With the development of natural philosophy, the issue of wave motion has gradually attracted attention. There are numerous wave motion problems in the science and engineering fields, such as in earthquake engineering, marine engineering and acoustic vibration research. The purpose of wave motion research includes exploring the basic principles of wave propagation and solving practical problems in science and engineering. Its research paradigms includes a data-driven paradigm and principle-driven paradigm. Wave motion problems are usually expressed using differential equations or variational principles. For a long time in the past, differential equations or variational equations of wave motion problems had been solved through mathematical physics simulations. Mathematical physics simulations include numerical simulation and analytical methods. With the development of computers, intelligent models have gradually been applied to solve scientific and engineering problems requiring a large amount of computation and data, including wave motion. There are data-driven intelligent models, physics-informed intelligent models and coupled data-driven and physics-driven intelligent models. Data-driven intelligent models require a theory and knowledge of artificial intelligence and data analysis, including machine learning, image processing and signal processing. Physics-driven intelligent models require a theory and knowledge of artificial intelligence and numerical analysis, including network structures, network geometries and residual penalties. The use of intelligent models to solve wave motion problems has gradually become a mainstream and hot topic; however, the natural philosophical value of intelligent models and mathematical physics simulations in solving wave motion problems should be regarded dialectically. For instance, deep learning models with large numbers of parameters, often with more than a billion or even tens of billions or trillions of parameters, can handle complex wave motion problems. Therefore, intelligent models can provide more accurate target identification, more efficient solutions and faster prediction. Compared to mathematical physics simulations, however, they lack natural philosophical interpretability, physical consistency and basic mathematical principles. In conclusion, intelligent models and mathematical physics simulations have independent and high philosophical values in wave motion research, and they should be given equal attention.