Tensor-train formulation reduces multidimensional inverse Laplace transform cost from exponential to polynomial under low-rank assumptions.
Arenstein , author M
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Matrix product state simulations of 2D Rayleigh-Bénard convection recover Nusselt number statistics with 1.8% error and a 9-fold reduction in degrees of freedom at Ra=10^10 using bond dimensions comparable to lower Ra cases.
Tensor-network fractional-step method simulates incompressible flows in curvilinear coordinates with up to 20x field compression and 1000x operator compression while keeping errors below 0.3% versus finite differences.
A quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.
citing papers explorer
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A tensor-train multidimensional inverse Laplace transform
Tensor-train formulation reduces multidimensional inverse Laplace transform cost from exponential to polynomial under low-rank assumptions.
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Quantum-Inspired Simulation of 2D Turbulent Rayleigh-B\'enard Convection
Matrix product state simulations of 2D Rayleigh-Bénard convection recover Nusselt number statistics with 1.8% error and a 9-fold reduction in degrees of freedom at Ra=10^10 using bond dimensions comparable to lower Ra cases.
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Quantum-Inspired Tensor-Network Fractional-Step Method for Incompressible Flow in Curvilinear Coordinates
Tensor-network fractional-step method simulates incompressible flows in curvilinear coordinates with up to 20x field compression and 1000x operator compression while keeping errors below 0.3% versus finite differences.
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Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation
A quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.