Preprocessing algorithms for the estimation of ordinary differential equation models with polynomial nonlinearities

Abstract

AbstractThe data analysis task of determining a model for an ordinary differential equation (ODE) system from given noisy solution data is addressed. Since modeling with ODE is ubiquitous in science and technology, finding ODE models from data is of paramount importance. Based on a previously published parameter estimation method for ODE models, four related model estimation algorithms were developed. The algorithms are tested for over 20 different polynomial ordinary equation systems comprising 60 equations at various noise levels. Two algorithms frequently compute the correct model. They are compared to the prominent SINDy-family for those SINDy-algorithms that have simple default hyperparameters. This demonstrates that they are comparable to SINDy and more resilient towards noise than the tested SINDy algorithms.