Nonlinear Mixed Effects Modeling of Deterministic and Stochastic Dynamical Systems in Wolfram Mathematica
Paper in proceeding, 2021

Nonlinear mixed effects (NLME) modeling is a powerful tool to analyze timeseries data from several individual entities in an experiment. In this paper, we give a brief overview of a package for NLME modeling in Wolfram Mathematica entitled NLMEModeling, implementing the first-order conditional estimation method with sensitivity equation-based gradients for parameter estimation. NLMEModeling supports mixed effects modeling of dynamical systems where the underlying dynamics are described by either ordinary or stochastic differential equations combined with observation equations with flexible observation error models. Moreover, NLMEModeling is a user-friendly package with functionality for parameter estimation, model diagnostics (such as goodness-of-fit analysis and visual predictive checks), and model simulation. The package is freely available and provides an extensible add-on to Wolfram Mathematica.

Stochastic differential equations

Ordinary differential equations

Nonlinear mixed effects

Modeling software

Wolfram Mathematica

First-order conditional estimation (FOCE)

Dynamical system models

Author

Jacob Leander

Fraunhofer-Chalmers Centre

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

AstraZeneca AB

Joachim Almquist

AstraZeneca R&D

Anna Johnning

Fraunhofer-Chalmers Centre

Julia Larsson

Fraunhofer-Chalmers Centre

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Mats Jirstrand

Fraunhofer-Chalmers Centre

IFAC-PapersOnLine

2405-8963 (ISSN) 24058963 (eISSN)

Vol. 54 7 409-414

19th IFAC Symposium on System Identification (SYSID)
Padova, Italy,

Subject Categories

Applied Mechanics

Probability Theory and Statistics

Control Engineering

DOI

10.1016/j.ifacol.2021.08.394

More information

Latest update

3/2/2022 1