Abstract
Calculating the evolution of a passive scalar in a turbulent flow requires resolving the intricate stretching and folding of the scalar field. Traditionally, this requires that the computational mesh is much smaller than the smallest scale of the concentration field. Here we demonstrate the use of machine learning to learn discretizations of the governing equation that give accurate computations with a coarser mesh. The model learns the universal small scale structures of the concentration field stretching, allowing it to accurately interpolate with less information.
Highlights
A key problem in the numerical simulation of complex phenomena is the need to accurately resolve spatiotemporal features over a wide range of length scales
Incorporating machine learning into numerical models facilitates the adoption of emerging hardware, considering that the fastest growth in computing power relies on domain-specific architectures such as graphical processing units (GPUs) [11] and tensor processing units (TPUs) [12,13] that are optimized for machine learning tasks
We developed a data-driven discretization for solving passive scalar advection in one or two dimensions
Summary
A key problem in the numerical simulation of complex phenomena is the need to accurately resolve spatiotemporal features over a wide range of length scales. The extra computing power made available through Moore’s law has been used to increase grid resolution dramatically, leading to breakthroughs in turbulence modeling [1], weather prediction [2], and climate projection [3]. There is still a formidable gap towards resolving the finest spatial scales of interest [4], especially with the recent slowdown of Moore’s law [5,6]. Incorporating machine learning into numerical models facilitates the adoption of emerging hardware, considering that the fastest growth in computing power relies on domain-specific architectures such as graphical processing units (GPUs) [11] and tensor processing units (TPUs) [12,13] that are optimized for machine learning tasks
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