A locally sequential refinement of the growth dynamics identification

IF 1.1 4区工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Inverse Problems in Science and Engineering Pub Date : 2021-07-02 DOI:10.1080/17415977.2021.1948025

Mikhail Rem Romanovski

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引用次数: 1

Abstract

The approach is developed to specify a reconstruction of complicated functions using samples of limited size with invariant properties regarding the desired parameters. The idea is based on solutions to inverse problems, which should identify various representations of unknown parameters of a mathematical model and do so in a series. The sequential solutions to inverse problems ensure the identifiability of desired parameters that belong to an invariant family. The locally sequential refinement restricts local spikes additionally to the general regularization under a scheme of separate matching with observations. A simulation with inverse problems is applied to refine the known features of population dynamics. The reconstruction shows that the parameters of the Verhulst equation should be introduced as oscillatory functions. Based on the novel functional representation of the Verhulst equation parameters, the patterns of the COVID-19 spread and its progression in a given region are determined. The results emphasize the Verhulst equation’s character as a generalized and fruitful model for an object growth simulation.

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生长动力学识别的局部序列精化

该方法被开发为使用具有关于期望参数的不变性质的有限大小的样本来指定复杂函数的重构。这个想法是基于反问题的解决方案，反问题应该识别数学模型未知参数的各种表示，并以一系列的方式进行识别。逆问题的序列解确保了属于不变族的期望参数的可识别性。在与观测值单独匹配的方案下，除了一般正则化之外，局部序列细化还限制了局部尖峰。应用反问题模拟来精化种群动力学的已知特征。重建表明，Verhulst方程的参数应作为振荡函数引入。基于Verhulst方程参数的新函数表示，确定了新冠肺炎在给定区域的传播和发展模式。结果强调了Verhulst方程作为一个广义且富有成效的对象生长模拟模型的特点。

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来源期刊

Inverse Problems in Science and Engineering 工程技术-工程：综合

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Inverse Problems in Science and Engineering provides an international forum for the discussion of conceptual ideas and methods for the practical solution of applied inverse problems. The Journal aims to address the needs of practising engineers, mathematicians and researchers and to serve as a focal point for the quick communication of ideas. Papers must provide several non-trivial examples of practical applications. Multidisciplinary applied papers are particularly welcome. Topics include: -Shape design: determination of shape, size and location of domains (shape identification or optimization in acoustics, aerodynamics, electromagnets, etc; detection of voids and cracks). -Material properties: determination of physical properties of media. -Boundary values/initial values: identification of the proper boundary conditions and/or initial conditions (tomographic problems involving X-rays, ultrasonics, optics, thermal sources etc; determination of thermal, stress/strain, electromagnetic, fluid flow etc. boundary conditions on inaccessible boundaries; determination of initial chemical composition, etc.). -Forces and sources: determination of the unknown external forces or inputs acting on a domain (structural dynamic modification and reconstruction) and internal concentrated and distributed sources/sinks (sources of heat, noise, electromagnetic radiation, etc.). -Governing equations: inference of analytic forms of partial and/or integral equations governing the variation of measured field quantities.