Work

Chebyshev Feature Neural Network for Accurate Function Approximation

Year: 2025

Type: article

Abstract: We present a new deep neural network (DNN) architecture capable of approximating functions up to machine accuracy. Termed the Chebyshev feature neural network (CFNN), the new structure employs Chebyshev functions with learnable frequencies as the first hidden layer, followed by the standard fully connected hidden layers. The learnable frequencies of the Chebyshev layer are initialized with exponential distributions to cover a wide range of frequencies. Combined with a multistage training strategy, we demonstrate that this CFNN structure can achieve machine accuracy during training. A comprehensive set of numerical examples for dimensions up to 20 are provided to demonstrate the effectiveness and scalability of the method.

Source: Journal of Machine Learning for Modeling and Computing

DOI: 10.1615/jmachlearnmodelcomput.2025056536

Authors: Zhongshu Xu, Yuan Chen, Dongbin Xiu

Institution: The Ohio State University

Language: English

Topic: Neural Networks and Applications

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funder: Air Force Office of Scientific Research

Awards: G1523888516, G1847533296