[2603.03922] Hierarchical Inference and Closure Learning via Adaptive Surrogates for ODEs and PDEs

Computer Science > Machine Learning arXiv:2603.03922 (cs) [Submitted on 4 Mar 2026] Title:Hierarchical Inference and Closure Learning via Adaptive Surrogates for ODEs and PDEs Authors:Pengyu Zhang, Arnaud Vadeboncoeur, Alex Glyn-Davies, Mark Girolami View a PDF of the paper titled Hierarchical Inference and Closure Learning via Adaptive Surrogates for ODEs and PDEs, by Pengyu Zhang and 3 other authors View PDF HTML (experimental) Abstract:Inverse problems are the task of calibrating models to match data. They play a pivotal role in diverse engineering applications by allowing practitioners to align models with reality. In many applications, engineers and scientists do not have a complete picture of i) the detailed properties of a system (such as material properties, geometry, initial conditions, etc.); ii) the complete laws describing all dynamics at play (such as friction laws, complicated damping phenomena, and general nonlinear interactions). In this paper, we develop a principled methodology for leveraging data from collections of distinct yet related physical systems to jointly estimate the individual model parameters of each system, and learn the shared unknown dynamics in the form of an ML-based closure model. To robustly infer the unknown parameters for each system, we employ a hierarchical Bayesian framework, which allows for the joint inference of multiple systems and their population-level statistics. To learn the closures, we use a maximum marginal likelihood e...