Bayesian Nonparametric Mixed-Effect ODEs with Gaussian Processes

• URL: http://arxiv.org/abs/2605.13088v1
• Date: Wed, 13 May 2026 06:57:01 GMT
• Title: Bayesian Nonparametric Mixed-Effect ODEs with Gaussian Processes
• Abstract summary: Dynamical modelling is central to many scientific domains, including pharmacometrics, systems biology, physiology, and epidemiology.<n>We propose MEGPODE, a nonparametric mixed-effect ODE model in which each subject's vector field is quantified into a shared population component and a subject-specific deviation.
• Score: 8.718310015165025
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Dynamical modelling is central to many scientific domains, including pharmacometrics, systems biology, physiology, and epidemiology. In these settings, heterogeneity is often intrinsic: different subjects or units follow related but distinct continuous-time dynamics. Classical nonlinear mixed-effects Ordinary Differential Equation (ODE) models address this by combining population-level structure with subject-specific effects, but they rely on a parametric vector field and are therefore vulnerable to structural misspecification and unmodelled mechanisms. This motivates nonparametric approaches that can retain principled uncertainty quantification, yet existing nonparametric ODE methods typically assume a single shared dynamical system rather than an explicit mixed-effect hierarchy over subject-specific dynamics. We propose MEGPODE, a Bayesian nonparametric mixed-effect ODE model in which each subject's vector field is decomposed into a shared population component and a subject-specific deviation, both endowed with Gaussian process (GP) priors. To avoid repeated ODE solves per subject during training, we combine state-space GP trajectory priors with virtual collocation observations, yielding Kalman-smoothing trajectory updates and closed-form regressions for the vector fields. Across controlled heterogeneous ODE benchmarks spanning oscillatory, biomedical systems, MEGPODE improves population-field recovery and subject-level trajectory prediction relative to strong baselines.

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