Abstract
AbstractIn this paper, we present a deep neural network-based framework for solving nonlinear partial differential equations (PDEs) and applying in denoising image. A loss function that relies on form PDEs, initial and boundary condition (I/BC) residual was proposed. The proposed loss function is discretization-free and highly parallelizable. The network parameters are determined by using stochastic gradient descent algorithm. We demonstrated the performance of proposed method in solving nonlinear partial diferential equation and applying image denoising. The experimental results from this method were compared to the efficient PDE’s numerical method. We showed that the method attains significant improvements in term image denoising.KeywordsNonlinear diffusion equationNeural networkDeep learningImage denoising
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