FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learning (2509.12344v1)

Abstract: Deep Operator Networks (DeepONets) have recently emerged as powerful data-driven frameworks for learning nonlinear operators, particularly suited for approximating solutions to partial differential equations (PDEs). Despite their promising capabilities, the standard implementation of DeepONets, which typically employs fully connected linear layers in the trunk network, can encounter limitations in capturing complex spatial structures inherent to various PDEs. To address this, we introduce Fourier-embedded trunk networks within the DeepONet architecture, leveraging random Fourier feature mappings to enrich spatial representation capabilities. Our proposed Fourier-embedded DeepONet, FEDONet demonstrates superior performance compared to the traditional DeepONet across a comprehensive suite of PDE-driven datasets, including the two-dimensional Poisson equation, Burgers' equation, the Lorenz-63 chaotic system, Eikonal equation, Allen-Cahn equation, Kuramoto-Sivashinsky equation, and the Lorenz-96 system. Empirical evaluations of FEDONet consistently show significant improvements in solution reconstruction accuracy, with average relative L2 performance gains ranging between 2-3x compared to the DeepONet baseline. This study highlights the effectiveness of Fourier embeddings in enhancing neural operator learning, offering a robust and broadly applicable methodology for PDE surrogate modeling.