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Optimization Bayesian Inversion Using Markov Chain Quasi-Monte Carlo Sampling on Amplitude.

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Optimization Bayesian Inversion Using Markov Chain Quasi-Monte Carlo Sampling on Amplitude.

Figure: Bayesian Optimization

Figure: Bayesian Optimization

Outline:

Introduction

Bayesian Optimization

  • Definition
  • Applications

References

1. Introduction:

In various fields of study, optimization methods are used to create solutions that maximize or minimize specific research parameters, such as minimizing expenses in the manufacture of a thing or service, maximizing earnings, minimizing raw materials in the development of a good or maximizing productivity. The word is widely given to Jonas Mockus, who coined it in a series of writings on global optimization in the 1970s and 1980s.

2. Bayesian Optimization:

Definition:

Bayesian Optimization is a method that uses the Bayes theorem to direct the search for the minimum or maximum of an objective function. It is a good strategy for objective functions that are complex, noisy, and/or expensive to evaluate.

The Bayesian optimization approach is a good choice for improving the hyperparameters of classification and regression models. Functions that are nondifferentiable, discontinuous, and time-consuming to evaluate can be optimized using Bayesian optimization.

Simply put, you can utilize it in any application area where you have a lot of diverse or noisy data or where you require a clear knowledge of your uncertainty. Markov chain Monte Carlo (MCMC) is a simulation technique that can be used to determine and sample from the posterior distribution. As a result, it is used to fit a model and pull samples from the model parameters' joint posterior distribution.

The main purpose of is to create an effective Bayesian inversion [1] framework for analyzing marine seismic Amplitude Versus Angle and Controlled-Source Electromagnetic data for marine reservoir characterization in this article. The framework employs a multi-chain Markov-chain Monte Carlo sampler that is a cross between the Differential Evolution Adaptive Metropolis and the Adaptive Metropolis samplers.

Using marine seismic and Controlled-Source Electromagnetic data, the inversion framework is put to the test by calculating reservoir-fluid saturations and porosity. The multi-chain Markov-chain Monte Carlo method is scalable in terms of chain count and is beneficial for computationally demanding Bayesian model calibration in scientific and engineering situations.

As an example, the approach is utilized to estimate the porosity and saturations in a realistic layered synthetic reservoir rapidly and effectively. The results show that the joint inversion of seismic Amplitude Versus Angle and Controlled-Source Electromagnetic gives better estimation of reservoir saturations than the seismic Amplitude Versus Angle single inversion, especially for parameters in deep reservoirs.

Applications of Bayesian Optimization:

The best adjusting technique, however, might not be Bayesian optimization. Numerous studies have shown that compared to random search, the Bayesian optimization strategy only makes a small amount of additional progress. Additionally, the Bayesian optimization struggles in large dimensionality. There are many applications of Bayesian Optimization some discussed here,

  • Bayesian Optimization is used to Handle the difficulties:
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The method has been used to handle a variety of difficulties, including learning to rank, computer graphics, and visual design.

  • Bayesian Optimization is Used in Robotics Network:

Bayesian Optimization is used in robotics [2] sensor networks automated algorithm configuration [3]. Robotics uses optimization to discover the best way to improve 3D space accuracy, reduce vibrations, select the ideal robot base point for applications to cut down on application time, and find constructive or functional factors that ensure lower energy consumption.

  • Bayesian Optimization is Used in Machine Learning:

Bayesian Optimization is used in automated machine learning toolboxes reinforcement learning, planning, visual attention. To fine-tune the hyperparameters of a given well-performing model on a validation dataset, Bayesian optimization is frequently employed in applied machine learning.

  • Bayesian Optimization is used in Architecture Configuration:

Bayesian Optimization is used in deep learning architecture configuration, static programmed analysis.

  • Bayesian Optimization is used in experimental particle physics chemistry:

Bayesian Optimization is used in experimental particle physics chemistry,

  • Bayesian Optimization is used in material designing:

Bayesian Optimization is used in designing material.

  • Bayesian Optimization is used in drug development:

Bayesian Optimization is used for drug development [4,5]. As a technique for overall mixed-race function optimization, Bayesian optimization has received research in several disciplines. We used these strategies to speed up method for development duties and improve pharmaceutical product formulation and manufacturing processes by eliminating the unnecessary experiments.

References:

[1] H. Ren, J. Ray, Z. Hou, M. Huang, J. Bao, and L. Swiler, "Bayesian inversion of seismic and electromagnetic data for marine gas reservoir characterization using multi-chain Markov chain Monte Carlo sampling," Journal of Applied Geophysics, vol. 147, pp. 68-80, 2017.

[2] J. Mockus, Bayesian approach to global optimization: theory and applications vol. 37: Springer Science & Business Media, 2012.

[3] F. Hutter, H. H. Hoos, and K. Leyton-Brown, "Sequential model-based optimization for general algorithm configuration," in international conference on learning and intelligent optimization, 2011, pp. 507-523.

[4] P. Ilten, M. Williams, and Y. Yang, "Event generator tuning using Bayesian optimization," Journal of Instrumentation, vol. 12, p. P04028, 2017.

[5] E. Cisbani, A. Del Dotto, C. Fanelli, M. Williams, M. Alfred, F. Barbosa, et al., "AI-optimized detector design for the future Electron-Ion Collider: the dual-radiator RICH case," Journal of Instrumentation, vol. 15, p. P05009, 2020.

This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.

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