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arXiv · 2505.15329

Fourier-Invertible Neural Encoder (FINE) for Homogeneous Flows

Anqiao Ouyang·Hongyi Ke·Qi Wang
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Abstract

We present the Fourier-Invertible Neural Encoder (FINE), a compact and interpretable architecture for dimension reduction in translation-equivariant datasets. FINE integrates reversible filters and monotonic activation functions with a Fourier truncation bottleneck, achieving information-preserving compression that respects translational symmetry. This design offers a new perspective on symmetry-aware learning, linking spectral truncation to group-equivariant representations. The proposed FINE architecture is tested on one-dimensional nonlinear wave interaction, one-dimensional Kuramoto-Sivashinsky turbulence dataset, and a two-dimensional turbulence dataset. FINE achieves an overall 4.9-9.1 times lower reconstruction error than convolutional autoencoders while using only 13-21% of their parameters. The results highlight FINE's effectiveness in representing complex physical systems with minimal dimension in the latent space. The proposed framework provides a principled framework for interpretable, low-parameter, and symmetry-preserving dimensional reduction, bridging the gap between Fourier representations and modern neural architectures for scientific and physics-informed learning.

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Anqiao Ouyang, Hongyi Ke, Qi Wang. 2025-05-21. Fourier-Invertible Neural Encoder (FINE) for Homogeneous Flows. https://arxiv.org/abs/2505.15329

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