Real vs. Complex Spectral Bases for Neural Operators: The Role of Green's Function Alignment
arXiv:2606.24851v1 Announce Type: new Abstract: Fourier Neural Operators (FNO) learn solution operators of partial differential equations by parameterizing global convolutions in the complex Fourier domain. For real-valued PDE solutions, the complex FFT carries representational redundancy through conjugate symmetry. We introduce the Hartley Neural Operator (HNO), the exact real-valued mirror of FNO: it replaces the FFT with the purely real Discrete Hartley Transform and learns a single real multiplier per retained spectral mode, with no complex arithmetic. Because the real Hartley spectrum is
The continuous evolution of AI algorithms necessitates constant optimization for real-world applications, driving research into more efficient computational methods for neural operators.
This development proposes a more computationally efficient approach to neural operators, potentially reducing resource requirements for training and inference, which is crucial for scaling AI applications.
By replacing complex Fourier transforms with real-valued Hartley transforms, the Hartley Neural Operator (HNO) offers a streamlined architecture for solving PDEs with real outputs, potentially improving performance and reducing computational overhead.
- · AI researchers
- · Deep learning practitioners
- · Sectors using PDE-solvers (e.g., climate modeling, fluid dynamics)
- · Existing FNO implementations not optimized for real-valued data
Improved efficiency in training and deploying deep learning models for scientific computing applications.
Accelerated development of new AI-driven solutions in fields like engineering and physics due to reduced computational barriers.
Potential for broader adoption of neural operators on less powerful hardware, democratizing access to advanced AI models.
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Read at arXiv cs.LG