Least-Squares ReLU Neural Network (LSNN) Method For Scalar Nonlinear Hyperbolic Conservation Law. (arXiv:2105.11627v4 [math.NA] UPDATED)

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

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 …

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