Adaptive two-layer ReLU neural network: I. Best least-squares approximation
Adaptive two-layer ReLU neural network: I. Best least-squares approximation
复制标题
DOI：
10.1016/j.camwa.2022.03.005
复制
发表时间：
2022-03-17
影响因子：
2.9
通讯作者：
Chen, Jingshuang
中科院分区：
文献类型：
--
作者：
Liu, Min;Cai, Zhiqiang;Chen, Jingshuang
在本文中，我们介绍了自适应网络增强（ANE）方法，使用双层ReLU神经网络（NN）进行最佳最小二乘逼近。对于给定的函数f（x），ANE方法生成两层ReLU NN和数值积分网格，使得近似精度在规定的公差范围内。ANE方法提供了一个自然的过程来获得一个良好的初始化，这对于训练非线性优化问题至关重要。两个变量的函数表现出相交的界面奇异性或尖锐的内部层的数值结果表明ANE方法的效率。
In this paper, we introduce adaptive network enhancement (ANE) method for the best least-squares approximation using two-layer ReLU neural networks (NNs). For a given function f(x), the ANE method generates a two-layer ReLU NN and a numerical integration mesh such that the approximation accuracy is within the prescribed tolerance. The ANE method provides a natural process for obtaining a good initialization which is crucial for training nonlinear optimization problems. Numerical results for functions of two variables exhibiting either intersecting interface singularities or sharp interior layers demonstrate efficiency of the ANE method.