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In this paper, we propose the idea of radial scaling in frequency domain andactivation functions with compact support to produce a multi-scale DNN(MscaleDNN), which will have the multi-scale capability in approximating highfrequency and high dimensional functions and speeding up the solution of highdimensional PDEs. Numerical results on high dimensional function fitting andsolutions of high dimensional PDEs, using loss functions with either Ritzenergy or least squared PDE residuals, have validated the increased power ofmulti-scale resolution and high frequency capturing of the proposed MscaleDNN.

Multi-scale Deep Neural Networks for Solving High Dimensional PDEs