Machine learning changes the rules for flux limiters

Learning to integrate non-linear equations from highly resolved direct numerical simulations has seen recent interest for reducing the computational load fluid simulations. Here, we focus on determining a flux-limiter shock capturing methods. Focusing flux limiters provides specific plug-and-play component existing Since their introduction, an array of been designed. Using coarse-grained Burgers' equation, show that flux-limiters may be rank-ordered in terms log-error relative high-resolution data. We then develop theory find optimal and present outperform others tested integrating equation lattices with 2×, 3×, 4×, 8× coarse-grainings. train continuous piecewise linear limiter by minimizing mean-squared misfit six-grid point segments data, averaged over all segments. While are generally designed have output ϕ(r)=1 at ratio r = 1, our not bound this rule yet produce smaller error than standard limiters. machine learned distinctive features provide new rules-of-thumb development improved Additionally, use learn across range values (as opposed fixed value) coarse-graining, number discretized bins, diffusion parameter. This demonstrates ability should more broadly useful general applications.