This paper presents a method for successfully simulating turbulent high-speed fluid flows using physics-informed neural networks (PINNs), a deep learning model based on physical equations. Without the need for a traditional computational grid or training data, the system directly learns two- and three-dimensional fully turbulent flows by combining adaptive network architectures, causal training, and advanced optimization methods. It accurately reproduces key flow statistics, such as energy spectrum, kinetic energy, eddy, and Reynolds stress, and demonstrates its ability to handle complex chaotic systems.
