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		题名	作者	年代	出处	被引量
	1	A Local Deep Learning Method for Solving High Order Partial Differential Equations显示文摘At present, deep learning based methods are being employed to resolvethe computational challenges of high-dimensional partial differential equations(PDEs). But the computation of the high order derivatives of neural networks iscostly, and high order derivatives lack robustness for training purposes. We proposea novel approach to solving PDEs with high order derivatives by simultaneously approximating the function value and derivatives. We introduce intermediate variablesto rewrite the PDEs into a system of low order differential equations as what is donein the local discontinuous Galerkin method. The intermediate variables and the solutions to the PDEs are simultaneously approximated by a multi-output deep neuralnetwork. By taking the residual of the system as a loss function, we can optimizethe network parameters to approximate the solution. The whole process relies onlow order derivatives. Numerous numerical examples are carried out to demonstrate that our local deep learning is efficient, robust, flexible, and is particularlywell-suited for high-dimensional PDEs with high order derivatives.	Jiang Yang Quanhui Zhu	2022	Numerical Mathematics(Theory,Methods and Applications)2022，15，1：	0

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