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arXiv 2103.08313cs.LGcs.AI
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生成神经架构只需偏微分方程——物理人工智能系统理论

Partial Differential Equations is All You Need for Generating Neural Architectures -- A Theory for Physical Artificial Intelligence Systems

Beijing Normal University（北京师范大学）；Duke Kunshan University（昆山杜克大学）；Harbin Institute of Technology at ShenZhen（哈尔滨工业大学（深圳））

Ping Guo, Kaizhu Huang, Zenglin Xu

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15 pages, 5 figures
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AI总结：

本文将物理方程推广为神经偏微分方程（NPDE），通过有限差分法离散化生成深度神经网络基础架构及学习策略，为可解释神经网络和物理人工智能奠定理论基础。

摘要：

在本研究中，我们将统计物理中的反应扩散方程、量子力学中的薛定谔方程以及近轴光学中的亥姆霍兹方程推广为神经偏微分方程（NPDE），该方程可被视为人工智能研究领域的基方程。我们采用有限差分法对NPDE进行离散化以求解数值解，从而生成了深度神经网络架构的基础构建模块，包括多层感知机、卷积神经网络和循环神经网络。此外，还提出了学习策略，如自适应矩估计、L-BFGS、伪逆学习算法以及偏微分方程约束优化。我们认为，给出可解释深度神经网络清晰的物理图像具有重要意义，这使得将其应用于模拟计算设备设计成为可能，并为物理人工智能铺平了道路。

英文摘要：

In this work, we generalize the reaction-diffusion equation in statistical physics, Schrödinger equation in quantum mechanics, Helmholtz equation in paraxial optics into the neural partial differential equations (NPDE), which can be considered as the fundamental equations in the field of artificial intelligence research. We take finite difference method to discretize NPDE for finding numerical solution, and the basic building blocks of deep neural network architecture, including multi-layer perceptron, convolutional neural network and recurrent neural networks, are generated. The learning strategies, such as Adaptive moment estimation, L-BFGS, pseudoinverse learning algorithms and partial differential equation constrained optimization, are also presented. We believe it is of significance that presented clear physical image of interpretable deep neural networks, which makes it be possible for applying to analog computing device design, and pave the road to physical artificial intelligence.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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