static elastic modulus ranging from 0.7 to 1.4 Gpa, which can be utilized for the accurate and fast prediction of the weathering degrees of Yungang Grottoes sandstone.

Modeling Many-Body Interactions in Water with Gaussian Process Regression.

We report a first-principles water dimer potential that captures many-body interactions through Gaussian process regression (GPR). Modeling is upgraded from previous work by using a custom kernel function implemented through the KeOps library, allowing for much larger GPR models to be constructed and interfaced with the next-generation machine learning force field FFLUX. A new synthetic water dimer data set, called WD24, is used for model training. The resulting models can predict 90% of dimer geometries within chemical accuracy for a test set and in a simulation. The curvature of the potential energy surface is captured by the models, and a successful geometry optimization is completed with a total energy error of just 2.6 kJ mol-1, from a starting structure where water molecules are separated by nearly 4.3 Å. Dimeric modeling of a flexible, noncrystalline system with FFLUX is shown for the first time.

Remaining useful life prediction of high-capacity lithium-ion batteries based on incremental capacity analysis and Gaussian kernel function optimization

Remaining useful life (RUL) is a key indicator for assessing the health status of lithium (Li)-ion batteries, and realizing accurate and reliable RUL prediction is crucial for the proper operation of battery systems. As high-capacity Li batteries have more complex chemical properties, most of the current RUL prediction methods rely mainly on a priori knowledge to make judgments. As a result, prediction accuracy is not high. In this study, we developed a health indicator-capacity (HI-C) dual Gaussian process regression (GPR) model based on incremental capacity analysis (ICA) and optimized its kernel function to achieve accurate RUL prediction for 280 Ah high-capacity Li batteries. Validation against the United States National Aeronautics and Space Administration’s four battery test datasets showed that the use of the HI-C dual GPR model resulted in a mean absolute percentage error and root mean square error of less than 0.02 and 0.04, respectively, for the four battery-rated capacity predictions. Additionally, this model achieved an absolute error of less than five battery failure turns. Compared with a single model, the HI-C dual GPR model not only had high accuracy but also solved the problem that the HI was not measurable in the actual battery operation, which made it more suitable for RUL prediction of Li batteries.

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.