Physics-informed manifold learning for high-dimensional chaotic dynamics: Vortex-induced instabilities in aerostatic bearings

Extracting interpretable low-dimensional dynamics from high-dimensional vortex-dominated flows remains a fundamental challenge in nonlinear science. This study presents a physics-informed deep learning framework that discovers the governing laws of vortex-induced chaotic dynamics, using the complex fluid-structure interaction in aerostatic bearings as a representative high-Reynolds-number system. Unlike traditional linear subspace projections, we propose a Joint-Physics Latent Embedding (JPLE) coupled with a Residual Sparse Autoencoder (Res-SAE) to compress the strange attractor into a compact, differentiable nonlinear manifold. This approach explicitly preserves critical topological features—specifically vortex cores—by enforcing physical constraints via the Q-criterion. Furthermore, we employ Ensemble Sparse Identification of Nonlinear Dynamics (SINDy) to identify the latent evolution laws, revealing a hierarchical control mechanism where dominant coherent structures drive subsidiary fluctuations through quadratic nonlinearities. The identified model faithfully reconstructs the geometry of the strange attractor and achieves a speedup of O102 over Large Eddy Simulation (LES). These findings bridge the gap between black-box deep learning and dynamical systems theory, offering a robust pathway for real-time state estimation in complex chaotic flows.