Resource Efficient Datasets for Inferring Parameters of Differential Equations

Several real-world systems are described by parametric non-linear ordinary differential equations (ODEs) with unknown parameters.The nonlinearity makes parameter identification challenging, especially with only limited and noisy observations. To address this, we propose a novel framework that extends classical Optimal Experiment Design (OED) by linearizing non-linear ODE through neural network embeddings, transforming the system into a linear one. This allows us to apply linear OED techniques to non-linear systems. In particular, we demonstrate our approach on a task that involves selecting measurement points to identify the unknown parameters of the underlying ODE. Our method demonstrates improved parameter estimation and tighter confidence intervals compared to equidistant sampling in two non-linear test systems, showcasing its potential in optimizing experimental designs for more complex dynamical systems.