Neural Network-Assisted Refinement of Traditional Schemes for One-Dimensional Scalar Conservation Laws
A clear link is established between conventional numerical methods and neural network approximations for solving one-dimensional scalar conservation laws. The focus is on the construction of an appropriate flux term in the case of convex flux functions for improving the classical schemes. The first neural network developed here is able to rediscover Godunov's method, while the second one emulates the behavior of a second-order slope-limiter function. In this way, by merging them, second-order reconstruction-based schemes can be developed. The networks presented here employ a minimal number of parameters, significantly reducing the complexity compared to previous approaches. These networks...
| Authors | Imre Fekete, Ferenc Izsák, Vendel P. Kupás |
|---|---|
| Primary category | math.NA |
| Published | 26 September 2026 |
| Last updated at source | 26 September 2026 |
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