![]() 11, 12 employed neural networks to solve multiscale problems. 10 proposed a neural network-based indicator to correct the irregular solution in the discontinuous Galerkin scheme. ![]() 7, 8 Due to its high computational efficiency and scalability, especially on heterogeneous platforms, DNN has become a promising technique in scientific computing and even provides the possibility for real-time PDE solving 9. In recent years, deep neural network (DNN), which reveals superior capability to process and to predict complicated systems, has been widely employed in a variety of fields, e.g., natural language processing 5, computer vision 6, etc. Classic iterative solvers assure the precision and the reliability of the solutions but bring the challenge in terms of computational consumption. The discrete PDEs form sparse linear equations and are usually solved by iteration methods, e.g., the Gauss–Seidel method 1, the conjugate gradient (PCG) method, etc. The numerical methods for solving partial differential equations (PDEs) are among the most challenging and critical engineering problems.
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