Implement Wavelet Neural Operator (WNO)

Summary

Implement WNO, which uses wavelet transforms instead of Fourier transforms for operator learning, providing localization in both space and frequency.

Reference

• Tripura & Chakraborty, "Wavelet neural operator for solving parametric partial differential equations in computational mechanics problems," Computer Methods in Applied Mechanics and Engineering, 2023. arXiv:2205.02191

Description

WNO replaces the Fourier transform in the neural operator framework with wavelet transforms. Unlike Fourier (which is global in space), wavelets provide localization in both space/time AND frequency, enabling better tracking of localized features, sharp gradients, and discontinuities. This makes WNO particularly suited for problems with shocks, boundary layers, or multi-scale localized phenomena.

This would require:

• A new WaveletTransform implementing the AbstractTransform interface in src/transform.jl
• Integration with existing OperatorConv / OperatorKernel layers
• A Julia wavelet implementation (e.g., via Wavelets.jl)

Start in src/transform.jl by reading the AbstractTransform interface, then inspect the existing OperatorConv and OperatorKernel integration points. Evaluate the proposed Wavelets.jl dependency and define how a WaveletTransform fits the existing neural-operator framework. Done means WNO is implemented with wavelet-based localization and integrated with those layers.