题 目 一：Regularization methods for dynamic system identification
摘 要 一：Kernel-based regularization methods (KRMs) have opened up a new paradigm for system identification in comparison with classic identification methods. The KRM has two key issues: kernel design and hyperparameter estimation. Kernel design is to parameterize prior knowledge of dynamic systems and hyperparameter estimation is to estimate the hyperparameters in the parameterization by the data. This talk will mainly focus on the asymptotic optimality of the KRM for hyperparameter estimation, particularly, 1) to introduce the optimality criteria; 2) to derive the properties of the optimal kernel matrices and the optimal hyperparameter estimators; 3) to investigate the asymptotic optimality of practical estimators, e.g., empirical Bayes, Stein’s unbiased risk estimator, and cross validation.
报告人二：周涛 研究员（计算与科学工程计算数学研究所）
题 目 二：Deep adaptive sampling for numerical PDEs
摘 要 二: Adaptive computation is of great importance in numerical simulations. The ideas for adaptive computations can be dated back to adaptive finite element methods in 1970s. In this talk, we shall first review some recent development for adaptive method with applications. Then, we shall propose a deep adaptive sampling method for solving PDEs where deep neural networks are utilized to approximate the solutions. In particular, we propose the failure informed PINNs (FI-PINNs), which can adaptively refine the training set with the goal of reducing the failure probability. Compared to the neural network approximation obtained with uniformly distributed collocation points, the developed algorithms can significantly improve the accuracy, especially for low regularity and high-dimensional problems.
学术报告会
概况介绍