Abstract: We propose a novel machine learning algorithm inspired by complex analysis. Our algorithm has a better mathematical formulation and can approximate universal functions more efficiently. The algorithm can be implemented in two self-learning neural networks: The CauchyNet and the X-Net. The CauchyNet is very efficient for low-dimensional problems such as extrapolation, imputation, numerical solutions of PDEs and ODEs. The X-Net, on the other hand, works for large dimensional problems such as mage and voice recognitions, transformer and large language models. We will present some examples that works well with our algorithms. We show that it is much more efficient than many popular PINN models for various scientific computations. Also, for a set of brain tumor images we tested, it can increase accuracy from 88% to 98%. Our algorithm is yet to be tested on large complex problems.
报告人简介：夏志宏，美国西北大学数学系潘克讲席教授，大湾区大学（筹）讲座教授。主要研究兴趣为动力系统、太阳系动力学，人工智能算法。主要成就包括解决百年悬而未决的庞勒维猜想。曾获多项国际重大学术奖励，包括美国国家青年研究者奖、Sloan Research Fellowship、首届布拉门塞尔纯数学进步奖、Monroe Martin应用数学奖。2015年创建南方科技大学数学系并任系主任。2015年参与建立未来科学大奖，是大奖科学委员会创始成员；2022年起担任《知识分子》杂志总编辑之一。夏志宏1982年毕业于南京大学天文系，1988年获得美国西北大学数学博士学位。
