Reinforcement learning of numerical methods

Paper Title:

First-principle-like reinforcement learning of nonlinear numerical schemes for conservation laws

Published on:

20 December 2023

Primary Category:

Computational Physics

Paper Authors:

Hao-Chen Wang,

Meilin Yu,

Heng Xiao

Bullets

Key Details

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Presents reinforcement learning method for nonlinear numerical scheme design

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Uses stability and accuracy principles, not reference data, to guide training

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Learned scheme balances numerical dissipation and precision well

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Outperforms standard 3rd-order MUSCL scheme with van Albada limiter

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Shows universality: scheme trained only on 1D Burgers' simulates 1D and 2D Euler

Explore the topics in this paper

burgers equation

computational fluid dynamics

euler equations

numerical schemes

reinforcement learning

AI generated summary

Reinforcement learning of numerical methods

This paper develops a reinforcement learning framework to design nonlinear numerical schemes for computational fluid dynamics. It uses fundamental principles like controlling total variation and accuracy, instead of reference data, to balance numerical stability and precision. The method is shown to outperform standard schemes on test cases, and a scheme trained only on 1D Burgers' equation could directly simulate 1D and 2D Euler equations, demonstrating universality.