Greedy identification of latent dynamics from parametric flow data

Projection-based reduced-order models (ROMs) play a crucial role in simplifying the complex dynamics of fluid systems. Such models are achieved by projecting the Navier-Stokes equations onto a lower-dimensional subspace while preserving essential dynamics. However, this approach requires prior knowledge of the underlying high-fidelity model, limiting its effectiveness when applied to black-box data. This article introduces a novel, non-intrusive, data-driven method–Greedy Identification of Latent Dynamics (GILD)–for constructing parametric fluid ROMs. Unlike traditional methods, GILD constructs models directly from data, without relying on specific high-fidelity model information. It also employs interpolation within the manifold $R_{\ast }^{N\times q}/O_q$ to accommodate parameter variability. Numerical experiments on various fluid dynamics scenarios, including lid-driven cavity flow, flow past a cylinder with varying Reynolds number, and Ahmed body flow with variable geometry, demonstrate GILD’s robust performance across both training and unseen parameter values. GILD’s ability to accurately capture system dynamics and its adaptability to diverse data sources highlight its potential as a powerful tool for constructing parametric reduced-order models in an easy and general way for complex fluid dynamics and beyond.