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arXiv · 2403.15726

Convection-Diffusion Equation: A Theoretically Certified Framework for Neural Networks

Tangjun Wang·Chenglong Bao·Zuoqiang Shi
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Abstract

In this paper, we study the partial differential equation models of neural networks. Neural network can be viewed as a map from a simple base model to a complicate function. Based on solid analysis, we show that this map can be formulated by a convection-diffusion equation. This theoretically certified framework gives mathematical foundation and more understanding of neural networks. Moreover, based on the convection-diffusion equation model, we design a novel network structure, which incorporates diffusion mechanism into network architecture. Extensive experiments on both benchmark datasets and real-world applications validate the performance of the proposed model.

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Tangjun Wang, Chenglong Bao, Zuoqiang Shi. 2024-03-23. Convection-Diffusion Equation: A Theoretically Certified Framework for Neural Networks. https://arxiv.org/abs/2403.15726

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