Generalized Ordinary Differential Equation Models
نویسندگان
چکیده
منابع مشابه
Robust estimation for ordinary differential equation models.
Applied scientists often like to use ordinary differential equations (ODEs) to model complex dynamic processes that arise in biology, engineering, medicine, and many other areas. It is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers. We propose a robust method to address this problem. The dynamic process is represented with a n...
متن کاملA Universal Ordinary Differential Equation
An astonishing fact was established by Lee A. Rubel in 81: there exists a fixed non-trivial fourthorder polynomial differential algebraic equation (DAE) such that for any positive continuous function φ on the reals, and for any positive continuous function (t), it has a C∞ solution with |y(t) − φ(t)| < (t) for all t. Lee A. Rubel provided an explicit example of such a polynomial DAE. Other exam...
متن کاملFast integration-based prediction bands for ordinary differential equation models
MOTIVATION To gain a deeper understanding of biological processes and their relevance in disease, mathematical models are built upon experimental data. Uncertainty in the data leads to uncertainties of the model's parameters and in turn to uncertainties of predictions. Mechanistic dynamic models of biochemical networks are frequently based on nonlinear differential equation systems and feature ...
متن کاملCause and cure of sloppiness in ordinary differential equation models.
Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objecti...
متن کاملScalable Inference of Ordinary Differential Equation Models of Biochemical Processes
Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about the behavior of latent variables or the process under new experimental conditions. Complementarily, inference of model structure can be used to identify the mo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the American Statistical Association
سال: 2014
ISSN: 0162-1459,1537-274X
DOI: 10.1080/01621459.2014.957287