Tensor Networks and Fluid Turbulence

=======
Abstract
=======
Tensor-train compression offers a fundamentally new way to tame the computational brutality of high-Reynolds‐number turbulence. By encoding the velocity fields on a discrete mesh as a sequence of low-rank tensors, known as tensor Trains, the number of degrees of freedom grows only polylogarithmically with resolution. This approach yet retains all hallmark statistical features of fully developed turbulence—like the energy spectra. Building on this insight, we demonstrate not only that individual turbulent snapshots admit an efficient tensor‐train representation, but also that the incompressible Navier–Stokes equations can be advanced directly within this compressed form, and that synthetic turbulent-like fields can be efficiently generated with correct statistical signatures. Our results constitute a turning point in the quantum-inspired approach to computational fluid dynamics, showing that a favorable scaling of the number of parameters still applies when dealing with complex flows.

===============
About the Speaker
===============
Stefano Pisoni is a PhD candidate at the Technical University of Hamburg (TUHH), under the supervision of prof. Martin Kliesch. He is also a researcher at the Technology Innovation Institute (TII) in Abu Dhabi. His interests span tensor network techniques applied to high-dimensional PDEs and more recently to error mitigation schemes.