Uncertainty-Aware Sparse Identification of Dynamical Systems via Bayesian Model Averaging

2026-04-12

AI Summary

This work addresses the challenge of dynamical system identification when governing equations are unknown and numerous candidate models exist, a setting where traditional point estimation can be misleading due to model non-identifiability or limited data. The study introduces Bayesian model averaging into sparse dynamical modeling for the first time, enabling joint inference of both interaction structures and functional forms of the system. By leveraging posterior inclusion probabilities, the approach quantifies uncertainty in model selection and supports searching over high-dimensional candidate libraries. Notably, even when the true governing equations lie outside the assumed model class, the method accurately identifies relevant dynamical components—including higher-order harmonics, phase lags, and multi-body couplings—while providing robust uncertainty quantification.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In many problems of data-driven modeling for dynamical systems, the governing equations are not known a priori and must be selected phenomenologically from a large set of candidate interactions and basis functions. In such situations, point estimates alone can be misleading, because multiple model components may explain the observed data comparably well, especially when the data are limited or the dynamics exhibit poor identifiability. Quantifying the uncertainty associated with model selection is therefore essential for constructing reliable dynamical models from data. In this work, we develop a Bayesian sparse identification framework for dynamical systems with coupled components, aimed at inferring both interaction structure and functional form together with principled uncertainty quantification. The proposed method combines sparse modeling with Bayesian model averaging, yielding posterior inclusion probabilities that quantify the credibility of each candidate interaction and basis component. Through numerical experiments on oscillator networks, we show that the framework accurately recovers sparse interaction structures with quantified uncertainty, including higher-order harmonic components, phase-lag effects, and multi-body interactions. We also demonstrate that, even in a phenomenological setting where the true governing equations are not contained in the assumed model class, the method can identify effective functional components with quantified uncertainty. These results highlight the importance of Bayesian uncertainty quantification in data-driven discovery of dynamical models.

Problem

• dynamical systems
• model selection uncertainty
• sparse identification
• Bayesian model averaging
• data-driven modeling

Innovation

• Bayesian model averaging
• sparse identification
• uncertainty quantification
• dynamical systems
• posterior inclusion probability