Quantum-Inspired Fluid Simulation of 2D Turbulence with GPU Acceleration

TL;DR

This paper introduces a quantum-inspired tensor network method for simulating 2D turbulence, leveraging GPU acceleration to significantly improve computational efficiency and explore the potential advantages over traditional methods in turbulent regimes.

Contribution

It adapts tensor network algorithms for fluid simulation using MPS and GPU acceleration, demonstrating improved speed and scalability for high Reynolds number turbulence.

Findings

Simulation speed increased by up to 12.1 times with GPU acceleration.

The algorithm effectively simulates high Reynolds number turbulence up to 10^7.

Derived scaling law for the bond dimension in turbulent flow fields.

Abstract

Tensor network algorithms can efficiently simulate complex quantum many-body systems by utilizing knowledge of their structure and entanglement. These methodologies have been adapted recently for solving the Navier-Stokes equations, which describe a spectrum of fluid phenomena, from the aerodynamics of vehicles to weather patterns. Within this quantum-inspired paradigm, velocity is encoded as matrix product states (MPS), effectively harnessing the analogy between interscale correlations of fluid dynamics and entanglement in quantum many-body physics. This particular tensor structure is also called quantics tensor train (QTT). By utilizing NVIDIA's cuQuantum library to perform parallel tensor computations on GPUs, our adaptation speeds up simulations by up to 12.1 times. This allows us to study the algorithm in terms of its applicability, scalability, and performance. By simulating two qualitatively different but commonly encountered 2D flow problems at high Reynolds numbers up to $1\times10^7$ using a fourth-order time stepping scheme, we find that the algorithm has a potential advantage over direct numerical simulations in the turbulent regime as the requirements for grid resolution increase drastically. In addition, we derive the scaling $\chi=\mathcal{O}(\text{poly}(1/\epsilon))$ for the maximum bond dimension $\chi$ of MPS representing turbulent flow fields, with an error $\epsilon$, based on the spectral distribution of turbulent kinetic energy. Our findings motivate further exploration of related quantum algorithms and other tensor network methods.