A philosophy exploration on intelligent models and mathematical physics simulations for the wave motion problems

The improvement of natural philosophy epistemology and methodologies contributes to progress and development of the science and engineering. At same time, development of the science and engineering also extends natural philosophy epistemology and methodologies. Wave motion belongs to natural philosophy, science and engineering fields. Wave motion problems can be explored through scientific computation. However, with the development of big data and artificial intelligence, both new and traditional computing methods are facing opportunities and challenges. A philosophy exploration is therefore carried out, aiming to provide a good computing idea and way for wave motion problems. This philosophy exploration employs logic decision and dialectical reasoning. Logic decision needs true premises and strict thinking models. It can give the reasonable explanation and illustration. More importantly, it is extensively used in philosophy and mathematics. Dialectical reasoning is based on the dialectical logic, dynamic perspectives and scientific facts for exploring the uncertain problems. It also maintains a balance between the form and content of thought. Intelligent models are considered as new computing methods for wave motion problems. Besides, mathematical physics simulations are considered as traditional computing methods for wave motion problems. Intelligent models for wave motion problems are programs for abstract simulations of phenomena and laws of wave motion through mathematics and algorithms. Intelligent models include data-driven intelligent models, physics-informed intelligent models and coupled data-driven and physics-driven intelligent models. Moreover, mathematical physics simulations for wave motion problems are formulae describing phenomena and laws of wave motion through mathematics and physics. Mathematical physics simulations include numerical simulation and analytical methods. Data-driven and physics-informed intelligent models can be updated and improved based on existing algorithmic program components to solve practical complex wave motion problems. However, compared with mathematical physics simulations, data-driven and physics-informed intelligent models lack the strict reasoning and proof of fundamental mathematics when solving wave motion problems. In addition, they lack the description and explanation of natural phenomena and change processes. The computing results may seriously deviate from the true objective patterns and changing characteristics of natural or engineering physical phenomena. In conclusion, data-driven and physics-informed intelligent models are more suitable for complex wave motion problems with a large number of parameters. Mathematical physics simulations are applicable to the study of the patterns and characteristics of fundamental steady-state and transient wave motion problems. This philosophy exploration offers new ideas for solving wave motion problems, and advances the wave motion sustainable development.