{"id":3822,"date":"2024-09-12T13:31:40","date_gmt":"2024-09-12T10:31:40","guid":{"rendered":"https:\/\/engage.cyi.ac.cy\/?post_type=news&p=3822"},"modified":"2024-09-12T13:31:54","modified_gmt":"2024-09-12T10:31:54","slug":"engage-article-compressibility-of-data-in-computational-fluid-dynamics","status":"publish","type":"news","link":"https:\/\/engage.cyi.ac.cy\/?news=engage-article-compressibility-of-data-in-computational-fluid-dynamics","title":{"rendered":"ENGAGE Article: Compressibility of data in computational fluid dynamics"},"content":{"rendered":"\n
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by Takis Angelides<\/strong><\/p>\n<\/div><\/div>\n\n\n\n

In this article we will explore the capability of a popular form of tensor networks called matrix product states (MPS) [1] in compressing the amount of data we keep in memory during simulations of computational fluid dynamics (CFD).<\/p>\n\n\n\n

High dimensional tensors are ubiquitous in the sciences having applications in quantum physics, general relativity, machine learning, fluid dynamics and many more. An MPS is a way to express a high dimensional tensor as a product of lower dimensional tensors. This gives us the ability to compress the amount of information we keep from the original tensor in a controlled manner such that only irrelevant information are discarded. The parameter that controls this is the so called bond dimension D<\/em> which determines the size of the lower dimensional tensors.<\/p>\n\n\n\n

The model we will use to exemplify the power of MPS is the Burger’s equation which has applications in turbulence modelling, shock wave formation, acoustics, traffic flow, heat conduction and diffusion processes. The Burger’s equation is given by<\/p>\n\n\n\n

\\[\\frac{\\partial u}{\\partial t} + u\\frac{\\partial u}{\\partial x}= \\nu\\frac{\\partial^2 u}{\\partial x^2}. (1) \\]