scholarly journals Semiparametric Mixed-Effects Ordinary Differential Equation Models with Heavy-Tailed Distributions

2021 ◽  
Author(s):  
Baisen Liu ◽  
Liangliang Wang ◽  
Yunlong Nie ◽  
Jiguo Cao
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Mixed Effects ◽  
Heavy Tailed Distributions ◽  
Differential Equation Models ◽  
Heavy Tailed

On the Existence of Optimal Controls

1962 ◽  
Vol 84 (1) ◽  
pp. 13-20 ◽  
Author(s):  
L. Markus ◽  
E. B. Lee
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Optimal Control ◽  
Optimal Controls ◽  
Optimum Control ◽  
Existence Of Optimal Controls ◽  
Differential Equation Models ◽  
Controlling Processes

The problem of existence of various types of optimum controls for controlling processes which are described by ordinary differential equation models is considered. The results presented enable one to test if there does exist an optimum control in the class of controls under consideration before proceeding to the construction of an optimal control.

scholarly journals Generalized Ordinary Differential Equation Models

2014 ◽  
Vol 109 (508) ◽  
pp. 1672-1682 ◽  
Author(s):  
Hongyu Miao ◽  
Hulin Wu ◽  
Hongqi Xue
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equation Models

scholarly journals Fides: Reliable Trust-Region Optimization for Parameter Estimation of Ordinary Differential Equation Models

2021 ◽  
Author(s):  
Fabian Froehlich ◽  
Peter Karl Sorger
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Ordinary Differential Equation ◽  
Model Calibration ◽  
Trust Region ◽  
Mass Action ◽  
Approximation Schemes ◽  
Benchmark Problems ◽  
Mass Action Kinetics ◽  
Differential Equation Models

Motivation: Because they effectively represent mass action kinetics, ordinary differential equation models are widely used to describe biochemical processes. Optimization-based calibration of these models on experimental data can be challenging, even for low-dimensional problems. However, reliable model calibration is a prerequisite for many subsequent analysis steps, including uncertainty analysis, model selection and biological interpretation. Although multiple hypothesis have been advanced to explain why optimization based calibration of biochemical models is challenging, there are few comprehensive studies that test these hypothesis and tools for performing such studies are also lacking. Results: We implemented an established trust-region method as a modular python framework (fides) to enable structured comparison of different approaches to ODE model calibration involving Hessian approximation schemes and trust-region subproblem solvers. We evaluate fides on a set of benchmark problems that include experimental data. We find a high variability in optimizer performance among different implementations of the same algorithm, with fides performing more reliably that other implementations investigated. Our investigation of possible sources of poor optimizer performance identify shortcomings in the widely used Gauss-Newton approximation. We address these shortcomings by proposing a novel hybrid Hessian approximation scheme that enhances optimizer performance.

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