AI for Design
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In this talk, we will use fiction stir welding as a case study to illustrate the idea of AI for design. The friction stir welding process can be modelled using a system of heat transfer and Navier-Stokes equations with a shear dependent viscosity. Finding numerical solutions of this system of nonlinear partial differential equations over a set of parameter space, however, is extremely time-consuming. Therefore, it is desirable to find a computationally efficient method that can be used to obtain an approximation of the solution with acceptable accuracy. In this paper, we present a reduced basis method for solving the parametrized coupled system of heat and Navier-Stokes equations using a proper orthogonal decomposition (POD). In addition, we apply a machine learning algorithm based on an artificial neural network (ANN) to learn (approximately) the relationship between relevant parameters and the POD coefficients. This is joint work with X. Ca, Z. Song, K. Fraser and C. Drummer.
黄华雄教授，北京师范大学-香港浸会大学联合国际学院讲座教授、学术副校长，BNU-UIC联合数学研究中心讲座教授、执行主任。黄华雄教授于1984年本科毕业于复旦大学数学系，1992年获加拿大UBC应用数学博士学位。加入北京师范大学前，任加拿大国立Fields数学研究所常务副所长、YORK大学数学系教授，加拿大自然科学基金会应用数学部门主任委员，加拿大工业与应用数学学会理事。黄华雄教授的研究方向为应用数学，包括科学计算，数学建模，生物及金融数学，在Nature Communications、JFM、JCP等国际期刊上已发表100余篇学术论文，剑桥出版社出版专著1部。近20年来为促进工业数学和应用数学发展，作为主持或者联合主持组织了50余场国际、以及中加之间的应用数学学术交流会。担任Frontiers in Genetics, Mathematical Biosciences and Engineering, Journal of Engineering Mathematics等5个国际期刊主编或副主编。获得加拿大应用与工业数学学会Fields奖，美国Pacific Institute 工业数学杰出成就奖。
