Web: http://arxiv.org/abs/2105.11627

Jan. 26, 2022, 2:11 a.m. | Zhiqiang Cai, Jingshuang Chen, Min Liu

cs.LG updates on arXiv.org arxiv.org

We introduced the least-squares ReLU neural network (LSNN) method for solving
the linear advection-reaction problem with discontinuous solution and showed
that the method outperforms mesh-based numerical methods in terms of the number
of degrees of freedom. This paper studies the LSNN method for scalar nonlinear
hyperbolic conservation law. The method is a discretization of an equivalent
least-squares (LS) formulation in the set of neural network functions with the
ReLU activation function. Evaluation of the LS functional is done by using …

arxiv law least math network neural neural network squares

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