scholarly journals Investigating the Predictive Performance of Gaussian Process Regression in Evaluating Reservoir Porosity and Permeability

Energies ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 3261 ◽  
Author(s):  
Solomon Asante-Okyere ◽  
Chuanbo Shen ◽  
Yao Yevenyo Ziggah ◽  
Mercy Moses Rulegeya ◽  
Xiangfeng Zhu
Keyword(s):  
Neural Network ◽  
Gaussian Process ◽  
Covariance Function ◽  
Back Propagation ◽  
Gaussian Process Regression ◽  
Kernel Functions ◽  
Generalized Regression Neural Network ◽  
Model Parameters ◽  
Porosity And Permeability ◽  
Reservoir Porosity

In this paper, a new predictive model based on Gaussian process regression (GPR) that does not require iterative tuning of user-defined model parameters has been proposed to determine reservoir porosity and permeability. For this purpose, the capability of GPR was appraised statistically for predicting porosity and permeability of the southern basin of the South Yellow Sea using petrophysical well log data. Generally, the performance of GPR is deeply reliant on the type covariance function utilized. Therefore, to obtain the optimal GPR model, five different kernel functions were tested. The resulting optimal GPR model consisted of the exponential covariance function, which produced the highest correlation coefficient (R) of 0.85 and the least root mean square error (RMSE) of 0.037 and 6.47 for porosity and permeability, respectively. Comparison was further made with benchmark methods involving a back propagation neural network (BPNN), generalized regression neural network (GRNN), and radial basis function neural network (RBFNN). The statistical findings revealed that the proposed GPR is a powerful technique and can be used as a supplement to the widely used artificial neural network methods. In terms of computational speed, the GPR technique was computationally faster than the BPNN, GRNN, and RBFNN methods in estimating reservoir porosity and permeability.

scholarly journals Wireless Indoor Localization Using Convolutional Neural Network and Gaussian Process Regression

Sensors ◽  
2019 ◽  
Vol 19 (11) ◽  
pp. 2508 ◽  
Author(s):  
Guolong Zhang ◽  
Ping Wang ◽  
Haibing Chen ◽  
Lan Zhang
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Gaussian Process ◽  
Hybrid Model ◽  
Nearest Neighbor ◽  
Gaussian Process Regression ◽  
Kernel Functions ◽  
Training Dataset ◽  
K Nearest Neighbor ◽  
Positive Effects

This paper presents a localization model employing convolutional neural network (CNN) and Gaussian process regression (GPR) based on Wi-Fi received signal strength indication (RSSI) fingerprinting data. In the proposed scheme, the CNN model is trained by a training dataset. The trained model adapts to complex scenes with multipath effects or many access points (APs). More specifically, the pre-processing algorithm makes the RSSI vector which is formed by considerable RSSI values from different APs readable by the CNN algorithm. The trained CNN model improves the positioning performance by taking a series of RSSI vectors into account and extracting local features. In this design, however, the performance is to be further improved by applying the GPR algorithm to adjust the coordinates of target points and offset the over-fitting problem of CNN. After implementing the hybrid model, the model is experimented with a public database that was collected from a library of Jaume I University in Spain. The results show that the hybrid model has outperformed the model using k-nearest neighbor (KNN) by 61.8%. While the CNN model improves the performance by 45.8%, the GPR algorithm further enhances the localization accuracy. In addition, the paper has also experimented with the three kernel functions, all of which have been demonstrated to have positive effects on GPR.

scholarly journals Hybrid Grey Wolf Optimization-Based Gaussian Process Regression Model for Simulating Deterioration Behavior of Highway Tunnel Components

Processes ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 36
Author(s):  
Eslam Mohammed Abdelkader ◽  
Abobakr Al-Sakkaf ◽  
Nehal Elshaboury ◽  
Ghasan Alfalah
Keyword(s):  
Neural Network ◽  
Gaussian Process ◽  
Back Propagation ◽  
Gaussian Process Regression ◽  
Percentage Error ◽  
Support Vector ◽  
Grey Wolf ◽  
Elman Neural Network ◽  
Deterioration Model ◽  
Highway Tunnel

Highway tunnels are one of the paramount infrastructure systems that affect the welfare of communities. They are vulnerable to higher limits of deterioration, yet there are limited available funds for maintenance and rehabilitation. This state of circumstances entails the development of a deterioration model to forecast the performance condition behavior of critical tunnel elements. Accordingly, this research paper proposes an integrated deterioration prediction model for five highway tunnel elements, namely, cast-in-place tunnel liners, concrete interior walls, concrete portal, concrete ceiling slab, and concrete slab on grade. The developed deterioration model is envisioned in two fundamental components, which are model calibration and model assessment. In the first component, an integrated model of Gaussian process regression and a grey wolf optimization algorithm (GWO-GPR) is introduced for deterioration behavior prediction of highway tunnel elements. In this regard, the grey wolf optimizer is exploited to improve the prediction accuracies of the Gaussian process through optimal estimation of its hyper parameters and to automatically interpret the significant deterioration factors. The second component involves three tiers of performance evaluation comparison, statistical significance comparisons, and consolidated ranking to assess the prediction accuracies of the developed GWO-GPR model. In this regard, the developed model is validated against six widely acknowledged machine learning models, which are back-propagation artificial neural network, Elman neural network, cascade forward neural network, generalized regression neural network, support vector machines, and regression tree. Results demonstrate that the developed GWO-GPR model significantly outperformed other deterioration prediction models in the five tunnel elements. In cast-in-place tunnel liners it accomplished a mean absolute percentage error, mean absolute error, root mean square percentage error, root relative squared error, and relative absolute error of 1.65%, 0.018, 0.21%, 0.018, and 0.147, respectively. In this context, it was inferred that the developed GWO-GPR model managed to reduce the prediction errors of the back-propagation artificial neural network, Elman neural network, and support vector machines by 84.71%, 76.91%, and 69.6%, respectively. It can be concluded that the developed deterioration model can assist transportation agencies in creating timely and cost-efficient maintenance schedules of highway tunnels.

Evaluation of Gaussian process regression kernel functions for improving groundwater prediction

2021 ◽  
pp. 126960
Author(s):  
Yue Pan ◽  
Xiankui Zeng ◽  
Hongxia Xu ◽  
Yuanyuan Sun ◽  
Dong Wang ◽  
...  
Keyword(s):  
Gaussian Process ◽  
Gaussian Process Regression ◽  
Kernel Functions

Topographic Kernels for Gaussian Process Regression in Digital Soil Mapping

2021 ◽  
Author(s):  
Thomas Gläßle ◽  
Kerstin Rau ◽  
Thomas Scholten ◽  
Philipp Hennig
Keyword(s):  
Gaussian Process ◽  
Domain Knowledge ◽  
Gaussian Process Regression ◽  
Kernel Functions ◽  
Soil Mapping ◽  
Digital Soil Mapping ◽  
Base Case ◽  
Training Samples ◽  
Additive Regression Model ◽  
Additive Regression

<p>Gaussian Processes provide a theoretically well-understood regression framework that is widely used in the context of Digital Soil Mapping. Among the reasons to use Gaussian Process Regression (GPR) are its interpretability, its builtin support for uncertainty quantification, and its ability to handle unevenly spaced and correlated training samples through a user-specified covariance kernel. The base case of GPR is performed with covariance models that are specified functions of Euclidean distance. In order to incorporate information other than the relative positions, regression-kriging extends GPR by an additive regression model of choice, and co-kriging considers a covariance model between covariates and the target variable. In this work, we use the alternative approach of incorporating topographic information directly into the kernel function by use of a non-Euclidean, non-stationary distance function. In particular, we devise kernels based on a path of least effort, where <em>effort</em> is locally specified as a function constructed from prior knowledge. It can e.g. be derived from local topographic variables. We demonstrate that our candidate models improve prediction accuracy over the base model. This shows that domain knowledge can be integrated into the model by means of handcrafted kernel functions. The approach is not per se restricted to topographic variables, but could be used for any covariate quantity that is available at output resolution.</p>

A Comparison of Numerical Optimizers in Developing High Dimensional Surrogate Models

2019 ◽  
Author(s):  
Yanwen Xu ◽  
Pingfeng Wang
Keyword(s):  
Gaussian Process ◽  
Process Model ◽  
Likelihood Function ◽  
Surrogate Models ◽  
Kernel Functions ◽  
Function Optimization ◽  
High Dimensional ◽  
Model Parameters ◽  
Gradient Based ◽  
Gp Model

Abstract The Gaussian Process (GP) model has become one of the most popular methods to develop computationally efficient surrogate models in many engineering design applications, including simulation-based design optimization and uncertainty analysis. When more observations are used for high dimensional problems, estimating the best model parameters of Gaussian Process model is still an essential yet challenging task due to considerable computation cost. One of the most commonly used methods to estimate model parameters is Maximum Likelihood Estimation (MLE). A common bottleneck arising in MLE is computing a log determinant and inverse over a large positive definite matrix. In this paper, a comparison of five commonly used gradient based and non-gradient based optimizers including Sequential Quadratic Programming (SQP), Quasi-Newton method, Interior Point method, Trust Region method and Pattern Line Search for likelihood function optimization of high dimension GP surrogate modeling problem is conducted. The comparison has been focused on the accuracy of estimation, the efficiency of computation and robustness of the method for different types of Kernel functions.

scholarly journals Evaluating Parameter Uncertainty in a Simulation Model of Cancer Using Emulators

2019 ◽  
Vol 39 (4) ◽  
pp. 405-413 ◽  
Author(s):  
Tiago M. de Carvalho ◽  
Eveline A. M. Heijnsdijk ◽  
Luc Coffeng ◽  
Harry J. de Koning
Keyword(s):  
Prostate Cancer ◽  
Simulation Model ◽  
Gaussian Process ◽  
Prediction Error ◽  
Life Histories ◽  
Gaussian Process Regression ◽  
Computation Time ◽  
Computational Effort ◽  
Sensitivity Analyses ◽  
Model Parameters

Background. Microsimulation models have been extensively used in the field of cancer modeling. However, there is substantial uncertainty regarding estimates from these models, for example, overdiagnosis in prostate cancer. This is usually not thoroughly examined due to the high computational effort required. Objective. To quantify uncertainty in model outcomes due to uncertainty in model parameters, using a computationally efficient emulator (Gaussian process regression) instead of the model. Methods. We use a microsimulation model of prostate cancer (microsimulation screening analysis [MISCAN]) to simulate individual life histories. We analyze the effect of parametric uncertainty on overdiagnosis with probabilistic sensitivity analyses (ProbSAs). To minimize the number of MISCAN runs needed for ProbSAs, we emulate MISCAN, using data pairs of parameter values and outcomes to fit a Gaussian process regression model. We evaluate to what extent the emulator accurately reproduces MISCAN by computing its prediction error. Results. Using an emulator instead of MISCAN, we may reduce the computation time necessary to run a ProbSA by more than 85%. The average relative prediction error of the emulator for overdiagnosis equaled 1.7%. We predicted that 42% of screen-detected men are overdiagnosed, with an associated empirical confidence interval between 38% and 48%. Sensitivity analyses show that the accuracy of the emulator is sensitive to which model parameters are included in the training runs. Conclusions. For a computationally expensive simulation model with a large number of parameters, we show it is possible to conduct a ProbSA, within a reasonable computation time, by using a Gaussian process regression emulator instead of the original simulation model.

scholarly journals Detecting periodicities with Gaussian processes

2016 ◽  
Vol 2 ◽  
pp. e50 ◽  
Author(s):  
Nicolas Durrande ◽  
James Hensman ◽  
Magnus Rattray ◽  
Neil D. Lawrence
Keyword(s):  
Hilbert Space ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Covariance Function ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Gaussian Process Regression ◽  
Inner Product ◽  
Input Output ◽  
Periodic Data

We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression, which provides a flexible non-parametric framework for modelling periodic data. We introduce a novel decomposition of the covariance function as the sum of periodic and aperiodic kernels. This decomposition allows for the creation of sub-models which capture the periodic nature of the signal and its complement. To quantify the periodicity of the signal, we derive a periodicity ratio which reflects the uncertainty in the fitted sub-models. Although the method can be applied to many kernels, we give a special emphasis to the Matérn family, from the expression of the reproducing kernel Hilbert space inner product to the implementation of the associated periodic kernels in a Gaussian process toolkit. The proposed method is illustrated by considering the detection of periodically expressed genes in thearabidopsisgenome.

scholarly journals Four-dimensional mesospheric and lower thermospheric wind fields using Gaussian process regression on multistatic specular meteor radar observations

2021 ◽  
Author(s):  
Ryan Volz ◽  
Jorge L. Chau ◽  
Philip J. Erickson ◽  
Juha P. Vierinen ◽  
J. Miguel Urco ◽  
...  
Keyword(s):  
Gaussian Process ◽  
Wind Velocity ◽  
Wind Field ◽  
Gaussian Process Regression ◽  
Small Scale ◽  
Model Parameters ◽  
Meteor Radar ◽  
Wind Fields ◽  
Data Set ◽  
Uncertainty Estimates

Abstract. Mesoscale dynamics in the mesosphere and lower thermosphere (MLT) region have been difficult to study from either ground- or satellite-based observations. For understanding of atmospheric coupling processes, important spatial scales at these altitudes range between tens to hundreds of kilometers in the horizontal plane. To date, this scale size is challenging observationally, and so structures are usually parameterized in global circulation models. The advent of multistatic specular meteor radar networks allows exploration of MLT mesocale dynamics on these scales using an increased number of detections and a diversity of viewing angles inherent to multistatic networks. In this work, we introduce a four dimensional wind field inversion method that makes use of Gaussian process regression (GPR), a non-parametric and Bayesian approach. The method takes measured projected wind velocities and prior distributions of the wind velocity as a function of space and time, specified by the user or estimated from the data, and produces posterior distributions for the wind velocity. Computation of the predictive posterior distribution is performed on sampled points of interest and is not necessarily regularly sampled. The main benefits of the GPR method include this non-gridded sampling, the built-in statistical uncertainty estimates, and the ability to horizontally-resolve winds on relatively small scales. The performance of the GPR implementation has been evaluated on Monte Carlo simulations with known distributions using the same spatial and temporal sampling as one day of real meteor measurements. Based on the simulation results we find that the GPR implementation is robust, providing wind fields that are statistically unbiased and with statistical variances that depend on the geometry and are proportional to the prior velocity variances. A conservative and fast approach can be straightforwardly implemented by employing overestimated prior variances and distances, while a more robust but computationally intensive approach can be implemented by employing training and fitting of model parameters. The latter GPR approach has been applied to a 24-hour data set and shown to compare well to previously used homogeneous and gradient methods. Small scale features have reasonably low statistical uncertainties, implying geophysical wind field horizontal structures as low as 20–50 km. We suggest that this GPR approach forms a suitable method for MLT regional and weather studies.

scholarly journals Towards estimation of CO2 adsorption on highly porous MOF-based adsorbents using gaussian process regression approach

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Majedeh Gheytanzadeh ◽  
Alireza Baghban ◽  
Sajjad Habibzadeh ◽  
Amin Esmaeili ◽  
Otman Abida ◽  
...  
Keyword(s):  
Gaussian Process ◽  
Fossil Fuels ◽  
Global Climate ◽  
Gaussian Process Regression ◽  
Accurate Estimate ◽  
Kernel Functions ◽  
Predictive Tool ◽  
Input Variables ◽  
Capture Techniques ◽  
The Impact

AbstractIn recent years, new developments in controlling greenhouse gas emissions have been implemented to address the global climate conservation concern. Indeed, the earth's average temperature is being increased mainly due to burning fossil fuels, explicitly releasing high amounts of CO2 into the atmosphere. Therefore, effective capture techniques are needed to reduce the concentration of CO2. In this regard, metal organic frameworks (MOFs) have been known as the promising materials for CO2 adsorption. Hence, study on the impact of the adsorption conditions along with the MOFs structural properties on their ability in the CO2 adsorption will open new doors for their further application in CO2 separation technologies as well. However, the high cost of the corresponding experimental study together with the instrument's error, render the use of computational methods quite beneficial. Therefore, the present study proposes a Gaussian process regression model with four kernel functions to estimate the CO2 adsorption in terms of pressure, temperature, pore volume, and surface area of MOFs. In doing so, 506 CO2 uptake values in the literature have been collected and assessed. The proposed GPR models performed very well in which the exponential kernel function, was shown as the best predictive tool with R2 value of 1. Also, the sensitivity analysis was employed to investigate the effectiveness of input variables on the CO2 adsorption, through which it was determined that pressure is the most determining parameter. As the main result, the accurate estimate of CO2 adsorption by different MOFs is obtained by briefly employing the artificial intelligence concept tools.

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