scholarly journals Expectation-Maximization Algorithm for the Calibration of Complex Simulator Using a Gaussian Process Emulator

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 53
Author(s):  
Yun Am Seo ◽  
Jeong-Soo Park
Keyword(s):  
Iterative Method ◽  
Gaussian Process ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Tuning Parameters ◽  
Squared Error ◽  
Model Study ◽  
Calibration Methods ◽  
Gp Model ◽  
Gaussian Process Emulator

The approximated non-linear least squares (ALS) tunes or calibrates the computer model by minimizing the squared error between the computer output and real observations by using an emulator such as a Gaussian process (GP) model. A potential defect of the ALS method is that the emulator is constructed once and it is no longer re-built. An iterative method is proposed in this study to address this difficulty. In the proposed method, the tuning parameters of the simulation model are calculated by the conditional expectation (E-step), whereas the GP parameters are updated by the maximum likelihood estimation (M-step). These EM-steps are alternately repeated until convergence by using both computer and experimental data. For comparative purposes, another iterative method (the max-min algorithm) and a likelihood-based method are considered. Five toy models are tested for a comparative analysis of these methods. According to the toy model study, both the variance and bias of the estimates obtained from the proposed EM algorithm are smaller than those from the existing calibration methods. Finally, the application to a nuclear fusion simulator is demonstrated.

scholarly journals A Novel Methodology for Hydrocarbon Depth Prediction in Seabed Logging: Gaussian Process-Based Inverse Modeling of Electromagnetic Data

2021 ◽  
Vol 11 (4) ◽  
pp. 1492
Author(s):  
Hanita Daud ◽  
Muhammad Naeim Mohd Aris ◽  
Khairul Arifin Mohd Noh ◽  
Sarat Chandra Dass
Keyword(s):  
Gaussian Process ◽  
Inverse Modeling ◽  
Mean Squared Error ◽  
Computational Effort ◽  
Percentage Error ◽  
Depth Prediction ◽  
Receiver System ◽  
Realistic Representation ◽  
And Performance ◽  
Gp Model

Seabed logging (SBL) is an application of electromagnetic (EM) waves for detecting potential marine hydrocarbon-saturated reservoirs reliant on a source–receiver system. One of the concerns in modeling and inversion of the EM data is associated with the need for realistic representation of complex geo-electrical models. Concurrently, the corresponding algorithms of forward modeling should be robustly efficient with low computational effort for repeated use of the inversion. This work proposes a new inversion methodology which consists of two frameworks, namely Gaussian process (GP), which allows a greater flexibility in modeling a variety of EM responses, and gradient descent (GD) for finding the best minimizer (i.e., hydrocarbon depth). Computer simulation technology (CST), which uses finite element (FE), was exploited to generate prior EM responses for the GP to evaluate EM profiles at “untried” depths. Then, GD was used to minimize the mean squared error (MSE) where GP acts as its forward model. Acquiring EM responses using mesh-based algorithms is a time-consuming task. Thus, this work compared the time taken by the CST and GP in evaluating the EM profiles. For the accuracy and performance, the GP model was compared with EM responses modeled by the FE, and percentage error between the estimate and “untried” computer input was calculated. The results indicate that GP-based inverse modeling can efficiently predict the hydrocarbon depth in the SBL.

scholarly journals Slash Truncation Positive Normal Distribution and Its Estimation Based on the EM Algorithm

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2164
Author(s):  
Héctor J. Gómez ◽  
Diego I. Gallardo ◽  
Karol I. Santoro
Keyword(s):  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
R Software ◽  
Data Application ◽  
The Em Algorithm ◽  
Kurtosis Parameter ◽  
Computational Implementation ◽  
Moments Method

In this paper, we present an extension of the truncated positive normal (TPN) distribution to model positive data with a high kurtosis. The new model is defined as the quotient between two random variables: the TPN distribution (numerator) and the power of a standard uniform distribution (denominator). The resulting model has greater kurtosis than the TPN distribution. We studied some properties of the distribution, such as moments, asymmetry, and kurtosis. Parameter estimation is based on the moments method, and maximum likelihood estimation uses the expectation-maximization algorithm. We performed some simulation studies to assess the recovery parameters and illustrate the model with a real data application related to body weight. The computational implementation of this work was included in the tpn package of the R software.

scholarly journals Gaussian Process-Based Response Surface Method for Slope Reliability Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Hu ◽  
Guo-shao Su ◽  
Jianqing Jiang ◽  
Yilong Xiao
Keyword(s):  
Gaussian Process ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Failure Probability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Gp Model

A new response surface method (RSM) for slope reliability analysis was proposed based on Gaussian process (GP) machine learning technology. The method involves the approximation of limit state function by the trained GP model and estimation of failure probability using the first-order reliability method (FORM). A small amount of training samples were firstly built by the limited equilibrium method for training the GP model. Then, the implicit limit state function of slope was approximated by the trained GP model. Thus, the implicit limit state function and its derivatives for slope stability analysis were approximated by the GP model with the explicit formulation. Furthermore, an iterative algorithm was presented to improve the precision of approximation of the limit state function at the region near the design point which contributes significantly to the failure probability. Results of four case studies including one nonslope and three slope problems indicate that the proposed method is more efficient to achieve reasonable accuracy for slope reliability analysis than the traditional RSM.

scholarly journals NIMG-52. UNCERTAINTY QUANTIFICATION IN RADIOMICS

2019 ◽  
Vol 21 (Supplement_6) ◽  
pp. vi172-vi173
Author(s):  
Lujia Wang ◽  
Hyunsoo Yoon ◽  
Andrea Hawkins-Daarud ◽  
Kyle Singleton ◽  
Kamala Clark-Swanson ◽  
...  
Keyword(s):  
Gaussian Process ◽  
Copy Number ◽  
Prediction Accuracy ◽  
Clinical Decision Making ◽  
Diffusion Tensor ◽  
Feature Space ◽  
Training Sample ◽  
P Value ◽  
The Impact ◽  
Gp Model

Abstract INTRODUCTION The quantification of intratumoral heterogeneity – through radiomics-based approaches - can help resolve the regionally distinct genetic drug targets that may co-exist within a single Glioblastoma (GBM) tumor. While this offers potential diagnostic value under the paradigm of individualized oncology, clinical decision-making must also consider the degree of uncertainty associated with each model. In this study, we evaluate the performance of a novel machine-learning (ML) algorithm, called Gaussian Process (GP) modeling, that can quantify the impact of multiple sources of uncertainty in ML model development and prediction accuracy, including variabilities in the copy number measurement, radiomics features, training sample characteristics, and training sample size. METHOD We collected 95 image-localized biopsies from 25 primary GBM patients. We coregistered stereotactic locations with preoperative multi-parametric MRI features (conventional MRI, DSC perfusion, Diffusion Tensor Imaging) to generate spatially matched pairs of MRI and copy number variants (CNV) for for each biopsy. We developed a Gaussian Process (GP) model to predict CNV for Epidermal Growth Factor Receptor (EGFR) based on MRI radiomic features in each patient. We used leave-one-patient-out cross validation to quantify prediction accuracy and model uncertainty. Spatial prediction and uncertainty (p-value) maps were overlaid to help visualize regional genetic variation of EGFR and uncertainty of the radiomic predictions. RESULT: The initial GP radiomics model for EGFR amplification (CNV > 3.5) produced a sensitivity of 0.8 and specificity of 0.8. Samples/regions associated with high uncertainty (p-value >0.05) correlated with either 1) extrapolation of radiomic features from the training set-defined feature space or 2) insufficient training samples in the feature space. CONCLUSION We present a ML-based model that quantifies spatial genetic heterogeneity in GBM, while also estimating model uncertainties that result from multi-source data variabilities. This approach lays the groundwork for prospective clinical integration of modeling-based diagnostic approaches in the paradigm of individualized medicine.

scholarly journals A Gaussian Process Model for Color Camera Characterization: Assessment in Outdoor Levantine Rock Art Scenes

Sensors ◽  
2019 ◽  
Vol 19 (21) ◽  
pp. 4610 ◽  
Author(s):  
Adolfo Molada-Tebar ◽  
Gabriel Riutort-Mayol ◽  
Ángel Marqués-Mateu ◽  
José Luis Lerma
Keyword(s):  
Gaussian Process ◽  
Process Model ◽  
Rock Art ◽  
Predictive Performance ◽  
Practical Applications ◽  
Nonparametric Models ◽  
Novel Approach ◽  
Characterization Procedure ◽  
Leave One Out ◽  
Gp Model

In this paper, we propose a novel approach to undertake the colorimetric camera characterization procedure based on a Gaussian process (GP). GPs are powerful and flexible nonparametric models for multivariate nonlinear functions. To validate the GP model, we compare the results achieved with a second-order polynomial model, which is the most widely used regression model for characterization purposes. We applied the methodology on a set of raw images of rock art scenes collected with two different Single Lens Reflex (SLR) cameras. A leave-one-out cross-validation (LOOCV) procedure was used to assess the predictive performance of the models in terms of CIE XYZ residuals and Δ E a b * color differences. Values of less than 3 CIELAB units were achieved for Δ E a b * . The output sRGB characterized images show that both regression models are suitable for practical applications in cultural heritage documentation. However, the results show that colorimetric characterization based on the Gaussian process provides significantly better results, with lower values for residuals and Δ E a b * . We also analyzed the induced noise into the output image after applying the camera characterization. As the noise depends on the specific camera, proper camera selection is essential for the photogrammetric work.

Optimization for Liquid Cooling Cylindrical Battery Thermal Management System Based on Gaussian Process Model

2020 ◽  
Vol 13 (2) ◽  
Author(s):  
Wei Li ◽  
Akhil Garg ◽  
Mi Xiao ◽  
Liang Gao
Keyword(s):  
Pressure Drop ◽  
Gaussian Process ◽  
Thermal Management ◽  
Management System ◽  
Process Model ◽  
Liquid Cooling ◽  
Battery Thermal Management ◽  
Thermal Management System ◽  
Battery Thermal Management System ◽  
Gp Model

Abstract The power of electric vehicles (EVs) comes from lithium-ion batteries (LIBs). LIBs are sensitive to temperature. Too high and too low temperatures will affect the performance and safety of EVs. Therefore, a stable and efficient battery thermal management system (BTMS) is essential for an EV. This article has conducted a comprehensive study on liquid-cooled BTMS. Two cooling schemes are designed: the serpentine channel and the U-shaped channel. The results show that the cooling effect of two schemes is roughly the same, but the U-shaped channel can significantly decrease the pressure drop (PD) loss. The U-shaped channel is parameterized and modeled. A machine learning method called the Gaussian process (GP) model has been used to express the outputs such as temperature difference, temperature standard deviation, and pressure drop. A multi-objective optimization model is established using GP models, and the NSGA-II method is employed to drive the optimization process. The optimized scheme is compared with the initial design. The main findings are summarized as follows: the velocity of cooling water v decreases from 0.3 m/s to 0.22 m/s by 26.67%. Pressure drop decreases from 431.40 Pa to 327.11 Pa by 24.18%. The optimized solution has a significant reduction in pressure drop and helps to reduce parasitic power. The proposed method can provide a useful guideline for the liquid cooling design of large-scale battery packs.

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.

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