# Finite Volume Least-Squares Neural Network (FV-LSNN) Method for Scalar Nonlinear Hyperbolic Conservation Laws

@article{Cai2021FiniteVL, title={Finite Volume Least-Squares Neural Network (FV-LSNN) Method for Scalar Nonlinear Hyperbolic Conservation Laws}, author={Zhiqiang Cai and Jingshuang Chen and Min Liu}, journal={ArXiv}, year={2021}, volume={abs/2110.10895} }

In [4], we introduced the least-squares ReLU neural network (LSNN) method for solving the linear advection-reaction problem with discontinuous solution and showed that the number of degrees of freedom for the LSNN method is significantly less than that of traditional mesh-based methods. The LSNN method is a discretization of an equivalent least-squares (LS) formulation in the class of neural network functions with the ReLU activation function; and evaluation of the LS functional is done by…

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Least-Squares ReLU Neural Network (LSNN) Method For Scalar Nonlinear Hyperbolic Conservation Law

- Mathematics, Computer ScienceArXiv
- 2021

Numerical results of some test problems show that the LSNN method is capable of approximating the discontinuous interface of the underlying problem automatically through the free breaking lines of the ReLU neural network.

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Numerical results of some test problems show that the LSNN method is capable of approximating the discontinuous interface of the underlying problem automatically through the free breaking lines of the ReLU neural network.

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