Year: 2025
Type: article
Abstract: . Fitting models to data to obtain distributions of consistent parameter values is important for uncertainty quantification, model comparison, and prediction. Standard Markov chain Monte Carlo (MCMC) approaches for fitting ordinary differential equations (ODEs) to time-series data involve proposing trial parameter sets, numerically integrating the ODEs forward in time, and accepting or rejecting the trial parameter sets. When the model dynamics depend nonlinearly on the parameters, as is generally the case, trial parameter sets are often rejected, and MCMC approaches become prohibitively computationally costly to converge. Here, we build on methods for numerical continuation and trajectory optimization to introduce an approach in which we use Langevin dynamics in the joint space of variables and parameters to sample models that satisfy constraints on the dynamics. We demonstrate the method by sampling Hopf bifurcations and limit cycles of a model of a biochemical oscillator in a Bayesian framework for parameter estimation, and we attain performance that matches or exceeds the performance of leading MCMC approaches that require numerically integrating the ODEs forward in time. We describe numerical experiments that provide insight into the speedup. The method is general and can be used in any framework for parameter estimation and model selection.
DOI: 10.1137/24m1691569
Authors: Chris Chi, Jonathan Weare, Aaron R. Dinner
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: Using systematic computational approaches to elucidate the molecular and network dynamics underlying a circadian clock, G2170237104, DMS/NIGMS 1: Design and Analysis of Machine Learning Approaches for Long Timescale Prediction from Short Trajectory Data, NSF-Simons National Institute for Theory and Mathematics in Biology, G4225273607, G718488500
OpenAlex ID: W4413771190