rodeo: Probabilistic Methods of Parameter Inference for Ordinary Differential Equations

TL;DR

rodeo is a Python library that offers fast, scalable probabilistic ODE solvers and parameter inference methods, improving reliability by accounting for numerical uncertainty in dynamical system analysis.

Contribution

The paper introduces rodeo, a new Python library that combines probabilistic ODE solvers with efficient parameter inference techniques, leveraging AD and JIT for speed and scalability.

Findings

rodeo provides linear scaling in evaluation points and system variables.

Probabilistic solvers improve parameter estimation accuracy.

The library demonstrates fast and reliable inference across various ODE systems.

Abstract

Parameter estimation for ordinary differential equations (ODEs) plays a fundamental role in the analysis of dynamical systems. Generally lacking closed-form solutions, ODEs are traditionally approximated using deterministic solvers. However, there is a growing body of evidence to suggest that probabilistic ODE solvers produce more reliable parameter estimates by better accounting for numerical uncertainty. Here we present rodeo, a Python library providing a fast, lightweight, and extensible interface to a broad class of probabilistic ODE solvers, along with several associated methods for parameter inference. At its core, rodeo provides a probabilistic solver that scales linearly in both the number of evaluation points and system variables. Furthermore, by leveraging state-of-the-art automatic differentiation (AD) and just-in-time (JIT) compiling techniques, rodeo is shown across several examples to provide fast, accurate, and scalable parameter inference for a variety of ODE systems.