A Sensitivity-based Framework for Calibrating Coupled Ordinary Differential Equations under Model Discrepancy

2026-10-06

AI Summary

This study addresses the challenges of parameter estimation bias and poor identifiability in coupled ODE models arising from inter-individual heterogeneity by proposing a sensitivity-based Bayesian calibration framework. The method computes forward gradients through the joint integration of sensitivity equations and incorporates automatic model structure constraints for regularization, effectively overcoming the reliance of conventional approaches on specific priors. Efficient posterior inference is achieved via an adaptive Metropolis-within-Gibbs sampler. Experimental evaluations on oscillator, infectious disease, and neuronal dynamics models demonstrate that the proposed framework substantially improves parameter estimation accuracy and predictive performance, offering a generalizable and robust solution for modeling heterogeneous dynamical systems.

Abstract

Coupled systems of ordinary differential equations (ODEs) are widely used to model complex physical and biological processes. In these applications, ODE model parameters must be calibrated to field data to enable prediction and parameter inference. In practice, the governing ODEs are an imperfect approximation to the true system, leading to non-negligible model discrepancy that must be incorporated to avoid biased parameter estimates. However, it is well known that highly flexible discrepancy models can confound discrepancy and simulator parameters, leading to poor identifiability. As a result, practitioners often must impose problem-specific prior constraints to adequately regularize the discrepancy, which can be challenging and cumbersome. In this work, we propose a novel calibration framework for coupled, multi-output ODE systems that enforces automatic, model-structural constraints on the discrepancy, improving identifiability without requiring application-specific discrepancy priors. Forward-model gradients are computed via sensitivity equations, solved jointly with the ODE system as a coupled initial value problem. Posterior inference is performed using an adaptive Metropolis-within-Gibbs sampler tailored to the resulting constrained posterior. We demonstrate the approach on three model systems: a mass-spring oscillator, a model of infectious disease spread, and a neuron firing model. We show that our method leads to improved parameter inference and predictive accuracy compared to standard calibration approaches.

Problem

• Model Discrepancy
• Parameter Calibration
• Coupled ODEs
• Identifiability
• Prior Constraints

Innovation

• Model Discrepancy
• Coupled ODEs
• Sensitivity Equations
• Parameter Identifiability
• Metropolis-within-Gibbs Sampler