FWF-Net: A Learnable Fourier-Wavelet Fusion Network for PDE Operator Learning

Le résumé fourni par la source

Solvers for Partial Differential Equations (PDEs) have increasingly adopted data-driven approaches that approximate complex operator computations by learning input-output mappings. While frequency domain techniques reduce the computational burden of integral operators, existing methods remain insufficient for complex and varying physical fields because they focus solely on network architecture improvements. To bridge this gap, we propose the Fourier-Wavelet Fusion Network (FWF-Net). FWF-Net employs learnable parameters to balance low- and high-frequency components for global accuracy, while integrating learnable wavelet transforms to improve local adaptability across different PDEs. Experimental validation on multiple standard PDE datasets demonstrates that our method achieves state-of-the-art performance across most datasets, with improvements up to 25.0%, highlighting the significant potential of learnable frequency-domain approaches for numerical PDE applications.

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