Tensor network compression method for fluid dynamics data using matrix product states
By
[Submitted on 4 Jun 2026]
A respectable bake. You'd come back tomorrow for another.
Summary
This paper presents a tensor network compression method (using matrix product states/tensor trains) for extreme-scale scientific data, using fluid dynamics as a testbed. The method is demonstrated for one-dimensional compression, showing lossless compression for random Fourier series at sufficient bond dimension, and lossy compression within acceptable error for fluid simulations. It is tested on Burger's equation with excellent results, and demonstrates a tensor network periodic convolution that can be orders of magnitude faster than FFT-based methods. The approach is also translatable to quantum computing paradigms.
Key quotes
· 5 pulledFluid dynamics data in general do not exhibit these features and so are attractive test beds for generic compression techniques that are objective, robust, and tuneable with respect to information lost due to compression.
Lossless compression is demonstrated for random Fourier series for sufficiently high bond dimension of the tensor network, with the memory required to store the tensor network scaling directly proportional to the bond dimension.
The lossy compression exhibited at lower bond dimension can be well within the relative error of many fluid simulations.
We additionally demonstrate the capability to perform computations in the compressed form through a tensor network periodic convolution that can be orders of magnitude faster than using fast Fourier transforms and the convolution theorem.
In addition to being an attractive method for working with data sets generated by existing computers, the tensor network methods utilised are directly translatable to the emerging paradigm of quantum computing.
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