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Neural Operator for Multidisciplinary Engineering Design

发布者:文明办发布时间:2024-06-27浏览次数:82


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.