Local descriptor fields versus classical modal decompositions for low-dimensional representations of incompressible flows

Building reliable low-dimensional representations of fluid flows is central to data-driven modeling, control, and design, yet it remains unclear when modern local feature encoders offer advantages over classical global decompositions within a fixed configuration. Here, we compare a Galilean-invariant local descriptor field that encodes each grid point from a small neighborhood using relative geometric and physical differences and advances descriptors with a lightweight pointwise latent dynamics model, against baselines: a raw patch autoencoder, local principal component analysis, a global convolutional autoencoder, and global proper orthogonal decomposition (POD). We benchmark two-dimensional incompressible flows spanning an analytic Taylor–Green vortex, lid-driven cavity flows at Re = 100 and 500, and channel Poiseuille flow. Under a common protocol with matched training budgets, we evaluate one-step field error and physics-aware metrics beyond mean-squared error, including vorticity and divergence errors, a Galilean invariance diagnostic, one-step latent prediction error, and multi-step full-field rollouts obtained by iterating the learned latent dynamics. On self-dataset evaluation, global POD achieves near-oracle one-step accuracy, explained by rapid energy saturation in POD diagnostics. Among learned models, the descriptor is competitive in one-step prediction while consistently reducing divergence and latent dynamics errors relative to global convolutional compression. Rollout evaluation highlights stability trade-offs under iteration, underscoring that one-step accuracy alone is insufficient to characterize dynamical usability. These results quantify practical trade-offs between global modal and local descriptor-based encodings under a reproducible benchmark and provide a physics-aware baseline for future descriptor designs in computational fluid dynamics.