The Tensor-Network Kinetic Solver - Classical, Deployable Today

Abstract

The kinetic distribution function is highly compressible in a low-rank tensor-network representation, and that yields a practical classical solver, not a storage trick. On a 1D1V BGK test, a matrix-product-state truncation reaches relative-L² error 2×10−⁴ at rank 8 using ~0.19× the dense storage, with the error falling exponentially in rank. Unlike the fault-tolerant-horizon quantum route, this runs today.