Gaussian Process Regression Method Research Articles

Prediction of Rock's Brittleness and Dynamic Properties Utilizing Effective Artificial Intelligence Approaches

This research aims to determine the brittleness index (BI) and engineering properties of limestone specimens. In addition, this study evaluates the effect of moisture on the developed models to predict the BI and shear wave velocity (Vs), based on the point load index (Is50), dry and saturated tensile strength (Ts-d and Ts-s), and porosity. Gaussian process regression (GPR), multilayer feed-forward neural network (MFFNN), and multiple linear regression (MLR) predictive models were utilized. Microscopic examination of the limestone specimens revealed that calcite is the predominant mineral. It was observed that samples with higher calcite content exhibited greater brittleness and strength properties while having lower porosity. The results obtained from the MLR analysis demonstrated that it is possible to accurately forecast the brittleness index (BI), as well as the dry and saturated shear wave velocities (Vs-d and Vs-s) at the specific sites under investigation. The moisture effect on developed models showed that Vs prediction in dry conditions (Vs-d) was less accurate compared to the saturated conditions (Vs-s). Conversely, the relationships developed for estimating the BI in dry conditions exhibited higher accuracy. The analysis of all model assumptions using MLR indicated that the models could be reliably utilized. However, the MFFNN and GPR methods were found to be more conservative in estimating these properties. Moreover, the study identified the best transfer function and training algorithm for predicting Vs and BI. The evaluation metrics, such as R2 and RMSE revealed that GPR demonstrated higher precision compared to MFFNN and MLR.

CO2 emission from the electricity sector in Iran; calculation, prediction and reduction policies

Fossil fuel power plants produce a significant amount of CO2 emissions, and this pollutant causes global warming, respiratory and heart diseases, and other significant issues. Electricity interprets as a primary and rising demand in each energy system; thus, in this paper, carbon dioxide (CO2) emission reduction was selected as the objective value for 2025. Power plant fuel consumption was surveyed to calculate the CO2 emission caused by each fuel. Also, Esfahan province (an industrial province in Iran) was investigated as the study case. Forecasting the fuel consumption for 2025 was run by two parameters: population and Gross Domestic Production (GDP), which were forecasted by the report of the Iran Statics Center and the Gaussian Process Regression (GPR) method, respectively. The CO2 emission of power plants was obtained using the coefficients of each fuel. Based on Iran's commitment to the Paris Agreement, a 4% reduction of CO2 emissions is the main objective. Thus, this study aims to reach this goal by implementing four scenarios: a) adding renewable energies, b) adding renewable energies and improving the generation efficiency, c) adding renewable energies and decreasing the grid losses, and d) combining the three scenarios mentioned above. According to these scenarios, reformation strategies compensated 10.5% of the required power, which was satisfied by renewable energies, and finally, this province can gradually satisfy a 4% reduction until 2025.

Robust Gaussian Process Regression Method for Efficient Tunneling Pathway Optimization: Application to Surface Processes.

Simulation of surface processes is a key part of computational chemistry that offers atomic-scale insights into mechanisms of heterogeneous catalysis, diffusion dynamics, and quantum tunneling phenomena. The most common theoretical approaches involve optimization of reaction pathways, including semiclassical tunneling pathways (called instantons). The computational effort can be demanding, especially for instanton optimizations with an ab initio electronic structure. Recently, machine learning has been applied to accelerate reaction-pathway optimization, showing great potential for a wide range of applications. However, previous methods still suffer from numerical and efficiency issues and were not designed for condensed-phase reactions. We propose an improved framework based on Gaussian process regression for general transformed coordinates, which has improved efficiency and numerical stability, and we propose a descriptor that combines internal and Cartesian coordinates suitable for modeling surface processes. We demonstrate with 11 instanton optimizations in three representative systems that the improved approach makes ab initio instanton optimization significantly cheaper, such that it becomes not much more expensive than a classical transition-state theory rate calculation.

Modelling stochastic and quasi-periodic behaviour in stellar time-series: Gaussian process regression versus power-spectrum fitting

Abstract As the hunt for an Earth-like exoplanets has intensified in recent years, so has the effort to characterise and model the stellar signals that can hide or mimic small planetary signals. Stellar variability arises from a number of sources, including granulation, supergranulation, oscillations and activity, all of which result in quasi-periodic or stochastic behaviour in photometric and/or radial velocity observations. Traditionally, the characterisation of these signals has mostly been done in the frequency domain. However, the recent development of scalable Gaussian process regression methods makes direct time-domain modelling of stochastic processes a feasible and arguably preferable alternative, obviating the need to estimate the power spectral density of the data before modelling it. In this paper, we compare the two approaches using a series of experiments on simulated data. We show that frequency domain modelling can lead to inaccurate results, especially when the time sampling is irregular. By contrast, Gaussian process regression results are often more precise, and systematically more accurate, in both the regular and irregular time sampling regimes. While this work was motivated by the analysis of radial velocity and photometry observations of main sequence stars in the context of planet searches, we note that our results may also have applications for the study of other types of astrophysical variability such as quasi-periodic oscillations in X-ray binaries and active galactic nuclei variability.

A fuzzy Gaussian process regression function approach for forecasting problem

A fuzzy regression function approach is a fuzzy inference system method whose rules cannot be determined based on expert opinion, unlike a classical fuzzy inference system. In a fuzzy regression function approach, an input matrix consists of memberships obtained by the fuzzy clustering method and lagged variables of the time series. In the fuzzy regression function approach, the output vector corresponding to this input matrix is also created and the parameter estimation for the method is carried out with the ordinary least square method. As it is known, the ordinary least square method assumes that the data are linear. In addition, although it is very useful to include a priori information describing the formation of the data in the model, in most cases this information is not available. It is also inappropriate to use a model that does not accurately characterize the data. However, it is not appropriate to estimate parameters for nonlinear data using the ordinary least square method. One of the methods to be used in such a situation is the Gaussian process regression method. While the parameters of a selected basis function are fitted in the ordinary least squares regression method, how all measured data are related is determined in the Gaussian process regression. Besides, Gaussian process regression is a Bayesian approach, it can provide uncertainty measurements on forecasts. In this study, a fuzzy Gaussian process regression function is proposed. The contribution of this paper is to propose a new fuzzy inference system that can be used to solve nonlinear data by proposing a fuzzy Gaussian process regression function. The performance of the newly proposed method is evaluated based on the closing values of the Bitcoin and Crude oil time series. The performance comparison of the proposed method is evaluated with many different forecasting methods and it is concluded that the proposed method has superior forecasting performance.

Stochastic Optimal Control for Robot Manipulation Skill Learning Under Time-Varying Uncertain Environment.

In this article, a novel stochastic optimal control method is developed for robot manipulator interacting with a time-varying uncertain environment. The unknown environment model is described as a nonlinear system with time-varying parameters as well as stochastic information, which is learned via the Gaussian process regression (GPR) method as the external dynamics. Integrating the learned external dynamics as well as the stochastic uncertainties, the complete interaction system dynamics are obtained. Then the iterative linear quadratic Gaussian with learned external dynamics (ILQG-LEDs) method is presented to obtain the optimal manipulation control parameters, namely, the feedforward force, the reference trajectory, as well as the impedance parameters, subject to time-varying environment dynamics. The comparative simulation studies verify the advantages of the presented method, and the experimental studies of the peg-hole-insertion task prove that this method can deal with complex manipulation tasks.

Gaussian process-based state derivative estimator with temporal input in incremental flight control design

In this paper, a state derivative estimation technique is proposed using a derivative of Gaussian process regression method and applied to an incremental dynamics-based controller. The state derivative estimates of interest are with respect to time, and to obtain them, the temporal index array is used for Gaussian process state input. Using a Gaussian process, assumptions such as numerical differentiation of the state, parametric basis functions common in adaptive approaches, and the use of upper-bound information of the state derivative commonly used in robust methods are avoided. The proposed approach is compared with the backward difference formula (BDF) differentiator, first-order low-pass filter, second-order low-pass filter, and high-order sliding mode differentiator. Monte Carlo simulation with 1000 runs is performed under four different noise level measurement scenarios. The proposed Gaussian process-based differentiator with temporal index input resulted in better robustness and adaptability in state derivative estimation with similar or better performance.

Towards 21-cm intensity mapping at z = 2.28 with uGMRT using the tapered gridded estimator – IV. Wide-band analysis

ABSTRACT We present a Wide-band tapered gridded estimator (TGE), which incorporates baseline migration and variation of the primary beam pattern for neutral hydrogen ($H\, {\small I}$) 21-cm intensity mapping (IM) with large frequency bandwidth radio-interferometric observations. Here we have analysed $394-494 \, {\rm MHz}$ (z = 1.9–2.6) uGMRT data to estimate the Multifrequency Angular Power Spectrum (MAPS) Cℓ(Δν) from which we have removed the foregrounds using the polynomial fitting (PF) and Gaussian Process Regression (GPR) methods developed in our earlier work. Using the residual Cℓ(Δν) to estimate the mean-squared 21-cm brightness temperature fluctuation Δ2(k), we find that this is consistent with 0 ± 2σ in several k bins. The resulting 2σ upper limit $\Delta ^2(k) \lt (4.68)^2 \, \rm {mK^2}$ at $k=0.219\, \rm {Mpc^{-1}}$ is nearly 15 times tighter than earlier limits obtained from a smaller bandwidth ($24.4 \, {\rm MHz}$) of the same data. The 2σ upper limit $[\Omega _{H\, {\small I}} b_{H\, {\small I}}] \lt 1.01 \times 10^{-2}$ is within an order of magnitude of the value expected from independent estimates of the $H\, {\small I}$ mass density $\Omega _{H\, {\small I}}$ and the $H\, {\small I}$ bias $b_{H\, {\small I}}$. The techniques used here can be applied to other telescopes and frequencies, including $\sim 150 \, {\rm MHz}$ Epoch of Reionization observations.

A Combined Method for Short-Term Load Forecasting Considering the Characteristics of Components of Seasonal and Trend Decomposition Using Local Regression

In response to the complexity and high volatility of original load data affecting the accuracy of load forecasting, a combined method for short-term load forecasting considering the characteristics of components of seasonal and trend decomposition using local regression (STL) is proposed. The original load data are decomposed into a trend component, seasonal component, and residual component using STL. Then, considering the characteristics of each component, a long short-term memory (LSTM) neural network, a convolutional neural network (CNN), and Gaussian process regression (GPR) are used to predict the trend component, seasonal component, and residual component, respectively. The final outcome of the load forecasting is obtained by summing the forecasted results of each individual component. A specific case study is conducted to compare the proposed combined method with LSTM, CNN, GPR, STL-LSTM, STL-CNN, and STL-GPR prediction methods. Through comparison, the proposed combined method exhibits lower errors and higher accuracy, demonstrating the effectiveness of this method.

An Update-Strategy-Based Gaussian Process Regression Method for Aeroengines Fault Prediction

An Update-Strategy-Based Gaussian Process Regression Method for Aeroengines Fault Prediction

Asynchronous Parallel Large-Scale Gaussian Process Regression.

Gaussian process regression (GPR) is an important nonparametric learning method in machine learning research with many real-world applications. It is well known that training large-scale GPR is a challenging task due to the required heavy computational cost and large volume memory. To address this challenging problem, in this article, we propose an asynchronous doubly stochastic gradient algorithm to handle the large-scale training of GPR. We formulate the GPR to a convex optimization problem, i.e., kernel ridge regression. After that, in order to efficiently solve this convex kernel problem, we first use the random feature mapping method to approximate the kernel model and then utilize two unbiased stochastic approximations, i.e., stochastic variance reduced gradient and stochastic coordinate descent, to update the solution asynchronously and in parallel. In this way, our algorithm scales well in both sample size and dimensionality, and speeds up the training computation. More importantly, we prove that our algorithm has a global linear convergence rate. Our experimental results on eight large-scale benchmark datasets with both regression and classification tasks show that the proposed algorithm outperforms the existing state-of-the-art GPR methods.

Improved tropical cyclone wind speed estimation for microwave altimeter using machine learning

Satellite altimeters can provide excellent global wind speed at 10 m above the sea surface (U10), however, the U10 becomes inaccurate and difficult to measure in tropical cyclone conditions. The violent wind, rough waves and torrential rain manifest an exceptionally complex ocean-atmospheric environment for wind estimation. Although the backscatter signal is measured equally well in normal condition, the interpretation is not straightforward in tropical cyclones that requires complex associations with ocean-atmospheric geophysical variables. Typical U10 regression model developed in normal atmospheric conditions would inevitably reduce the estimation quality and encounter high modelling uncertainties from high dimensional input data that provide ill-posed solutions in extreme U10 estimation. However, other secondary parameters simultaneously measured by the altimeter have properties that convey additional atmospheric information to enhance U10 estimation accuracy in storm condition. Therefore, the present study proposes machine learning (ML) approaches based on artificial neural network (ANN), support vector machine (SVM), and Gaussian process regression (GPR) to integrate the multi-dimensional parameters and provide accurate U10 estimates for different parameter combination. Results suggest that the GPR method, considering atmospheric and sea surface related parameters, can provide the highest accuracy of U10 up to 35 ms−1 with quality perseverance against rain contamination. This study highlights the quality improvement of altimeter U10 estimation and the assessment method of ML in dealing with complex ocean-atmospheric interactions.

Optimizing Solar Energy Harvesting: Supervised Machine Learning-Driven Peak Power Point Tracking for Diverse Weather Conditions

Solar Power is one of the significant prevalent forms of clean energy due to its perceived to be pollution-free and easily accessible. The market for renewable energy was established by the rapid development in electrical energy consumption and the diminution of conventional energy resources (CER). Under varying weather condition extracted energy from solar system is not constant and maximum. This study suggests the applicability of machine learning algorithm (MLA) in Peak power point tracking (P3T) methods to maximize power of a PV arrangement under varying weather conditions. Machine learning methods optimize peak power point tracking in solar photovoltaic systems by bringing agility, data-driven decision-making, and increased accuracy. MLAs improve the overall efficiency, stability, and dependability of these systems by handling the unpredictability of solar energy production under varying weather circumstances and PSCs Because MLAs are able to learn and adjust to non-linear relationships between solar intensity and PVS output. In this study, the squared multiple squared exponential Gaussian process regression method SGPRA tested in three rapidly varying ecological conditions. The performance of ML-P3T methods is validated using Matlab/Simulink, and the simulation outcome are compared with one of the most used algorithms, the variable step size incremental conductance algorithm (VINA). The Matlab/Simulink findings show that SGPRA operates significantly better under varying weather circumstances, harnessing more peak power efficiency 90%, shorter tracking time 0.13 sec, a mean error of 0.042, and superior stability.

Crack localization in glass fiber composite beams by experimental modal analysis and multi variable Gaussian process regression method

PurposeEnsuring the early detection of structural issues in aircraft is crucial for preserving human lives. One effective approach involves identifying cracks in composite structures. This paper employs experimental modal analysis and a multi-variable Gaussian process regression method to detect and locate cracks in glass fiber composite beams.Design/methodology/approachThe present study proposes Gaussian process regression model trained by the first three natural frequencies determined experimentally using a roving impact hammer method with crystal four-channel analyzer, uniaxial accelerometer and experimental modal analysis software. The first three natural frequencies of the cracked composite beams obtained from experimental modal analysis are used to train a multi-variable Gaussian process regression model for crack localization. Radial basis function is used as a kernel function, and hyperparameters are optimized using the negative log marginal likelihood function. Bayesian conditional probability likelihood function is used to estimate the mean and variance for crack localization in composite structures.FindingsThe efficiency of Gaussian process regression is improved in the present work with the normalization of input data. The fitted Gaussian process regression model validates with experimental modal analysis for crack localization in composite structures. The discrepancy between predicted and measured values is 1.8%, indicating strong agreement between the experimental modal analysis and Gaussian process regression methods. Compared to other recent methods in the literature, this approach significantly improves efficiency and reduces error from 18.4% to 1.8%. Gaussian process regression is an efficient machine learning algorithm for crack localization in composite structures.Originality/valueThe experimental modal analysis results are first utilized for crack localization in cracked composite structures. Additionally, the input data are normalized and employed in a machine learning algorithm, such as the multi-variable Gaussian process regression method, to efficiently determine the crack location in these structures.

A data-driven simulation and Gaussian process regression model for hydraulic press condition diagnosis

Improving overall performance and increasing operational reliability are currently among the leading research topics in the field of hydraulic systems. In recent years, the use of artificial intelligence-based modeling and design techniques has developed rapidly to account for the nonlinear properties of Gaussian systems and to predict fault reasoning in hydraulic systems. In this study, feature acquisition and selection are proposed to prepare input data for a simulation-based learning approach. In addition, a cause-and-effect analysis is performed by considering various what-if scenarios as external disturbances that affect the response of the hydraulic press. While the objective of the sheet metal bending cycle and a pulley system is to initiate a load on the hydraulic press, an intelligent sensing system is used to observe the behavior of the hydraulic press during the phases of sheet metal bending cycle, i.e., the forming, leveling, and movement. In addition, the Gaussian process regression method is used to build data-driven prediction models with different predictors that contribute significantly to improving predictive accuracy. The condition diagnosis indicates the accurate performance of predictive models observing the coefficient of determination R2 at 0.998 for the bending phase, 0.962 for the leveling phase, and 0.999 for the movement phase. Although the approximation of the simulation model is efficient, it is found that certain features are reasonably well approximated with regard to the forming phases.

Data-driven based fracture prediction of notched components.

A data-driven approach is developed to predict the fracture load of a notched component. To do so, more than 1500 fracture tests (507 unique experimental data points) on mixed-mode I/II loading of notched brittle samples were collected from the literature. After pre-processing the raw data, six features of maximum tangential stress [Formula: see text], maximum tangential stress angle [Formula: see text], ultimate tensile strength [Formula: see text], fracture toughness [Formula: see text], notch opening angle [Formula: see text] and notch tip radius [Formula: see text] were selected by using the neighbourhood component analysis (NCA) technique. To predict the fracture load of various types of notched samples, several machine learning (ML) models were trained using the methods of Gaussian process regression (GPR), decision tree ensemble and artificial neural network (ANN). Then, the Bayesian optimization algorithm was applied to find the optimum hyperparameters for each model. Lastly, the performance of the models in predicting fracture load was evaluated against 124 unseen data points. The results revealed the high potential of data-driven methods for assessing the fracture load of notched brittle components with acceptable precisions of 92%, 89% and 88% accuracy, respectively, for GPR, decision tree ensemble and ANN models. The superior performance of the GPR method can be attributed to its ability to capture complex nonlinear relationships in the data while providing reliable uncertainty estimates. Furthermore, thanks to its interpolation capabilities, GPR is able to seamlessly fill the gaps between data points, resulting in more comprehensive and precise predictions across the entire range of input data. Additionally, the presented models were capable of predicting the fracture load of VO-shaped notched samples with acceptable accuracy, though this type of notch was not used in the model training process. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 2)'.

Potentiality of ultraspectral sensor in biophysical and biochemical vegetation parameter inversion

ABSTRACT Biophysical and biochemical vegetation parameters are important indicators for quantitatively monitoring vegetation growth status and ecosystem. Compared to hyperspectral data, the emergence of ultraspectral remote sensing technology supports the acquisition of thousands of more narrow bands in near-infrared spectrum. It is helpful to capture more detailed vegetation spectral features, thereby providing more accurate quantitative inversion. However, there are still many unknowns in utilizing ultraspectral sensors for vegetation biochemical and biophysical parameters inversion, particularly in extracting meaningful inversion information from thousands of spectral bands. Here, we discuss the potentiality, efficiency and accuracy of the ultraspectral sensor AisaIBIS in this field. Firstly, we conducted sensitivity analysis based on simulated sensor dataset and the PROSAIL model to determine the vegetation parameters suitable for inversion. Secondly, in order to enhance the inversion efficiency and reduce the effects of multicollinearity in ultraspectral data, we proposed the stepped asymptotic optimization strategy that combined random forest (RF) and Gaussian process regression (GPR-BAT) methods for dimensionality reduction. Lastly, using experimental data, we compared the inversion accuracy between traditional band selection methods and our proposed method, thereby validating the application potential of ultraspectral sensors. The experimental results indicate that leaf area index (LAI), chlorophyll content, and brown pigment are the most sensitive parameters to the spectral information and are suitable for inversion. Based on the stepped asymptotic optimization strategy, we effectively avoid incomplete information extraction caused by high correlation and spectral redundancy, achieving optimal bands covering the entire spectrum of the sensor. The LAI inversion shows a correlation of 0.691 and an RMSE of 1.955 with the original data, outperforming the accuracy of the traditional band selection methods RF and principal component analysis (PCA). Moreover, the inversion time has decreased by approximately 66% after the dimensionality reduction. This study illustrates the application value of monitoring vegetation parameters by ultraspectral sensor.

Transport properties of oil-CO2 mixtures in calcite nanopores: Physics and machine learning models

Fundamental understanding and quantitative models of the transport properties of oil-CO2 mixtures in nanopores are indispensable for physics-based models of CO2-enhanced oil recovery in unconventional oil reservoirs. This study determines the Maxwell-Stefan (M−S) diffusivities of CO2-decane (1: CO2; 2: decane /C10) mixtures in calcite nanopores with compositions relevant to CO2 Huff-n-Puff by molecular dynamics (MD) simulations. In the compositional space explored, D12 characterizing CO2-C10 interactions is relatively insensitive to composition, in contrast to that of bulk mixtures with similar compositions. D1,s characterizing CO2-wall interactions increases sharply with CO2 loading in the nanopore. In contrast, D2,s characterizing C10-wall interactions shows a nonmonotonic dependence on C10 loading. In addition, surprisingly, D2,s is negative, opposite to the expectations for dense fluid mixtures or pure decane confined in nanopores. These features of the M−S diffusivities can ultimately be traced to the fact that CO2 molecules adsorb far more strongly on pore walls than the C10 molecules, which leads to significantly heterogeneous distribution of CO2 and C10 in the nanopore and a low mobility of the adsorbed CO2 molecules. As MD simulations are computationally expensive, a non-parametric machine learning technique, called the multi-task Gaussian process regression method, is used to build a surrogate model to predict M−S diffusivities based on limited MD data. The surrogate model performs well in the compositional space it was trained with a relative root mean square error less than 10%.

Prediction of concrete strength using MCMC and GPR methods

Concrete strength prediction is a complex nonlinear regression task that involves multiple ingredients and age as key factors. In order to achieve accurate predictions, the Markov Chain Monte Carlo (MCMC) and Gaussian Process Regression (GPR) techniques are employed. The dataset, sourced from Kaggle repositories, comprises a comprehensive collection of 1030 data points. Alongside the existing features (content of ingredients, age and strength), we introduce new ones, including water-cement ratio, sand ratio, and water-binder ratio, to enhance the model's credibility. To determine the optimal kernel function, the dataset is partitioned into training and testing subsets. Notably, the MCMC method yields an R2 of 0.41, while GPR demonstrates a significantly improved R2 of 0.89. Further investigation is warranted to refine the model's fit and optimize its predictive capacity.

The e-MANTIS emulator: fast predictions of the non-linear matter power spectrum in f(R)CDM cosmology

ABSTRACT In order to probe modifications of gravity at cosmological scales, one needs accurate theoretical predictions. N-body simulations are required to explore the non-linear regime of structure formation but are very time consuming. In this work, we release a new public emulator, dubbed e-mantis, that performs an accurate and fast interpolation between the predictions of f(R) modified gravity cosmological simulations, run with ecosmog. We sample a wide 3D parameter space given by the current background scalar field value $10^{-7}\lt \left|f_{R_0}\right|\lt 10^{-4}$, matter density 0.24 < Ωm < 0.39, and primordial power spectrum normalization 0.6 < σ8 < 1.0, with 110 points sampled from a Latin hypercube. For each model we perform pairs of f(R)CDM and ΛCDM simulations covering an effective volume of $\left(560 \, h^{-1}\, \mathrm{Mpc}\right)^3$ with a mass resolution of ∼2 × 1010h−1M⊙. We build an emulator for the matter power spectrum boost B(k) = Pf(R)(k)/PΛCDM(k) using a Gaussian process regression method. The boost is mostly independent of h, ns, and Ωb, which reduces the dimensionality of the relevant cosmological parameter space. Additionally, it is more robust against statistical and systematic errors than the raw power spectrum, thus strongly reducing our computational needs. According to our dedicated study of numerical systematics, the resulting emulator has an estimated maximum error of 3 per cent across the whole cosmological parameter space, for scales $0.03 \ h\, \mathrm{Mpc}^{-1} \lt k \lt 7 \ h\, \mathrm{Mpc}^{-1}$, and redshifts 0 < z < 2, while in most cases the accuracy is better than 1 per cent. Such an emulator could be used to constrain f(R) gravity with weak lensing analyses.