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<p>This paper presents a Fourier-enhanced operator autoencoder (F-OAE) for decoder-free reconstruction and latent learning of dynamical systems. Conventional autoencoder-based reduced-order models compress high-dimensional fields into compact latent variables but recover the full physical fields via a nonlinear neural decoder, thereby introducing an additional reconstruction stage during prediction and deployment. In contrast, the proposed framework reformulates the reconstruction using the branch-trunk architecture. The branch network encodes each field snapshot or response sample into latent coefficients, while the trunk network learns shared spatial basis functions on a fixed coordinate grid. The full field is reconstructed through explicit linear superposition of the coefficients and learned basis functions. Fourier layers are introduced into the trunk network to improve the expressiveness of the learned basis functions for complex spatiotemporal fields. The proposed framework is evaluated through four representative dynamic case studies. The results show that F-OAE achieves accuracy comparable to or better than classical AE-based reduced-order models while providing a more efficient latent-to-field reconstruction path. In the cylinder wake case, F-OAE decreases the total inference time from 0.991&#xa0;s to 0.559&#xa0;s. In the physics-augmented Navier–Stokes benchmark, the training-epoch time is reduced from 54.10&#xa0;ms to 24.00&#xa0;ms compared with the AE baseline.</p>

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Decoder-free operator autoencoder for reduced-order modeling of dynamical systems

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • Xuandong Lu,
  • Yongming Liu

摘要

This paper presents a Fourier-enhanced operator autoencoder (F-OAE) for decoder-free reconstruction and latent learning of dynamical systems. Conventional autoencoder-based reduced-order models compress high-dimensional fields into compact latent variables but recover the full physical fields via a nonlinear neural decoder, thereby introducing an additional reconstruction stage during prediction and deployment. In contrast, the proposed framework reformulates the reconstruction using the branch-trunk architecture. The branch network encodes each field snapshot or response sample into latent coefficients, while the trunk network learns shared spatial basis functions on a fixed coordinate grid. The full field is reconstructed through explicit linear superposition of the coefficients and learned basis functions. Fourier layers are introduced into the trunk network to improve the expressiveness of the learned basis functions for complex spatiotemporal fields. The proposed framework is evaluated through four representative dynamic case studies. The results show that F-OAE achieves accuracy comparable to or better than classical AE-based reduced-order models while providing a more efficient latent-to-field reconstruction path. In the cylinder wake case, F-OAE decreases the total inference time from 0.991 s to 0.559 s. In the physics-augmented Navier–Stokes benchmark, the training-epoch time is reduced from 54.10 ms to 24.00 ms compared with the AE baseline.