scholarly journals Global Variance as a Utility Function in Bayesian Optimization

2021 ◽  
Vol 3 (1) ◽  
pp. 3
Author(s):  
Roland Preuss ◽  
Udo von Toussaint
Keyword(s):  
Utility Function ◽  
Parameter Space ◽  
Region Of Interest ◽  
Optimization Procedure ◽  
Target Surface ◽  
Good Choice ◽  
Fine Tuning ◽  
Bayesian Optimization ◽  
Surrogate Surface ◽  
Tool Set

A Gaussian-process surrogate model based on already acquired data is employed to approximate an unknown target surface. In order to optimally locate the next function evaluations in parameter space a whole variety of utility functions are at one’s disposal. However, good choice of a specific utility or a certain combination of them prepares the fastest way to determine a best surrogate surface or its extremum for lowest amount of additional data possible. In this paper, we propose to consider the global (integrated) variance as an utility function, i.e., to integrate the variance of the surrogate over a finite volume in parameter space. It turns out that this utility not only complements the tool set for fine tuning investigations in a region of interest but expedites the optimization procedure in toto.

scholarly journals Updated Kriging-Assisted Shape Optimization of a Gravity Dam

Water ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 87
Author(s):  
Yongqiang Wang ◽  
Ye Liu ◽  
Xiaoyi Ma
Keyword(s):  
Surrogate Model ◽  
Computational Cost ◽  
Region Of Interest ◽  
Optimization Procedure ◽  
Optimal Shape ◽  
Small Sample ◽  
Gravity Dam ◽  
Kriging Surrogate Model ◽  
Gravity Dams ◽  
Sample Set

The numerical simulation of the optimal design of gravity dams is computationally expensive. Therefore, a new optimization procedure is presented in this study to reduce the computational cost for determining the optimal shape of a gravity dam. Optimization was performed using a combination of the genetic algorithm (GA) and an updated Kriging surrogate model (UKSM). First, a Kriging surrogate model (KSM) was constructed with a small sample set. Second, the minimizing the predictor strategy was used to add samples in the region of interest to update the KSM in each updating cycle until the optimization process converged. Third, an existing gravity dam was used to demonstrate the effectiveness of the GA–UKSM. The solution obtained with the GA–UKSM was compared with that obtained using the GA–KSM. The results revealed that the GA–UKSM required only 7.53% of the total number of numerical simulations required by the GA–KSM to achieve similar optimization results. Thus, the GA–UKSM can significantly improve the computational efficiency. The method adopted in this study can be used as a reference for the optimization of the design of gravity dams.

scholarly journals Exploring the parameter space of modified supergravity for double inflation and primordial black hole formation

2021 ◽  
Author(s):  
Ryotaro Ishikawa ◽  
Sergei V Ketov
Keyword(s):  
Black Hole ◽  
Dark Matter ◽  
Power Spectrum ◽  
Parameter Space ◽  
Background Radiation ◽  
Fine Tuning ◽  
Primordial Black Hole ◽  
Peak Enhancement ◽  
Microwave Background Radiation ◽  
Cosmological Inflation

Abstract We study the parameter space of the effective (with two scalars) models of cosmological inflation and primordial black hole (PBH) formation in the modified (R+ R 2) supergravity. Our models describe double inflation, whose first stage is driven by Starobinsky’s scalaron coming from the R 2 gravity, and whose second stage is driven by another scalar belonging to the supergravity multiplet. The ultra-slow-roll regime between the two stages leads a large peak (enhancement) in the power spectrum of scalar perturbations, which results in efficient PBH formation. Both inflation and PBH formation are generic in our models, while those PBH can account for a significant part or the whole of dark matter. Some of the earlier proposed models in the same class are in tension (over 3σ) with the observed value of the scalar tilt ns , so that we study more general models with more parameters, and investigate the dependence of the cosmological tilts (ns,r) and the scalar power spectrum enhancement upon the parameters. The PBH masses and their density fraction (as part of dark matter) are also calculated. A good agreement (between 2σ and 3σ) with the observed value of ns requires fine tuning of the parameters, and it is only realized in the so-called δ-models. Our models offer the (super)gravitational origin of inflation, PBH and dark matter together, and may be confirmed or falsified by future precision measurements of the cosmic microwave background radiation and PBH-induced gravitational waves.

scholarly journals Machine-learning model selection and parameter estimation from kinetic data of complex first-order reaction systems

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0255675
Author(s):  
László Zimányi ◽  
Áron Sipos ◽  
Ferenc Sarlós ◽  
Rita Nagypál ◽  
Géza I. Groma
Keyword(s):  
Machine Learning ◽  
Time Window ◽  
Learning Algorithm ◽  
Optimization Procedure ◽  
Bayesian Optimization ◽  
Spectroscopic Methods ◽  
Spectroscopic Techniques ◽  
Technical Parameters ◽  
First Order ◽  
Dense Distribution

Dealing with a system of first-order reactions is a recurrent issue in chemometrics, especially in the analysis of data obtained by spectroscopic methods applied on complex biological systems. We argue that global multiexponential fitting, the still common way to solve such problems, has serious weaknesses compared to contemporary methods of sparse modeling. Combining the advantages of group lasso and elastic net—the statistical methods proven to be very powerful in other areas—we created an optimization problem tunable from very sparse to very dense distribution over a large pre-defined grid of time constants, fitting both simulated and experimental multiwavelength spectroscopic data with high computational efficiency. We found that the optimal values of the tuning hyperparameters can be selected by a machine-learning algorithm based on a Bayesian optimization procedure, utilizing widely used or novel versions of cross-validation. The derived algorithm accurately recovered the true sparse kinetic parameters of an extremely complex simulated model of the bacteriorhodopsin photocycle, as well as the wide peak of hypothetical distributed kinetics in the presence of different noise levels. It also performed well in the analysis of the ultrafast experimental fluorescence kinetics data detected on the coenzyme FAD in a very wide logarithmic time window. We conclude that the primary application of the presented algorithms—implemented in available software—covers a wide area of studies on light-induced physical, chemical, and biological processes carried out with different spectroscopic methods. The demand for this kind of analysis is expected to soar due to the emerging ultrafast multidimensional infrared and electronic spectroscopic techniques that provide very large and complex datasets. In addition, simulations based on our methods could help in designing the technical parameters of future experiments for the verification of particular hypothetical models.

scholarly journals Automatic Deep Feature Learning via Patch-Based Deep Belief Network for Vertebrae Segmentation in CT Images

2018 ◽  
Vol 9 (1) ◽  
pp. 69 ◽  
Author(s):  
Syed Furqan Qadri ◽  
Danni Ai ◽  
Guoyu Hu ◽  
Mubashir Ahmad ◽  
Yong Huang ◽  
...  
Keyword(s):  
Computational Cost ◽  
Feature Learning ◽  
Region Of Interest ◽  
Ct Images ◽  
Feature Reduction ◽  
Fine Tuning ◽  
Deep Feature ◽  
Image Patches ◽  
Contrastive Divergence ◽  
Vertebrae Segmentation

Precise automatic vertebra segmentation in computed tomography (CT) images is important for the quantitative analysis of vertebrae-related diseases but remains a challenging task due to high variation in spinal anatomy among patients. In this paper, we propose a deep learning approach for automatic CT vertebra segmentation named patch-based deep belief networks (PaDBNs). Our proposed PaDBN model automatically selects the features from image patches and then measures the differences between classes and investigates performance. The region of interest (ROI) is obtained from CT images. Unsupervised feature reduction contrastive divergence algorithm is applied for weight initialization, and the weights are optimized by layers in a supervised fine-tuning procedure. The discriminative learning features obtained from the steps above are used as input of a classifier to obtain the likelihood of the vertebrae. Experimental results demonstrate that the proposed PaDBN model can considerably reduce computational cost and produce an excellent performance in vertebra segmentation in terms of accuracy compared with state-of-the-art methods.

scholarly journals MFBO-SSM: Multi-Fidelity Bayesian Optimization for Fast Inference in State-Space Models

2019 ◽  
Vol 33 ◽  
pp. 7858-7865 ◽  
Author(s):  
Mahdi Imani ◽  
Seyede Fatemeh Ghoreishi ◽  
Douglas Allaire ◽  
Ulisses M. Braga-Neto
Keyword(s):  
State Space ◽  
Parameter Space ◽  
Sequential Monte Carlo ◽  
Optimization Techniques ◽  
State Space Models ◽  
Bayesian Optimization ◽  
Particle Methods ◽  
Estimation Methods ◽  
Nonlinear State Space Models ◽  
Nonlinear State

Nonlinear state-space models are ubiquitous in modeling real-world dynamical systems. Sequential Monte Carlo (SMC) techniques, also known as particle methods, are a well-known class of parameter estimation methods for this general class of state-space models. Existing SMC-based techniques rely on excessive sampling of the parameter space, which makes their computation intractable for large systems or tall data sets. Bayesian optimization techniques have been used for fast inference in state-space models with intractable likelihoods. These techniques aim to find the maximum of the likelihood function by sequential sampling of the parameter space through a single SMC approximator. Various SMC approximators with different fidelities and computational costs are often available for sample-based likelihood approximation. In this paper, we propose a multi-fidelity Bayesian optimization algorithm for the inference of general nonlinear state-space models (MFBO-SSM), which enables simultaneous sequential selection of parameters and approximators. The accuracy and speed of the algorithm are demonstrated by numerical experiments using synthetic gene expression data from a gene regulatory network model and real data from the VIX stock price index.

scholarly journals Vision-Based Lane Departure Detection Using a Stacked Sparse Autoencoder

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Zengcai Wang ◽  
Xiaojin Wang ◽  
Lei Zhao ◽  
Guoxin Zhang
Keyword(s):  
Polar Angle ◽  
Region Of Interest ◽  
Lane Detection ◽  
Fine Tuning ◽  
High Detection Rate ◽  
Softmax Classifier ◽  
Lane Departure ◽  
Detection Approach ◽  
Sparse Autoencoder ◽  
Stacked Sparse Autoencoder

This paper presents a lane departure detection approach that utilizes a stacked sparse autoencoder (SSAE) for vehicles driving on motorways or similar roads. Image preprocessing techniques are successfully executed in the initialization procedure to obtain robust region-of-interest extraction parts. Lane detection operations based on Hough transform with a polar angle constraint and a matching algorithm are then implemented for two-lane boundary extraction. The slopes and intercepts of lines are obtained by converting the two lanes from polar to Cartesian space. Lateral offsets are also computed as an important step of feature extraction in the image pixel coordinate without any intrinsic or extrinsic camera parameter. Subsequently, a softmax classifier is designed with the proposed SSAE. The slopes and intercepts of lines and lateral offsets are the feature inputs. A greedy, layer-wise method is employed based on the inputs to pretrain the weights of the entire deep network. Fine-tuning is conducted to determine the global optimal parameters by simultaneously altering all layer parameters. The outputs are three detection labels. Experimental results indicate that the proposed approach can detect lane departure robustly with a high detection rate. The efficiency of the proposed method is demonstrated on several real images.

scholarly journals Properties of Carbon-Oxygen White Dwarf Merger Remnants

2011 ◽  
Vol 7 (S281) ◽  
pp. 280-283 ◽  
Author(s):  
Chenchong Zhu ◽  
Philip Chang ◽  
Marten van Kerkwijk ◽  
James Wadsley
Keyword(s):  
Parameter Space ◽  
White Dwarf ◽  
Initial Conditions ◽  
Fine Tuning ◽  
Large Set

AbstractRecent studies have shown that for suitable initial conditions both super- and sub-Chandrasekhar mass carbon-oxygen white dwarf mergers produce explosions similar to observed SNe Ia. The question remains, however, how much fine tuning is necessary to produce these conditions. We performed a large set of SPH merger simulations, sweeping the possible parameter space. We find trends for merger remnant properties, and discuss how our results affect the viability of our recently proposed sub-Chandrasekhar merger channel for SNe Ia.

Exploring the overall behaviour of solutions of recursive computational models

2005 ◽  
Vol 24 (1) ◽  
pp. 167-178
Author(s):  
J.S. Hämäläinen ◽  
M. Aunola ◽  
S.R. Malm
Keyword(s):  
Case Studies ◽  
Parameter Space ◽  
Design Methodology ◽  
Computational Models ◽  
Simulation Models ◽  
Good Choice ◽  
Systematic Analysis ◽  
Content Type ◽  
The Stability

PurposeTo determine and/or examine overall behaviour of simulation models with large input using as few parameters as possible. To introduce a methodology describing stability of the partitioning of simulation results and the corresponding parameter space.Design/methodology/approachPartitionings of the parameter space are performed using real‐valued mappings called measures of merit. Tools for examining evolution of partitionings and correlations between different partitionings are developed. These tools are applied in two case studies within the field of electrical engineering.FindingsThe presented approach provides tools for systematic analysis of parametrised models. Since the classification of results is based on measures of merit, a good choice both simplifies the analysis and improves the stability of partitioning. Included case studies highlight these conclusions.Research limitations/implicationsThe present form of the methodology is targeted at recursive simulations. Use of more complex partitioning procedures could be the topic of further research.Originality/valueSolid framework for handling and analysing complex parametrised simulations.

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