Math 7390 - Topics in Numerical Analysis
Syllabus
Instructor: Xiaoliang Wan Lecture: MWF 1:30-2:20pm, 119 Lockett Hall Office Hours: TThW 10:00-11:30pm, or by appointment Description: Scientific machine learning has emerged as an important research topic, which deals with scientific computing problems using machine learning techniques. One essential feature of machine learning techniques is that they are data-driven, which shares similarities with traditional meshless methods. In this course, we pay particular attention to techniques related to data distribution and sample generation, including both classical methods and deep generative models. We first overview some fundamental approximation and machine learning problems, including interpolation, regression and classification. We then discuss some classical techniques for high-dimensional integral and sample generation, such as the Monte Carlo method and Markov Chain Monte Carlo. Finally, we introduce deep generative models, including normalizing flows, variational auto-encoder, and diffusion models, which are capable of merging PDF approximation and sample generation for high-dimensional distributions..
Homework
| Instructor: | Xiaoliang Wan |
| Lecture: | MWF 1:30-2:20pm, 119 Lockett Hall |
| Office Hours: | TThW 10:00-11:30pm, or by appointment |
| Description: | Scientific machine learning has emerged as an important research topic, which deals with scientific computing problems using machine learning techniques. One essential feature of machine learning techniques is that they are data-driven, which shares similarities with traditional meshless methods. In this course, we pay particular attention to techniques related to data distribution and sample generation, including both classical methods and deep generative models. We first overview some fundamental approximation and machine learning problems, including interpolation, regression and classification. We then discuss some classical techniques for high-dimensional integral and sample generation, such as the Monte Carlo method and Markov Chain Monte Carlo. Finally, we introduce deep generative models, including normalizing flows, variational auto-encoder, and diffusion models, which are capable of merging PDF approximation and sample generation for high-dimensional distributions.. |