scholarly journals Model identification of a hydropulse system with periodic external action

2019 ◽  
Author(s):  
V. G. Gorodetskyi
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Autonomous System ◽  
Model Identification ◽  
Identification Problem ◽  
External Action ◽  
Model Parameters ◽  
Impulse System ◽  
Constant Coefficients ◽  
Modeling Task

Functioning of hydro-impulse systems, usually involves the existence of some periodic external action, that determines the type of model. In this case they use, as a mathematical model, non-autonomous system of ordinary differential equations. Sometimes external action information is incomplete or absent. This may complicate the modeling task. For example, in the operation of hydro-pulse systems, not only their constant parameters but also the type of external action may be unknown. This study is devoted to the identification of a model of a hydro-impulse system in the form of a non-autonomous system of ordinary differential equations. The general form of the equations and one of the observed variables of the system are known, while the constant coefficients of the equations are unknown. We consider the identification problem when we know almost nothing about external action. Namely, we suppose that only its periodic character is known, and its form, period, and phase shift are unknown. Such a problem is obviously more complicated than a typical one, when the external action and the output are completely known, and only the constant coefficients of the equations of the system are to be found. As it is known, for some parameter sets and periodic external action, the observed variable may not be periodic, which makes it impossible to determine the period and other parameters of external oscillations in a simple way. Therefore, identification of the external action is also part of the formulated task. To solve this problem we use algorithm that allows to determine the model parameters with utilizing a known observed variable and incomplete information on the external action. Moreover, the observed variable can be either regular or chaotic.

Modeling eutrophic lakes: From mass balance laws to ordinary differential equations

2017 ◽  
Vol 14 (11) ◽  
pp. 1750151
Author(s):  
Addolorata Marasco ◽  
Luciano Ferrara ◽  
Antonio Romano
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Homogeneous Model ◽  
Stable Steady State ◽  
Model Parameters ◽  
Balance Laws ◽  
State Variables ◽  
Phosphorus Cycle ◽  
Eutrophic Lakes ◽  
The Mean

Starting from integral balance laws, a model based on nonlinear ordinary differential equations (ODEs) describing the evolution of Phosphorus cycle in a lake is proposed. After showing that the usual homogeneous model is not compatible with the mixture theory, we prove that an ODEs model still holds but for the mean values of the state variables provided that the nonhomogeneous involved fields satisfy suitable conditions. In this model the trophic state of a lake is described by the mean densities of Phosphorus in water and sediments, and phytoplankton biomass. All the quantities appearing in the model can be experimentally evaluated. To propose restoration programs, the evolution of these state variables toward stable steady state conditions is analyzed. Moreover, the local stability analysis is performed with respect to all the model parameters. Some numerical simulations and a real application to lake Varese conclude the paper.

scholarly journals Linearization of Two Second-Order Ordinary Differential Equations via Fiber Preserving Point Transformations

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Sakka Sookmee ◽  
Sergey V. Meleshko
Keyword(s):  
Linear System ◽  
General Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Point Transformations ◽  
Constant Coefficients ◽  
Linearizable System

The necessary form of a linearizable system of two second-order ordinary differential equations y1″=f1(x,y1,y2,y1′,y2′), y2″=f2(x,y1,y2,y1′,y2′) is obtained. Some other necessary conditions were also found. The main problem studied in the paper is to obtain criteria for a system to be equivalent to a linear system with constant coefficients under fiber preserving transformations. A linear system with constant coefficients is chosen because of its simplicity in finding the general solution. Examples demonstrating the procedure of using the linearization theorems are presented.

scholarly journals Systems biology informed deep learning for inferring parameters and hidden dynamics

2020 ◽  
Vol 16 (11) ◽  
pp. e1007575 ◽  
Author(s):  
Alireza Yazdani ◽  
Lu Lu ◽  
Maziar Raissi ◽  
George Em Karniadakis
Keyword(s):  
Deep Learning ◽  
Systems Biology ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Learning Algorithm ◽  
Optimization Procedure ◽  
System Level ◽  
Benchmark Problems ◽  
Model Parameters ◽  
Unknown Parameters

Mathematical models of biological reactions at the system-level lead to a set of ordinary differential equations with many unknown parameters that need to be inferred using relatively few experimental measurements. Having a reliable and robust algorithm for parameter inference and prediction of the hidden dynamics has been one of the core subjects in systems biology, and is the focus of this study. We have developed a new systems-biology-informed deep learning algorithm that incorporates the system of ordinary differential equations into the neural networks. Enforcing these equations effectively adds constraints to the optimization procedure that manifests itself as an imposed structure on the observational data. Using few scattered and noisy measurements, we are able to infer the dynamics of unobserved species, external forcing, and the unknown model parameters. We have successfully tested the algorithm for three different benchmark problems.

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