CENN: Conservative energy method based on neural networks with subdomains for solving variational problems involving heterogeneous and complex geometries. (arXiv:2110.01359v3 [math.NA] UPDATED)

Web: http://arxiv.org/abs/2110.01359

We propose a conservative energy method based on neural networks with
subdomains for solving variational problems (CENN), where the admissible
function satisfying the essential boundary condition without boundary penalty
is constructed by the radial basis function (RBF), particular solution neural
network, and general neural network. Loss term is the potential energy,
optimized based on the principle of minimum potential energy. The loss term at
the interfaces has the lower order derivative compared to the strong form PINN
with subdomains. The …

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