Systematic Analysis of Nonlinearities in Complex Models

Authors

Alexander Shumway, Brigham Young University
Mark Transtrum, Brigham Young University

Keywords

nonlinearities, complex models, mathematical models, Jacobian matrix

College

Physical and Mathematical Sciences

Department

Physics and Astronomy

Abstract

Mathematical models are ubiquitous in science. Many models are nonlinear in the parameters and may have dozens to thousands of parameters and make hundreds to thousands of predictions. Analysis and application of these models is thus theoretically complicated and computationally expensive.

The standard method of model analysis is a model-by-model approach that relies on the intuition of expert researchers. Recent research, however, has shown that many models—known as sloppy models—are statistically similar, despite coming from widely varied fields⁴. This suggests the possibility of developing a theory of modeling in place of relying on expert intuition. Our research works toward such a theory by leveraging recent advances in sloppy models and information geometry to classify and quantify parameter nonlinearities in complex models.

Recommended Citation

Shumway, Alexander and Transtrum, Mark (2016) "Systematic Analysis of Nonlinearities in Complex Models," Journal of Undergraduate Research: Vol. 2016: Iss. 1, Article 228.
Available at: https://scholarsarchive.byu.edu/jur/vol2016/iss1/228