Learning Correlations Between Computational Scale and Performance for Accurate Numerical Modeling: Application Case of Dam‐Break Flood Processes

Scientists aim to accurately simulate and characterize complex natural phenomena, thus revealing the underlying natural laws or physical mechanisms governing these phenomena. Conventional physical experiments require significant time and cost, and numerical methods offer an alternative solution. However, modeling complex phenomena such as fluid flow in dam‐break flood often demand extensive computational resources, which makes it impractical to perform accurate modeling the process of large‐scale dam‐break flood. This paper proposes a general knowledge‐data dually driven paradigm that enables accurate numerical modeling of complex natural phenomena without relying on large‐scale simulation data. The essential idea behind the proposed paradigm is to learn correlations between computational scale and performance by training small‐scale simulation data, thus achieving accurate modeling of large–scale complex phenomena. The steps of the proposed paradigm include (1) generating training data for small‐scale natural phenomena by integrating domain knowledge using numerical methods, (2) learning correlations between computational scale and performance using deep learning models, and (3) accurately modeling the processes of large–scale complex phenomena through resolution upscaling. We demonstrate the proposed paradigm using the case study of dam‐break flood processes and propose the smoothed particle hydrodynamics‐physics‐informed neural network (SPH‐PINN) method for accurate fine‐particle simulation of large‐scale dam‐break flood. Experimental results demonstrate that the proposed knowledge‐data dually driven paradigm provides an effective reference for accurately modeling and understanding complex natural phenomena. The proposed paradigm contributes to deeply analyzing and understanding the underlying laws and mechanisms of natural phenomena, offering valuable insights and guidance for scientific research and engineering applications.