Stability and Chaos Analysis of Nonlinear Fluid Flows Using AI-Accelerated Computational Techniques

Abstract

Nonlinear fluid dynamics often exhibit rich and complex behavior marked by transitions from stability to chaos. In this study, we investigate such transitions using AI-accelerated computational frameworks tailored for fluid flows governed by the Navier-Stokes equations. Our approach integrates physics-informed neural networks (PINNs) with chaos quantification techniques to detect bifurcations, strange attractors, and sensitivity to initial conditions in both laminar and transitional regimes. We model benchmark systems including the Lorenz flow and 2D Rayleigh–Bénard convection to demonstrate the accuracy of AI models in capturing spatiotemporal dynamics. Lyapunov exponents, Poincaré sections, and entropy measures are used to quantify chaos levels, and results are validated against traditional numerical solvers such as finite volume and finite element methods. The AI-based methods showed significant speed-ups (5–10x) without compromising accuracy. Our findings provide scalable alternatives for simulating turbulent systems in engineering and geophysical contexts.