scholarly journals Optimal models for estimating future infected cases of COVID-19 in Oman

2020 ◽  
Vol 9 (2) ◽  
pp. 53-66
Author(s):  
Ahmed Al-Siyabi ◽  
Mehiddin Al-Baali ◽  
Anton Purnama
Keyword(s):  
Optimization Problem ◽  
Nonlinear Least Squares ◽  
High Rate ◽  
Unknown Parameters ◽  
Numerical Experience ◽  
Fast Spreading ◽  
Modification Technique ◽  
Least Squares Optimization ◽  
Simple Ratio ◽  
Quasi Newton

The recent coronavirus disease 2019 (COVID-19) outbreak is of high importance in research topics due to its fast spreading and high rate of infections across the world. In this paper, we test certain optimal models of forecasting daily new cases of COVID-19 in Oman. It is based on solving a certain nonlinear least-squares optimization problem that determines some unknown parameters in fitting some mathematical models. We also consider extension to these models to predict the future number of infection cases in Oman. The modification technique introduces a simple ratio rate of changes in the daily infected cases. This average ratio is computed by employing the rule of Al-Baali [Numerical experience with a class of self-scaling quasi-Newton algorithms, JOTA, 96 (1998), pp. 533–553], in a sense to be defined, for measuring the infection changes.

scholarly journals Elastic Full-Waveform Inversion Using Migration‑Based Depth Reflector Representation in the Data Domain

2020 ◽  
Author(s):  
Vladimir Cheverda
Keyword(s):  
Seismic Data ◽  
Optimization Problem ◽  
Waveform Inversion ◽  
Nonlinear Least Squares ◽  
Model Space ◽  
Full Waveform Inversion ◽  
Brute Force ◽  
Data Inversion ◽  
Full Waveform ◽  
Least Squares Optimization

Full-waveform seismic data inversion has given rise to hope for the simultaneous and automated execution of tomography and imaging by solving a nonlinear least-squares optimization problem. As previously recognized, brute force minimization by classical methods is hopeless if the data lacks low temporal frequencies. The article developed a reliable numerical method for recovering smooth velocity using model space decomposition. We present realistic synthetic examples to test the presented algorithm.

Towards Adjoint-Based Inversion of the Lamé Parameter Field for Slender Structures With Cantilever Loading

2016 ◽  
Author(s):  
Soheil Fatehiboroujeni ◽  
Noemi Petra ◽  
Sachin Goyal
Keyword(s):  
Inverse Problem ◽  
Optimization Problem ◽  
Nonlinear Least Squares ◽  
Constitutive Law ◽  
Observation Error ◽  
Unknown Parameters ◽  
Cost Functional ◽  
Parameter Field ◽  
Dynamics Simulations ◽  
Slender Structures

Continuum models of slender structures are effective in simulating the mechanics of nano-scale filaments. However, the accuracy of these simulations strictly depends on the knowledge of the constitutive laws that may in general be non-homogeneous. It necessitates an inverse problem framework that can leverage the data provided by physical experiments and molecular dynamics simulations to estimate the unknown parameters in the constitutive law. In this paper, we formulate a simple but representative inverse problem as a nonlinear least-squares optimization problem whose cost functional is the misfit between synthetic observations of a cantilever displacement field and model predictions. A Tikhonov regularization term is added to the cost functional to render the problem well-posed and account for observational error. We solve this optimization problem with an adjoint-based inexact Newton-conjugate gradient method. We show that the reconstruction of the Lamé parameter field converges to the exact coefficient as the observation error decreases.

Adaptive Complex Method for Efficient Design Optimization

2007 ◽  
Author(s):  
Marcus Pettersson ◽  
Johan O¨lvander
Keyword(s):  
Design Optimization ◽  
Optimization Problem ◽  
Global Optimum ◽  
Direct Search ◽  
Complex Method ◽  
Efficient Design ◽  
Direct Search Methods ◽  
Simulation Based ◽  
Set Of Points ◽  
Quasi Newton

Box’s Complex method for direct search has shown promise when applied to simulation based optimization. In direct search methods, like Box’s Complex method, the search starts with a set of points, where each point is a solution to the optimization problem. In the Complex method the number of points must be at least one plus the number of variables. However, in order to avoid premature termination and increase the likelihood of finding the global optimum more points are often used at the expense of the required number of evaluations. The idea in this paper is to gradually remove points during the optimization in order to achieve an adaptive Complex method for more efficient design optimization. The proposed method shows encouraging results when compared to the Complex method with fix number of points and a quasi-Newton method.

Extraction of a Dynamic Multiport Compact Thermal Model for a Silicon Microthruster

2004 ◽  
Vol 1 (1) ◽  
pp. 30-38
Author(s):  
M. Salleras ◽  
J. Palacin ◽  
I. García ◽  
M. Puig ◽  
J. Samitier ◽  
...  
Keyword(s):  
Thermal Model ◽  
Nonlinear Least Squares ◽  
Element Model ◽  
Search Algorithms ◽  
Sequential Search ◽  
Complete Structure ◽  
Fem Model ◽  
Hybrid Combination ◽  
Least Squares Optimization ◽  
Thermal Simulations

In this work, a methodology to extract dynamic multiport compact thermal model from finite element model (FEM) thermal simulations is presented. The proposed methodology is applied to an innovative silicon microthruster. The boundary conditions of the FEM model have been estimated from experimental measurements. The analysis of these transients with the methodology presented delivers a dynamic multiport compact RC model representation of the complete structure. The topology and sizing of the components is provided by a hybrid combination of Sequential Search algorithms together with nonlinear least squares optimization.

scholarly journals Least Squares Optimization: From Theory to Practice

Robotics ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 51 ◽  
Author(s):  
Giorgio Grisetti ◽  
Tiziano Guadagnino ◽  
Irvin Aloise ◽  
Mirco Colosi ◽  
Bartolomeo Della Corte ◽  
...  
Keyword(s):  
Computer Vision ◽  
Least Squares ◽  
Open Source ◽  
State Of The Art ◽  
Nonlinear Least Squares ◽  
Research Community ◽  
Specific Domain ◽  
Theory To Practice ◽  
Least Squares Optimization ◽  
Computer Vision Systems

Nowadays, Nonlinear Least-Squares embodies the foundation of many Robotics and Computer Vision systems. The research community deeply investigated this topic in the last few years, and this resulted in the development of several open-source solvers to approach constantly increasing classes of problems. In this work, we propose a unified methodology to design and develop efficient Least-Squares Optimization algorithms, focusing on the structures and patterns of each specific domain. Furthermore, we present a novel open-source optimization system that addresses problems transparently with a different structure and designed to be easy to extend. The system is written in modern C++ and runs efficiently on embedded systemsWe validated our approach by conducting comparative experiments on several problems using standard datasets. The results show that our system achieves state-of-the-art performances in all tested scenarios.

scholarly journals Parameterized Nonlinear Least Squares for Unsupervised Nonlinear Spectral Unmixing

2019 ◽  
Vol 11 (2) ◽  
pp. 148 ◽  
Author(s):  
Risheng Huang ◽  
Xiaorun Li ◽  
Haiqiang Lu ◽  
Jing Li ◽  
Liaoying Zhao
Keyword(s):  
Least Squares ◽  
Optimization Problem ◽  
Nonnegative Matrix Factorization ◽  
Optimization Problems ◽  
State Of The Art ◽  
Synthetic Data ◽  
Nonnegative Matrix ◽  
Nonlinear Least Squares ◽  
Hyperspectral Data ◽  
Spectral Unmixing

This paper presents a new parameterized nonlinear least squares (PNLS) algorithm for unsupervised nonlinear spectral unmixing (UNSU). The PNLS-based algorithms transform the original optimization problem with respect to the endmembers, abundances, and nonlinearity coefficients estimation into separate alternate parameterized nonlinear least squares problems. Owing to the Sigmoid parameterization, the PNLS-based algorithms are able to thoroughly relax the additional nonnegative constraint and the nonnegative constraint in the original optimization problems, which facilitates finding a solution to the optimization problems . Subsequently, we propose to solve the PNLS problems based on the Gauss–Newton method. Compared to the existing nonnegative matrix factorization (NMF)-based algorithms for UNSU, the well-designed PNLS-based algorithms have faster convergence speed and better unmixing accuracy. To verify the performance of the proposed algorithms, the PNLS-based algorithms and other state-of-the-art algorithms are applied to synthetic data generated by the Fan model and the generalized bilinear model (GBM), as well as real hyperspectral data. The results demonstrate the superiority of the PNLS-based algorithms.

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