Transfer learning of neural operators for partial differential equations based on sparse network λ-FNO

• DOI: 10.1371/journal.pone.0321154
• Publication Date: 2025-05-22T17:51:17Z
• Authors: Jinghong Xu; Yuqian Zhou; Qian Liu; Kebing Li; Haolin Yang
• Keywords: Operator (biology)

When the solution domain, internal parameters, and initial boundary conditions of partial differential equation (PDE) are changed, many potential characteristics equation’s solutions still similar. This provides possibility to reduce cost PDE operator learning through transfer methods. Based on Fourier neural (FNO), we propose a novel sparse network named λ-FNO. By introducing λ parameter matrix using new pruning method make sparse, ability λ-FNO is greatly improved. Using can efficiently learn from discrete function space uniform grid unstructured grid, which not available in FNO. Finally, apply several specific tasks equations under conditional distributions demonstrate its excellent transferability. The experimental results show that when shape domain or parameters change, our framework capture invariant information complete related with less cost, higher accuracy, faster speed. In addition, has extension be easily extended other architectures enhance performance. Our model data generation code get https://github.com/Xumouren12/TL-FNO .