Neural Operator for Multidisciplinary Engineering Design

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.