It is well-known that artificial neural networks are universal approximators. The classical existence result proves that, given a continuous function on a compact set embedded in an $n$-dimensional space, there exists a one-hidden-layer feed-forward network that approximates the function. In this paper, a constructive approach to this problem is given for the case of a continuous function on triangulated spaces. Once a triangulation of the space is given, a two-hidden-layer feed-forward network with a concrete set of weights is computed. The level of the approximation depends on the refinement of the triangulation.

中文翻译：

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两层前馈网络是通用逼近器：一种构造方法。

众所周知，人工神经网络是通用近似器。经典的存在结果证明，在嵌入到$ñ$在三维空间中，存在一个逼近该函数的单层前馈网络。在本文中，针对三角空间上的连续函数，给出了针对此问题的构造方法。一旦给定了空间的三角剖分，就会计算出具有特定权重集的两层前馈网络。近似程度取决于三角剖分的细化程度。