Complete quantum-inspired framework for computational fluid dynamics

Abstract

Computational fluid dynamics is both a thriving research field and a key tool for advanced industry applications. The central challenge is to simulate turbulent flows in complex geometries, a compute-power intensive task due to the large vector dimensions required by discretized meshes. We present a full-stack method to solve for incompressible fluids with memory and runtime scaling poly-logarithmically in the mesh size. Our framework is based on matrix-product states, a powerful compressed representation of quantum states. It is complete in that it solves for flows around immersed objects of arbitrary geometries, with non-trivial boundary conditions, and self-consistent in that it can retrieve the solution directly from the compressed encoding, i.e. without ever passing through the expensive dense-vector representation. This machinery lays the foundations for a new generation of potentially radically more efficient solvers of real-life fluid problems.

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Cited by in corpus (15)

• Learning tensor networks with tensor cross interpolation: new algorithms and libraries
• Tensor networks enable the calculation of turbulence probability distributions
• Quantized tensor networks for solving the Vlasov-Maxwell equations
• Quantum-Inspired Fluid Simulation of 2D Turbulence with GPU Acceleration
• Compactness of quantics tensor train representations of local imaginary-time propagators
• Towards Variational Quantum Algorithms for generalized linear and nonlinear transport phenomena
• Tensor-Programmable Quantum Circuits for Solving Differential Equations
• Simulating Quantum Turbulence with Matrix Product States
• A Quantum-Inspired Algorithm for Wave Simulation Using Tensor Networks
• The Cytnx Library for Tensor Networks
• Self-consistent tensor network method for correlated super-moiré matter beyond one billion sites
• Tensor network method for real-space topology in quasicrystal Chern mosaics
• Inchworm tensor train hybridization expansion quantum impurity solver
• Entanglement across scales: Quantics tensor trains as a natural framework for renormalization
• Tensor Network Lattice Boltzmann Method for Data-Compressed Fluid Simulations