[2509.00203] Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements

Computer Science > Machine Learning arXiv:2509.00203 (cs) [Submitted on 29 Aug 2025 (v1), last revised 6 Apr 2026 (this version, v2)] Title:Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements Authors:Xuyang Li, Mahdi Masmoudi, Rami Gharbi, Nizar Lajnef, Vishnu Naresh Boddeti View a PDF of the paper titled Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements, by Xuyang Li and 4 other authors View PDF HTML (experimental) Abstract:Parameterized partial differential equations (PDEs) underpin the mathematical modeling of complex systems in diverse domains, including engineering, healthcare, and physics. A central challenge in using PDEs for real-world applications is to accurately infer the parameters, particularly when the parameters exhibit non-linear and spatiotemporal variations. Existing parameter estimation methods, such as sparse identification, physics-informed neural networks (PINNs), and neural operators, struggle in such cases, especially with nonlinear dynamics, multiphysics interactions, or limited observations of the system response. To address these challenges, we introduce Neptune, a general-purpose method capable of inferring parameter fields from sparse measurements of system responses. Neptune employs independent coordinate neural networks to continuously represent each parameter field in physical space or in state variables. Across various physical and biomedical problems, where direct parameter measurements are p...