主讲人：黄政宇 北京大学研究员
时间：2024年6月27日10：30
地点：三号楼332室
举办单位：数理学院
内容介绍：Deep learning surrogate models have shown promise in solving partial differential equations. These efficient deep learning surrogate models enable many-query computations in science and engineering, in particular the engineering design optimization we focus on. In this talk, I will first introduce a geometry-aware Fourier neural operator (Geo-FNO) to solve PDEs on arbitrary geometries, inspired by adaptive mesh motion and spectral methods. Furthermore, we study the cost-accuracy trade-off of different deep learning-based surrogate models, following traditional numerical error analysis, as the first step to building a complete theory of approximation error for these approaches. We demonstrate numerically the superior cost-accuracy trade-off of our approach. Finally, combining automatic differentiation tools of deep learning libraries, which efficiently compute gradients with respect to input variables enabling the use of gradient-based design optimization methods, our approach has demonstrated significant speed-up of airfoil design in transonic flow and real-world biomedical catheter design to prevent bacteria contamination.
