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.

开发该方法以使用具有关于所需参数的不变属性的有限大小的样本来指定复杂函数的重建。这个想法是基于逆问题的解决方案，它应该识别数学模型的未知参数的各种表示，并在一系列中这样做。逆问题的顺序解决方案确保了属于不变族的所需参数的可识别性。除了一般正则化之外，局部顺序细化还限制了局部尖峰在与观察单独匹配的方案下。应用具有逆问题的模拟来改进种群动态的已知特征。重构表明，Verhulst方程的参数应该作为振荡函数引入。基于 Verhulst 方程参数的新功能表示，确定了 COVID-19 传播的模式及其在给定区域的进展。结果强调了 Verhulst 方程作为对象生长模拟的通用且富有成效的模型的特征。