Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networks
Linear dimensionality reduction methods such as proper orthogonal decomposition (POD) make high-dimensional data amenable to analysis by identifying the principal components, or modes, that capture the most variance, or energy, in the data and constructing a low-dimensional representation in the subspace they span. Such linear methods struggle, however, for data with slowly decaying Kolmogorov $n$-widths, such as advection-dominated and turbulent flows, which require many modes for accurate reconstruction; moreover, energy-based truncation can discard low-energy modes needed to capture small-scale features. Recent nonlinear manifold methods using polynomial mappings with alternating or gr...
| Authors | Tomoki Koike, Prakash Mohan, Marc T. Henry de Frahan et al. |
|---|---|
| Primary category | physics.flu-dyn |
| Published | 26 May 2026 |
| Last updated at source | 30 June 2026 |
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