Quantized Tensor Train Compression For Turbulent Flow Simulation: O(log N) Scaling with Reynolds-Independent Bond Dimension

We present a hybrid Quantized Tensor Train (QTT) framework for compressing three-dimensional incompressible Navier-Stokes turbulence that achieves O(log N) memory scaling. The central question addressed is whether increasing Reynolds number forces growth in QTT bond dimension, potentially negating compression benefits.

Using decaying homogeneous isotropic turbulence benchmarks at fixed spatial resolution, we perform a systematic Reynolds number sweep over Re_lambda = 50–800. Across this range, the maximum observed bond dimension remains bounded at chi = 64, yielding an empirical scaling exponent alpha ≈ 0 in chi ~ Re^alpha. At 256^3 resolution, storage compression exceeds 10,000x relative to dense representation, with stable time integration and controlled numerical dissipation.

All physical operations are performed in dense Fourier space using GPU-accelerated FFTs, while QTT is employed exclusively as a storage representation between time steps. As such, the results address memory scaling rather than asymptotic computational complexity. These findings demonstrate that increasing nonlinear scale interactions associated with higher Reynolds number do not, by themselves, necessitate increased tensor-network complexity. Quantized tensor formats therefore offer a viable compression framework for turbulence simulations in memory-limited regimes.