Gaussian Processes for Hydrocarbon Depth Estimation in Forward Modeling of Seabed Logging

2019 ◽  
Vol 24 (3) ◽  
pp. 399-408
Author(s):  
Muhammad Naeim Mohd Aris ◽  
Hanita Daud ◽  
Sarat Chandra Dass ◽  
Khairul Arifin Mohd Noh
Keyword(s):  
Electric Field ◽  
Gaussian Processes ◽  
Depth Estimation ◽  
Forward Modeling ◽  
Hydrocarbon Reservoir ◽  
Offset Distance ◽  
Data Points ◽  
Gp Model ◽  
D Model ◽  
True Values

Seabed logging (SBL) is an application of the marine controlled-source electromagnetic (CSEM) technique to discover offshore hydrocarbon reservoirs underneath the seabed. This application is based on electrical resistivity contrast between hydrocarbon and its surroundings. In this paper, simulation and forward modeling were performed to estimate the hydrocarbon depths in one-dimensional (1-D) SBL data. 1-D data, consisted offset distance (input) and magnitude of electric field (output), were acquired from SBL models developed using computer simulation technology (CST) software. The computer simulated outputs were observed at various depths of hydrocarbon reservoir (250 m–2,750 m with an increment of 250 m) with frequency of 0.125 Hz. Gaussian processes (GP) was employed in the forward modeling by utilizing prior information which is electric field (E-field) at all observed inputs to provide E-field profile at unobserved/untried inputs with uncertainty quantification in terms of variance. The concept was extended for two-dimensional (2-D) model. All observations of E-field were then investigated with the 2-D forward GP model. Root mean square error (RMSE) and coefficient of variation (CV) were utilized to compare the acquired and modeled data at random untried hydrocarbon depths at 400 m, 950 m, 1,450 m, 2,100 m and 2,600 m. Small RMSE and CV values have indicated that developed model can fit well the SBL data at untried hydrocarbon depths. The measured variances of the untried inputs revealed that the data points (true values) were very close to the estimated values, which was 0.003 (in average). RMSEs obtained were very small as an average of 0.049, and CVs found as very reliable percentages, an average of 0.914%, which implied well fitting of the GP model. Hence, the 2-D forward GP model is believed to be capable of predicting unobserved hydrocarbon depths.

scholarly journals Reducing parametric uncertainty in limit-cycle oscillation computational models

2017 ◽  
Vol 121 (1241) ◽  
pp. 940-969 ◽  
Author(s):  
R. Hayes ◽  
R. Dwight ◽  
S. Marques
Keyword(s):  
Limit Cycle ◽  
Computational Models ◽  
Structural Parameters ◽  
Parametric Uncertainty ◽  
Limit Cycle Oscillation ◽  
Posterior Distributions ◽  
Input Parameters ◽  
Data Points ◽  
Cycle Oscillation ◽  
True Values

ABSTRACTThe assimilation of discrete data points with model predictions can be used to achieve a reduction in the uncertainty of the model input parameters, which generate accurate predictions. The problem investigated here involves the prediction of limit-cycle oscillations using a High-Dimensional Harmonic Balance (HDHB) method. The efficiency of the HDHB method is exploited to enable calibration of structural input parameters using a Bayesian inference technique. Markov-chain Monte Carlo is employed to sample the posterior distributions. Parameter estimation is carried out on a pitch/plunge aerofoil and two Goland wing configurations. In all cases, significant refinement was achieved in the distribution of possible structural parameters allowing better predictions of their true deterministic values. Additionally, a comparison of two approaches to extract the true values from the posterior distributions is presented.

Comparison of Machine Learning Algorithms in the Interpolation and Extrapolation of Flame Describing Functions

2019 ◽  
Author(s):  
Michael McCartney ◽  
Matthias Haeringer ◽  
Wolfgang Polifke
Keyword(s):  
Machine Learning ◽  
Gaussian Processes ◽  
Spline Interpolation ◽  
Learning Algorithms ◽  
Predictive Performance ◽  
Machine Learning Algorithms ◽  
Test Time ◽  
Minimal Amount ◽  
Data Points ◽  
The Impact

Abstract This paper examines and compares commonly used Machine Learning algorithms in their performance in interpolation and extrapolation of FDFs, based on experimental and simulation data. Algorithm performance is evaluated by interpolating and extrapolating FDFs and then the impact of errors on the limit cycle amplitudes are evaluated using the xFDF framework. The best algorithms in interpolation and extrapolation were found to be the widely used cubic spline interpolation, as well as the Gaussian Processes regressor. The data itself was found to be an important factor in defining the predictive performance of a model, therefore a method of optimally selecting data points at test time using Gaussian Processes was demonstrated. The aim of this is to allow a minimal amount of data points to be collected while still providing enough information to model the FDF accurately. The extrapolation performance was shown to decay very quickly with distance from the domain and so emphasis should be put on selecting measurement points in order to expand the covered domain. Gaussian Processes also give an indication of confidence on its predictions and is used to carry out uncertainty quantification, in order to understand model sensitivities. This was demonstrated through application to the xFDF framework.

Borehole dc resistivity response for a transitional invaded zone

Geophysics ◽  
1994 ◽  
Vol 59 (12) ◽  
pp. 1796-1805 ◽  
Author(s):  
K. K. Roy ◽  
D. J. Dutta
Keyword(s):  
Separation Of Variables ◽  
Electrode Array ◽  
Forward Model ◽  
Scale Model ◽  
Model Data ◽  
Mud Cake ◽  
Alternative Approach ◽  
Data Points ◽  
Invaded Zone ◽  
D Model

A borehole direct‐current resistivity boundary value problem for normal and lateral elctrode configuratin is soved assuming axial symmetry. The borehole mud, a flushed zone, an invaded zone, and an unciontaminated zone are all assumed to be present. A linear transition in resistivity is assumed for the invaded zone. Frobenius extended power series and the method of separation of variables are used to solved the 1-D problem. Single-run borehole resistivity sounding and solution of the inverse problem are suggested fo estimatingthe resisitivity of the uncontaminated zone and the radius of invasion. Finite‐difference modeling is dione to estimate the effect of shoulder beds ion borehole sounding. Some of the computed 1-D and 2-D model apparent reisivity curves are compared with the existing scale model data. The analysis reveals that the mud cake effect is negligible for normal and lateral electrode array and the invasion zone thickness is feflected in the forward models. Apparent resistivity curves with and without a transitional invaded zone are well separated. Resistivity departure curves are well separated for fixed resistivity and variable resistivity invaded zone models. A normal electrode configuration can feel the presence of the shoulder bed in a 2-D model when the bed thickness is about 12 time the electrode separation. One‐dimensional ridge regression inversion the synthetic forward model data is presented to suggest an alternative approach for determining the resistivey of the uncontaminated zone ([Formula: see text]) and the radius of invasion [Formula: see text]. We conclude that (1) a single run borehole sounding with 10 or 12 data points from a normal or lateral log may be used, rather than 3 points from a dual laterolog [Formula: see text] tool, for better estimation of [Formula: see text], and (2) a borehole forward model should include a transitional invaded zone. Finally, an alternative approach for the estimation of the radius of invasion is proposed.

Robust Optimization With Parameter and Model Uncertainties Using Gaussian Processes With Limited Samples

2017 ◽  
Author(s):  
Yanjun Zhang ◽  
Mian Li
Keyword(s):  
Robust Optimization ◽  
Engineering Design ◽  
Gaussian Processes ◽  
Parameter Uncertainty ◽  
Model Uncertainty ◽  
Computational Cost ◽  
Random Errors ◽  
Model Uncertainties ◽  
Uncertainty Model ◽  
Gp Model

Uncertainty is inevitable in engineering design. The existence of uncertainty may change the optimality and/or the feasibility of the obtained optimal solutions. In simulation-based engineering design, uncertainty could have various types of sources, such as parameter uncertainty, model uncertainty, and other random errors. To deal with uncertainty, robust optimization (RO) algorithms are developed to find solutions which are not only optimal but also robust with respect to uncertainty. Parameter uncertainty has been taken care of by various RO approaches. While model uncertainty has been ignored in majority of existing RO algorithms with the hypothesis that the simulation model used could represent the real physical system perfectly. In the authors’ earlier work, a RO framework was proposed to consider both parameter and model uncertainties using the Bayesian approach with Gaussian processes (GP), where metamodeling uncertainty introduced by GP modeling is ignored by assuming the constructed GP model is accurate enough with sufficient training samples. However, infinite samples are impossible for real applications due to prohibitive time and/or computational cost. In this work, a new RO framework is proposed to deal with both parameter and model uncertainties using GP models but only with limited samples. The compound effect of parameter, model, and metamodeling uncertainties is derived with the form of the compound mean and variance to formulate the proposed RO approach. The proposed RO approach will reduce the risk for the obtained robust optimal designs considering parameter and model uncertainties becoming non-optimal and/or infeasible due to insufficiency of samples for GP modeling. Two test examples with different degrees of complexity are utilized to demonstrate the applicability and effectiveness of the proposed approach.

Simulation of Quantum Efficiency Spectroscopy for Amorphous Silicon P-I-N Junctions

1999 ◽  
Vol 557 ◽  
Author(s):  
Rodney Estwick ◽  
Vikram L. Dalal
Keyword(s):  
Electric Field ◽  
Amorphous Silicon ◽  
Quantum Efficiency ◽  
Applied Voltage ◽  
Forward Bias ◽  
Hole Mobility ◽  
Limited Range ◽  
D Model ◽  
Defect Densities ◽  
Minority Carriers

AbstractQuantum efficiency(QE) spectroscopy of amorphous silicon and alloy solar cells has been used for many years now to determine the mobility-lifetime products for minority carriers. Similarly, matching of I(V) curves, assuming a linear model for collection as a function of applied voltage, has been used to quantify the effects of degradation on cell performance by estimating changes in the collection length [or range] of holes. In this paper, we do a numerical simulation of these techniques, using the AMPS I-D model developed by Fonash and his coworkers. The simulation shows that neither the lifetime nor the electric field in the devices is constant as a function of position. Nor is the electric field a linear function of applied voltage, particularly when the voltage exceeds about half the built-in voltage. The uniformity of the lifetime depends on the applied bias and on the defect densities in the material. This variation in electric field and lifetime and nonlinearity with applied voltage makes questionable some of the conclusions drawn from fitting device I(V) curves, particularly under forward bias. However, when one uses only a limited range of forward bias, or, preferably, make measurements in cells with thicker i layers under reverse bias, one c.an make reasonable estimates of the hole mobility-lifetime(μτ) product or the collection lengthl The simulations also show that indeed, it is the hole μτ product which is the limiting parameter.

scholarly journals A Trust-based Mixture of Gaussian Processes Model for Reliable Regression in Participatory Sensing

2017 ◽  
Author(s):  
Qikun Xiang ◽  
Jie Zhang ◽  
Ido Nevat ◽  
Pengfei Zhang
Keyword(s):  
Real World ◽  
Gaussian Processes ◽  
Spatial Regression ◽  
Participatory Sensing ◽  
Sensing Applications ◽  
Different Types ◽  
Inaccurate Estimation ◽  
Real World Datasets ◽  
Gp Model ◽  
Mixture Of Gaussian

Data trustworthiness is a crucial issue in real-world participatory sensing applications. Without considering this issue, different types of worker misbehavior, especially the challenging collusion attacks, can result in biased and inaccurate estimation and decision making. We propose a novel trust-based mixture of Gaussian processes (GP) model for spatial regression to jointly detect such misbehavior and accurately estimate the spatial field. We develop a Markov chain Monte Carlo (MCMC)-based algorithm to efficiently perform Bayesian inference of the model. Experiments using two real-world datasets show the superior robustness of our model compared with existing approaches.

scholarly journals Scalable Gaussian Processes for Data-Driven Design using Big Data with Categorical Factors (IDETC2021-71570)

2021 ◽  
pp. 1-36
Author(s):  
Liwei Wang ◽  
Suraj Yerramilli ◽  
Akshay Iyer ◽  
Daniel Apley ◽  
Ping Zhu ◽  
...  
Keyword(s):  
Machine Learning ◽  
Gaussian Processes ◽  
Building Blocks ◽  
Variational Inference ◽  
Data Driven ◽  
Ternary Oxide ◽  
Latent Space ◽  
Multiple Materials ◽  
Qualitative Factors ◽  
Gp Model

Abstract Scientific and engineering problems often require the use of artificial intelligence to aid understanding and the search for promising designs. While Gaussian processes (GP) stand out as easy-to-use and interpretable learners, they have difficulties in accommodating big datasets, qualitative inputs, and multi-type responses obtained from different simulators, which has become a common challenge for data-driven design applications. In this paper, we propose a GP model that utilizes latent variables and functions obtained through variational inference to address the aforementioned challenges simultaneously. The method is built upon the latent variable Gaussian process (LVGP) model where qualitative factors are mapped into a continuous latent space to enable GP modeling of mixed-variable datasets. By extending variational inference to LVGP models, the large training dataset is replaced by a small set of inducing points to address the scalability issue. Output response vectors are represented by a linear combination of independent latent functions, forming a flexible kernel structure to handle multi-type responses. Comparative studies demonstrate that the proposed method scales well for large datasets, while outperforming state-of-the-art machine learning methods without requiring much hyperparameter tuning. In addition, an interpretable latent space is obtained to draw insights into the effect of qualitative factors, such as those associated with “building blocks” of architectures and element choices in metamaterial and materials design. Our approach is demonstrated for machine learning of ternary oxide materials and topology optimization of a multiscale compliant mechanism with aperiodic microstructures and multiple materials.

Modeling the Response of a Transient Thermal System Using Gaussian Processes

2005 ◽  
Author(s):  
A. F. Emery ◽  
D. Bardot
Keyword(s):  
Response Surface ◽  
Gaussian Processes ◽  
Sampling Techniques ◽  
Thermal System ◽  
Variable Parameters ◽  
Global Sensitivity ◽  
Data Points ◽  
Parameter Interactions ◽  
Pass Through ◽  
Transient Thermal

Estimating sensitivities and the uncertainties associated with variable parameters can be prohibitively expensive for complex systems, particularly when sampling techniques, e.g., Monte Carlo, are employed. One approach is to define a response surface based on easy to compute functions using least squares fitting. However, such a surface does not pass through each of the data points and makes it difficult to determine the degree of interaction between the parameters of the system. Parameter interactions can be accurately determined using global sensitivity, but it is computationally expensive. Gaussian Processes can be used to create an inexpensive to evaluate response surface that is an accurate representation of the data. The paper describes the use of Gaussian Processes in conjunction with global sensitivity to examine the behavior of a thermal system, showing that the combination is an effective tool.

3D finite-element forward modeling of electromagnetic data using vector and scalar potentials and unstructured grids

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. E149-E165 ◽  
Author(s):  
Seyedmasoud Ansari ◽  
Colin G. Farquharson
Keyword(s):  
Finite Element ◽  
Electric Field ◽  
Half Space ◽  
Normal Component ◽  
Forward Modeling ◽  
Computational Domain ◽  
Disk Model ◽  
Weighted Residuals ◽  
Physical Scale ◽  
Scalar Potentials

We present a finite-element solution to the 3D electromagnetic forward-modeling problem in the frequency domain. The method is based on decomposing the electric field into vector and scalar potentials in the Helmholtz equation and in the equation of conservation of charge. Edge element and nodal element basis functions were used, respectively, for the vector and scalar potentials. This decomposition was performed with the intention of satisfying the continuity of the tangential component of the electric field and the normal component of the current density across the interelement boundaries, therefore finding an efficient solution to the problem. The computational domain was subdivided into unstructured tetrahedral elements. The system of equations was discretized using the Galerkin variant of the weighted residuals method, with the approximated vector and scalar potentials as the unknowns of a sparse linear system. A generalized minimum residual solver with an incomplete LU preconditioner was used to iteratively solve the system. The solution method was validated using five examples. In the first and second examples, the fields generated by small dipoles on the surface of a homogeneous half-space were compared against their corresponding analytic solutions. The third example provided a comparison with the results from an integral equation method for a long grounded wire source on a model with a conductive block buried in a less conductive half-space. The fourth example concerned verifying the method for a large conductivity contrast where a magnetic dipole transmitter-receiver pair moves over a graphite cube immersed in brine. Solutions from the numerical approach were in good agreement with the data from physical scale modeling of this scenario. The last example verified the solution for a resistive disk model buried in marine conductive sediments. For all examples, convergence of the solution that used potentials were significantly quicker than that using the electric field.

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