Spectrally Informed Autoencoders
Incorporating prior knowledge into machine learning methods can enhance accuracy, robustness, sample efficiency, and interpretability. Spectral statistics, which describe the energy distribution of a system, are often available even when the physics are not fully understood, arising from fundamental properties like dissipation and large-scale energy injection. Our method, the Spectrally Informed Autoencoder (SIAE), integrates these spectral properties into Koopman autoencoders (KAEs) by emphasizing low-frequency dynamics with higher power. This integration improves long-term prediction accuracy and results in learned models which better reflect the underlying physics of fluid flows in various scenarios.
Code accompanying: https://arxiv.org/pdf/2408.14407