Randomized tensor-train truncation on GPUs for quantum-inspired computational fluid dynamics

초록

Tensor-network computational fluid dynamics solvers, often termed quantum-inspired CFD (QIS–CFD), evolve the incompressible Navier–Stokes equations in Tensor-Train (TT/MPS) form by repeatedly constructing nonlinear operators via tensor contractions and then recompressing intermediate tensors to control the bond dimension. In standard TT workflows, recompression is performed with deterministic truncated singular value decompositions (SVDs); for bond dimension χ and fixed local mode size, the per-bond O(χ3) cost and limited GPU throughput of SVD routines make truncation a primary bottleneck in GPU-resident time stepping at moderate-to-large χ. We introduce a GPU-accelerated randomized TT truncation scheme (RTTD) based on randomized subspace iteration. RTTD replaces each deterministic truncated SVD with an oversampled randomized range finder and thin QR factorizations on low-dimensional projected matrices, shifting the truncation workload toward GEMM- and QR-dominated kernels while preserving the canonical constraints required by TT/MPS sweeps. We validate RTTD against direct numerical simulation (DNS) and an SVD-based baseline on two 2D benchmarks: a decaying turbulent jet (Re=105 for short-run sweeps and Re=2×105 for long-horizon validation) and the Taylor–Green vortex (Re=103). For χ ≥ 32, RTTD matches the SVD baseline and DNS in kinetic-energy evolution and divergence diagnostics. Computationally, RTTD accelerates the nonlinear Matrix-Product-Operator (MPO) construction phase by up to 7.8 ×  and reduces the end-to-end wall-clock time per step by up to 2.2 ×  relative to the deterministic baseline.

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