SirenFNO: Efficient and Full Frequency Learning of Fourier Neural Operators

SirenFNO introduces a novel framework that integrates sinusoidal representation networks (SIRENs) to improve Fourier neural operators (FNOs) by eliminating frequency truncation, allowing for full-grid spectrum learning with a constant, discretization-independent parameter count. This approach enhances learning efficiency and reduces parameters by approximately 4 to 15 times compared to traditional FNOs, with functional tensor decomposition variants achieving up to 73 times fewer parameters while maintaining performance across various PDE benchmarks. This advancement is significant for practitioners as it enables more efficient modeling of complex PDEs with high-frequency oscillations, improving the applicability of neural operators in scientific computing.