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Non-diffusive neural network method for hyperbolic conservation laws
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DOI：10.1016/j.jcp.2024.113161.png)
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摘要
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In this paper we develop a non -diffusive neural network (NDNN) algorithm for accurately computing weak solutions to hyperbolic conservation laws. The principle is to construct these weak solutions by computing smooth local solutions in subdomains bounded by discontinuity lines (DLs), the latter defined from the Rankine-Hugoniot jump conditions. The proposed approach allows to efficiently consider an arbitrary number of entropic shock waves, shock wave generation, as well as wave interactions. Some numerical experiments are presented to illustrate the strengths and properties of the algorithms.
Keyword:
Hyperbolic equations
Conservation laws
Weak solutions
Optimization
Neural network
Scientific machine learning
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期刊
IF:
3.8
论文数:
1.6W
被引数:
7.4W
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