本文用多层前向神经网络求解该非线性偏微分方程，从而逼近非线性系统的中心流形。

In this paper, multi-layer feedforward neural networks are used to solve the nonlinear partial differential equation, and approach the centre manifold of the nonlinear system.

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它遵循的主要附加要求是，该多组分直达波激发包括前向散射场马尔·琴科方程的迭代解决方案。

It follows that the main additional requirement is that the multicomponent direct arrival, needed to initiate the iterative solution of the Marchenko equation, includes the forward-scattered field.

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在光束传输法中只分析前向亥姆霍兹方程，而后向分量近似为零。

Only positive Helmholtz equation is considered in beam propagation method, while the negative component is approximately zero.

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