rodeo: Probabilistic Methods of Parameter Inference for Ordinary Differential Equations

2025/06/26 by Wu, Mohan, Lysy, Martin
#Computation (stat.CO) #FOS: Computer and information sciences

paper · doi:10.48550/arxiv.2506.21776

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.

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Related

• Stable Implementation of Probabilistic ODE Solvers
• Data-Adaptive Probabilistic Likelihood Approximation for Ordinary Differential Equations
• A Probabilistic State Space Model for Joint Inference from Differential Equations and Data
• Probabilistic ODE Solutions in Millions of Dimensions
• A probabilistic model for the numerical solution of initial value problems