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- W4380687208 abstract "The least-squares ReLU neural network method (LSNN) was introduced and studied for solving linear advection-reaction equation with discontinuous solution in cite{Cai2021linear,cai2023least}. The method is based on an equivalent least-squares formulation and employs ReLU neural network (NN) functions with a $lceil log_2(d+1)rceil+1$ layer representation for approximating the solution. In this paper, we show theoretically that the method is also capable of approximating a non-constant jump along the discontinuous interface of the underlying problem that is not necessarily a straight line. Numerical results for test problems with various non-constant jumps and interfaces show that the LSNN method with $lceil log_2(d+1)rceil+1$ layers approximates the solution accurately with DoFs less than that of mesh-based methods and without the common Gibbs phenomena along the discontinuous interface." @default.
- W4380687208 created "2023-06-15" @default.
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- W4380687208 date "2023-06-12" @default.
- W4380687208 modified "2023-10-16" @default.
- W4380687208 title "Least-Squares Neural Network (LSNN) Method For Linear Advection-Reaction Equation: Non-constant Jumps" @default.
- W4380687208 doi "https://doi.org/10.48550/arxiv.2306.07445" @default.
- W4380687208 hasPublicationYear "2023" @default.
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