🤖 AI Summary
Conventional ODE parameter estimation neglects numerical uncertainty in ODE solvers, leading to unreliable Bayesian inference. Method: We propose the first end-to-end probabilistic parameter inference framework for ODEs, featuring a lightweight, linear-complexity probabilistic ODE solver that explicitly incorporates numerical uncertainty into the Bayesian inference pipeline—integrated with automatic differentiation, just-in-time compilation, variational inference, and MCMC sampling. Contributions/Results: (1) We release the first open-source Python library enabling scalable probabilistic ODE solving; (2) Empirical evaluation across diverse ODE systems demonstrates faster convergence, higher estimation accuracy, and improved posterior calibration compared to deterministic baselines; (3) Inference speed improves by an order of magnitude, significantly enhancing the reliability and practicality of large-scale ODE parameter inference.
📝 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.