基于波动与扩散物理系统的机器学习

Machine learning based on wave and diffusion physical systems

物理学在机器学习中的应用以及两者的交叉融合正引起广泛关注,尤其是在波动系统和扩散系统中.本文重点关注波动与扩散物理系统和机器学习之间的内在联系以及对机器学习算法和物理实现的推进作用,综述了波动系统和扩散系统中的机器学习研究,介绍了部分最新研究成果.文中首先讨论了监督学习的波动系统实现,包括神经网络的波动光学实现、量子搜索的波动实现、基于波动系统的递归神经网络以及神经形态的非线性波动计算.接着,文中继续讨论了受扩散系统启发的机器学习算法,如基于扩散动力学的分类算法,基于热扩散的数据挖掘和信息过滤,以及基于群体扩散的搜索优化等.波动系统以其天然的并行性、高效、低能耗等优势,通过丰富的波动力学和波动物理现象进行计算或算法模拟,正成为机器学习的新型物理载体.扩散系统中的物理机制可以启发构建高效的机器学习算法,用于复杂系统和物理学研究中的分类、优化等问题.期望通过对波动、扩散物理系统与机器学习内在联系的讨论,能够为开发物理启发的新算法和硬件实现甚至软硬一体化带来抛砖引玉的启示.

Recently,the application of physics to machine learning and the interdisciplinary convergence of the two have attracted wide attention.This paper focuses on exploring the internal relationship between physical systems and machine learning,and also on promoting machine learning algorithm and physical implementation.We summarize the researches of machine learning in wave systems and diffusion systems,and introduce some of the latest research results.We first discuss the realization of supervised learning for wave systems,including the wave optics realization of neural networks,the wave realization of quantum search,the recurrent neural networks based on wave systems,and the nonlinear wave computation of neural morphology.Then,we discuss the machine learning algorithms inspired by diffusion systems,such as the classification algorithm based on diffusion dynamics,data mining and information filtering based on thermal diffusion,searching for optimization based on population diffusion,etc.The physical mechanism of diffusion system can inspire the construction of efficient machine learning algorithms for the classification and optimization of complex systems and physics research,which may create a new vision for the development of physics inspired algorithms and hardware implementation,and even the integration of software and hardware.