Reproduce “The Fractal Neural Operator: Overcoming Spectral Bias in Chaotic Attractors via Prime-Harmonic Weierstrass Encodings” on OpenResearch

About this paper

Kanishk Awadhiya

The Fractal Neural Operator (FNO) employs Prime-Weierstrass encodings to mitigate spectral bias in neural networks when modeling chaotic dynamical systems, particularly strange attractors. This approach extends the prediction horizon for the Lorenz-63 system to 347 Lyapunov times, surpassing geometric baselines by 21% and state-of-the-art Reservoir Computing by 2.3x, while also reducing prediction failure variance by 14%.

Key insights

• Overcoming spectral bias in neural networks for chaotic systems requires an explicit 'aperiodicity' inductive bias, moving away from inherent periodic assumptions in existing models.
• The non-resonant property of prime number frequencies is essential for creating embeddings that provide dense spectral coverage and accurately represent the infinite spectral density of strange attractors.
• Fixing prime frequencies in the embedding yields better long-term prediction stability than making them trainable, acting as a structural regularizer to prevent resonant frequency collapses.

Summary by alphaXiv.