Estimating field parameters from multiphysics governing equations with scarce data

Recent advances in physics-informed machine learning show promise in modeling diverse physical phenomena by integrating physics principles into neural networks. These methods effectively learn physics phenomena, assuming either known or unknown parameters. However, real-world phenomena often involve complex, coupled behaviors with spatially distributed, unknown physical properties and parameters, posing challenges, particularly with limited measurements or noisy observations. In this work, we introduce NeuralFD for estimating field parameters within partial differential equations (PDEs), where the parameters exhibit spatial distribution, a challenge that sparse regression methods struggle to address. We employ deep neural networks to model the field parameters while solving the PDEs in discretized form using the finite difference method (FDM). With just a few thousand measurements, NeuralFD accurately captures the physics behaviors and the underlying parameter distributions. Notably, employing a multiphysics framework focusing on cardiac electrophysiology, 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 estimation in some cases, whereas NeuralFD consistently performs well. Additionally, NeuralFD 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.