Estimating Field Parameters from Multiphysics Governing Equations with Scarce Data

Xuyang Li, Mahdi Masmoudi, Nizar Lajnef, Vishnu Boddeti

Keywords: Parameter estimation, Differential equations, Machine learning

TL;DR: We introduce NeuroPIPE for efficiently estimating field parameters in partial differential equations with sparse observations, addressing limitations where methods like sparse regression and PINN struggle or underperform.

Abstract: Real-world physical phenomena often involve complex, coupled behaviors influenced by spatially distributed physical properties. This complexity poses significant challenges for modeling, particularly when faced with limited or noisy observations. In this work, we introduce NeuroPIPE for field parameters inference in partial differential equations (PDEs). We employ deep neural networks to model the field parameters while solving the PDEs in discretized form using the finite difference method (FDM). Focusing on a representative example of cardiac electrophysiology with just a few hundred measurements, NeuroPIPE accurately captures the underlying parameters and physical behaviors. We demonstrated that our approach surpasses the state-of-the-art physics-informed neural networks (PINN) in terms of model robustness, parameter estimation accuracy, and training efficiency. Even with abundant training data, PINN fails in parameter inference in some cases, whereas NeuroPIPE consistently performs well. Additionally, NeuroPIPE achieves significantly higher inference accuracy by one order of magnitude. Our approach holds substantial promise for learning and understanding many complex physics problems with a significant reduction of training data.

Submission Number: 63