On the morning of May 10, 2026, at 10:00 AM, the latest installment of this semester's academic lecture series was held in Room 526 of the Xingjian Building. The keynote speaker was Professor Wenjun Ying from the Institute of Natural Sciences and the School of Mathematical Sciences at Shanghai Jiao Tong University, who is a recipient of national-level high-level talent honors. The lecture, titled "Neural Network-Integrated Numerical Methods for Compressible Flows", was chaired by Professor Wenjun Cai. Participants included Professor Zhiyue Zhang, Professor Feng Wang, Associate Professor Yuze Zhang, Dr. Caixia Nan, as well as several doctoral and master's students.During the presentation, Professor Ying introduced two innovative neural network-based numerical methods for compressible fluid dynamics. The first method achieves high-resolution, low-dissipation reconstruction by utilizing a neural network that automatically identifies whether to employ MUSCL or THINC schemes based on normalized data. This approach ensures the Total Variation Diminishing (TVD) property, effectively suppressing numerical oscillations while minimizing dissipation. Additionally, Professor Ying detailed a cavitation model (Equation of State) that fuses physical information with data. By applying logarithmic and exponential functions to the input and output stages of the neural network, the model eliminates system stiffness and ensures the positivity of pressure output. The report showcased various typical 2D and 3D compressible flow simulation cases, demonstrating the robustness and reliability of these deep learning-enhanced algorithms. As an expert in high-precision numerical methods for partial differential equations with a focus on engineering applications, Professor Ying shared insights from his extensive research supported by the National Natural Science Foundation of China and various national research institutes.The session concluded with a brief summary by Professor Ying, followed by an engaging discussion among the faculty regarding the integration of
neural networks with traditional numerical solvers and their practical implementation in industrial software. This academic report highlighted the frontier of solving partial differential equations through deep learning, significantly broadening the students' academic horizons. The college's seminar series will continue to focus on the mathematical foundations and cutting-edge developments in scientific computing and quantum dynamics.