Physical fidelity and forecasting in compressed active matter representations

Abstract Reduced descriptions of active fluids must capture physically meaningful states and support prediction of their evolution, yet the relationship between these requirements remains unclear. Here, we investigate how physical constraints affect reconstruction and forecasting in compressed representations of a simulated active suspension. We compare autoencoders incorporating soft cross-field penalties, hard concentration–orientation moment realizability, or both, with unconstrained autoencoders and weighted proper orthogonal decomposition at matched latent dimensions. Combining the constraints reduces the aggregate standardized reconstruction error across spatially averaged velocity intensity, enstrophy and local nematic order by 51–57% at latent dimensions of 128 and 256, with approximately a 1% increase in balanced field error. The combined model also eliminates detected violations of the enforced admissibility conditions and outperforms post-inference projection in observable reconstruction. These benefits extend selectively to forecasting. With linear latent dynamics, the combined model reduces ten-step observable error by 10–13% relative to the unconstrained autoencoder, while slightly increasing field error. Against persistence, field and observable metrics yield opposite rankings at the reference latent dimension. Linear-readout analyses further distinguish observable accessibility from decoder reconstruction accuracy. Together, these results demonstrate that physical constraints can substantially improve observable preservation, while their predictive benefits depend on the temporal model and quantity evaluated. They motivate assessing physical admissibility, retained information and temporal accuracy as complementary requirements for reduced active-fluid models.