Web: http://arxiv.org/abs/2201.09989

Jan. 26, 2022, 2:10 a.m. | Suchuan Dong, Jielin Yang

cs.LG updates on arXiv.org arxiv.org

We present a method for solving linear and nonlinear PDEs based on the
variable projection (VarPro) framework and artificial neural networks (ANN).
For linear PDEs, enforcing the boundary/initial value problem on the
collocation points leads to a separable nonlinear least squares problem about
the network coefficients. We reformulate this problem by the VarPro approach to
eliminate the linear output-layer coefficients, leading to a reduced problem
about the hidden-layer coefficients only. The reduced problem is solved first
by the nonlinear least …

artificial arxiv math networks neural neural networks numerical projection

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