Real-Time Topological Characterization of Turbulence via Sparse Graph Spectral Analysis

Characterizing complex turbulent flows in real time with limited sensor data remains a fundamental challenge in fluid dynamics and control engineering. Conventional approaches rely on computationally expensive Direct Numerical Simulations (DNS) or dense measurement grids, limiting their applicability in in-situ and real-time scenarios. Here we present a holographic reconstruction framework that infers the global topological state of turbulencia from a sparse set of randomly distributed sensors. Sensor measurements (position and velocity) are embedded into an adaptive k-nearest neighbor graph, from which a spectral topological invariant is extracted using the graph Laplacian Fiedler value. Validation against petascale DNS data from the Johns Hopkins Turbulence Database (JHTDB) demonstrates that the proposed invariant robustly discriminates between laminar shear, isotropic turbulence, and coherent wall-bounded structures. The method achieves >93% classification accuracy relative to high-resolution benchmarks while reducing data requirements by 94%. The optimized implementation reaches sub-millisecond inference times (≈ 0.87 ms), corresponding to an ≈1100× speedup over established gradient-based diagnostics (Jeong–Hussain λ2 criterion), and enabling kilohertz-rate sampling for ultra-fast feedback control.Together, these results establish a new paradigm for real-time turbulence diagnostics and active flow control.