Structured and Balanced Multi-Component and Multi-Layer Neural Networks
This work addresses efficiency and accuracy challenges in function approximation for computational applications, though it appears incremental as a modification of existing neural network architectures.
The paper tackles the problem of approximating complex functions with neural networks by proposing a balanced multi-component and multi-layer structure (MMNN), which reduces training parameters and computational cost while improving accuracy compared to fully connected networks, as shown in numerical experiments on highly oscillatory functions.
In this work, we propose a balanced multi-component and multi-layer neural network (MMNN) structure to accurately and efficiently approximate functions with complex features, in terms of both degrees of freedom and computational cost. The main idea is inspired by a multi-component approach, in which each component can be effectively approximated by a single-layer network, combined with a multi-layer decomposition strategy to capture the complexity of the target function. Although MMNNs can be viewed as a simple modification of fully connected neural networks (FCNNs) or multi-layer perceptrons (MLPs) by introducing balanced multi-component structures, they achieve a significant reduction in training parameters, a much more efficient training process, and improved accuracy compared to FCNNs or MLPs. Extensive numerical experiments demonstrate the effectiveness of MMNNs in approximating highly oscillatory functions and their ability to automatically adapt to localized features.