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.