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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.15329 |
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| _version_ | 1866911293206691840 |
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| author | Ouyang, Anqiao Ke, Hongyi Wang, Qi |
| author_facet | Ouyang, Anqiao Ke, Hongyi Wang, Qi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fourier-Invertible Neural Encoder (FINE) for Homogeneous Flows Ouyang, Anqiao Ke, Hongyi Wang, Qi Machine Learning 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. |
| title | Fourier-Invertible Neural Encoder (FINE) for Homogeneous Flows |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2505.15329 |