A priori Assessment of Tensor Networks Encoding for Reduced Order Modeling of Isotropic Turbulence

Tensor networks (TNs), originally developed to analyze many-body quantum systems, approximate high-dimensional fields as collections of low-rank tensors. Each of these tensors, obtained through successive singular-value decompositions, encodes information at each resolved length scale along a specific spatial direction. Two TN architectures, matrix product state (MPS) and multiscale entanglement renormalization ansatz (MERA), are employed to implement a truncated representation of 1024³ forced isotropic turbulence DNS data from the Johns Hopkins Turbulence Database. By discarding small singular values, TNs provide a controlled trade-off between the accuracy of captured correlations and the memory compression. Interleaved, split, and continuous-split ordering schemes, defined by spatial direction and length scale, are tested to minimize inter-tensor correlations. TN-reconstructed fields are compared with DNS via low- and high-order statistics. The results show that MPS offers high-fidelity representations of turbulent flows, enabling memory-efficient analysis of complex flow regimes. Additionally, a comparison between MPS and MERA highlights their relative strengths for low-order modeling. This work demonstrates the potential of TNs for scalable analysis of large-scale turbulence datasets, and motivates future research into TN-based Navier-Stokes simulations.