Additive Schwarz algorithms for neural network approximate solutions

11/01/2022

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by   Hee Jun Yang, et al.

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Additive Schwarz algorithms are proposed as an iterative procedure for neural network approximate solutions of partial differential equations. Based on the convergence analysis of the additive Schwarz algorithms in a general Hilbert space setting, the convergence of the neural network approximate solutions is analyzed for the one-level and two-level iterative schemes. Numerical results of the proposed methods are presented for test examples.