北京智源人工智能研究院（简称“智源研究院”）是落实“北京智源行动计划”的重要举措，是在科技部和北京市委市政府的指导和支持下，由北京市科委和海淀区政府于2018年11月推动成立的新型研发机构。

为支持科学家勇闯人工智能科技前沿“无人区”，挑战最基础的问题和最关键的难题，推动人工智能理论、方法、工具、系统和应用取得变革性、颠覆性突破，智源研究院先后成立了「人工智能的数理基础」、「机器学习」、「智能信息检索与挖掘」、「智能体系架构与芯片」、「自然语言处理」、「人工智能的认知神经基础」等六个重大研究方向。

「人工智能的数理基础」重大方向，以北京大学张平文院士牵头，分别来自北大、清华、中科院的12位学者，围绕当前人工智能面临的可计算性、可解释性、泛化性、稳定性的重大理论挑战，以期打破基于计算机实验和神经科学的人工智能惯用建模范式，建立以数学与统计理论为第一原理的新一代人工智能方法论。

为促进该领域最前沿研究在国内广泛、快速地传播，以及提供学科交叉碰撞的平台，智源研究院「人工智能的数理基础」方向的诸位学者将不定期邀请世界范围内的顶尖学者进行系列前沿报告。

本期报告，我们分别邀请了清华大学自动化系长聘副教授江瑞、香港科技大学助理教授夏冬、湖南大学数学学院教授杨海建，就其最新研究做报告讲解。

时间形式

1. 会议时间：2021年6月30日14:00-17:00

2. 活动形式：腾讯会议（ID ：635 124 674）

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报告一

报告主题：概率密度估计的深度循环生成对抗网络模型

报告人：江  瑞

个人简介：2002年毕业于清华大学自动化系获工学博士学位，后在南加州大学进行博士后研究，2007年至今任清华大学自动化系副教授、长聘副教授。从事生物信息学研究15年，致力于运用人工智能与机器学习的理论与方法，研究生物信息与智能健康的重大关键问题，突破单细胞数据分析及基因组序列分析瓶颈，在 ① 细胞类型辨识、② 基因调控模式识别、③ 致病遗传因素定位等方面建立了原创性理论与方法，取得了具有国际影响力的突破性成果。已在顶级国际期刊发表SCI检索论文80余篇，包括：Nature子刊5篇，美国科学院院刊（Proc Natl Acad Sci USA）4篇等。

报告摘要：概率密度估计是统计学和机器学习领域的一个基本问题。由于“维数灾难”问题，对高维数据进行概率密度估计十分困难，现有基于神经网络的概率密度估计方法由于对模型结构进行严格的约束，大大削弱了神经网络的表达能力，从而可能导致性能下降。为解决这一问题，我们提出了一种名为Roundtrip的原创方法来进行概率密度估计。该方法利用深度生成式模型的强大生成能力，使用循环式生成对抗网络来对低维隐空间与高维原始数据空间的双向映射进行建模，随后通过重要性采样和拉普拉斯近似的手段对数据空间的概率密度进行估计，从而支持数据生成和概率密度估计的协同进行。在一系列实验中，Roundtrip都体现了比传统神经网络密度估计方法更优异的性能。Roundtrip由于其模型结构的灵活性性，使得其在监督学习、非监督学习等任务中具有良好的可扩展性。

报告二

报告主题：Riemannian Optimization for (robust) Low-rank Tensor Estimation

报告人：夏  冬

个人简介：Dr. Dong XIA is an Assistant Professor in Department of Mathematics at Hong Kong University of Science and Technology. He was a Postdoctral Research Scientist in Department of Statistics at Columbia University and a Visiting Assistant Professor in Department of Statistics at University of Wisconsin-Madison. He obtained his Ph.D. in Computational Science and Enginering and Mathematics from Georgia Institute of Technology in 2016. His research interest lies in high-dimensional statistics, machine learning theory and optimization. He is currently an Associate Editor of Journal of Statistical Planning and Inference.

报告摘要：We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or heterogeneous signals that are unexplainable by the low-rank part. The framework is flexible covering both linear and non-linear models, and can easily handle continuous or categorical variables. We propose a fast algorithm by integrating the Riemannian gradient descent and a novel gradient pruning procedure. Under suitable conditions, the algorithm converges linearly and can simultaneously estimate both the low-rank and sparse tensors. The statistical error bounds of final estimates are established in terms of the gradient of loss function. The error bounds are generally sharp under specific statistical models, e.g., the robust tensor PCA and the community detection in hypergraph networks with outlier vertices. Moreover, our method achieves non-trivial error bounds for heavy-tailed tensor PCA whenever the noise has a finite 2+ε moment. We apply our method to analyze the international trade flow dataset and the statistician hypergraph co-authorship network, both yielding new and interesting finding.

报告三

报告主题：A parallel and fully implicit constraint preserving simulator for multiphase flow in porous media

报告人：杨海建

个人简介：杨海建，湖南大学数学学院教授，博士生导师，信息与计算科学系系主任。主要从事与大规模并行计算相关的数学建模、基础算法和应用研究，研究领域涉及计算流体力学和油藏模拟等应用领域。

报告摘要：The modeling of multiphase fluid flow in porous medium is of interest in the field of reservoir simulation. The promising numerical methods in the literature are mostly based on the explicit or semi-implicit approach, which both have certain stability restrictions on the time step size. In this work, we introduce and study a scalable fully implicit solver for the simulation of multiphase flow a porous medium, which is free from the limitations of the conventional methods. In the fully implicit framework, the resultant nonlinear system arising at each time step is solved in a monolithic way by using a Newton-Krylov type method. The corresponding linear system from the Newton iteration is large sparse, nonsymmetric and ill-conditioned, consequently posing a significant challenge to the fully implicit solver. To address this issue, the family of additive Schwarz preconditioners is taken into account to accelerate the convergence of the linear system, and thereby improves the robustness of the outer Newton method. Several test cases are used to validate the correctness of the scheme and examine the performance of the newly developed algorithm on parallel computers.