Transfer Learning Fourier Neural Operator for Solving Parametric Frequency-Domain Wave Equations

Fourier neural operator (FNO) is a recently proposed data-driven scheme to approximate the implicit operators characterized by partial differential equations (PDEs) between functional spaces. The infinite-dimensional functional mapping from the parameter space to the state variable space enables us to solve parametric PDEs efficiently. To explore the potential of neural operator learning in geophysics exploration, we devise a transfer learning approach with the fine-tuning FNO backbone, termed transfer learning FNO (TL-FNO), to gain good generalization ability in solving frequency-domain wave equations at multiple source locations and frequencies. The baseline FNO model is initially trained at a single source location and frequency and then shared with the downstream tasks for seamlessly predicting the frequency-domain wavefields at different sources and frequencies. We conduct an in-depth analysis of the behavior of TL-FNO in diverse training settings, exploring dimensions such as data scale, training scale, and fine-tuning recipes. Our focus extends to understanding the scaling and transfer learning dynamics, as well as the generalization performance in out-of-distribution (OOD) scenarios. This comprehensive study aims to unveil the intricate relationships between these factors and the efficacy of TL-FNO across a range of conditions. Numerical examples demonstrate the notable superiority of the proposed TL-FNO over vanilla FNO in terms of accuracy and efficiency. We anticipate that the proposed TL-FNO is expected to be an efficient surrogate model to accelerate forward simulations in parametric wave equation inversion problems.