Speaker: Xu Yang

Title: Machine Learning and Seismic Tomography

Abstract: The stochastic gradient descent (SGD) method and deep neural networks (DNN) are two main workhorses in machine learning. In this talk, we present some preliminary results on connecting SGD and DNN to the applications in seismic tomography. On the one hand, motivated by SGD, we propose to use random batch methods to construct the gradient for iterations in seismic tomography. On the other hand, we use deep neural networks to create a reliable PmP database from massive seismic data and study the case in Southern California. The major difficulty lies in that the identifiable PmP waves are rare, making the problem of identifying the PmP waves from a massive seismic database inherently unbalanced.

Short Bio:

Xu Yang got his Ph.D. at the University of Wisconsin-Madison in 2008, and spent two years at Princeton and two years at Courant Institute of NYU as a postdoc. He joined the University of California, Santa Barbara as an assistant professor in 2012, and became a full professor in 2020. His current research focuses on seismic imaging using realistic earthquake data. He has also been working on the applied analysis and numerical computation of scientific problems, including photonic graphene, ferromagnetic materials, and biological modeling.

Video: http://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=Machine_Learning_and_Seismic_Tomography.html 

Speaker: Ruimeng Hu

Title: Directed Chain Generative Adversarial Networks for Multimodal Distributed Financial Data

Abstract: Real-world financial data can be multimodal distributed, and generating multimodal distributed real-world data has become a challenge to existing generative adversarial networks (GANs). For example, neural stochastic differential equations (Neural SDEs), treated as infinite-dimensional GANs, are only capable of generating unimodal time series data. In this talk, we present a novel time series generator, named directed chain GANs (DC-GANs), which inserts a time series dataset (called a neighborhood process of the directed chain or input) into the drift and diffusion coefficients of the directed chain SDEs with distributional constraints. DC-GANs can generate new time series of the same distribution as the neighborhood process, and the neighborhood process will provide the key step in learning and generating multimodal distributed time series. Signature from rough path theory will be used to construct the discriminator. Numerical experiments on financial data are presented and show a consistent outperformance over state-of-the-art benchmarks with respect to measures of distribution, data similarity, and predictive ability. If time permits, I will also talk about using Signature to solve mean-field games with common noise.

Short Bio:

Dr. Hu is an assistant professor jointly appointed by the Department of Mathematics, and Department of Applied Probability and Statistics, at the University of California, Santa Barbara (UCSB), USA. Her research includes machine learning, financial mathematics, game theory, and stochastic partial differential equations. Her research has been supported by NSF and the Simons Foundation. She has published 20+ papers in top journals including Mathematical Finance, Notices of AMS, ICML, SIAM Journal on Control and Optimization, and SIAM Journal on Financial Mathematics. She is currently an associated editor of Digital Finance and has co-edited a special issue on machine learning in finance for Mathematical Finance.

Video: http://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=Directed_Chain_Generative_Adversarial_Networks_for_Multimodal_Distributed_Financial_Data.html