In this paper, the problem of estimating the level set of a black-box function from noisy and expensive evaluation queries is considered. A new algorithm for this problem in the Bayesian framework with a Gaussian Process (GP) prior is proposed. The proposed algorithm employs a hierarchical sequence of partitions to explore different regions of the search space at varying levels of detail depending upon their proximity to the level set boundary. It is shown that this approach results in the algorithm having a low complexity implementation whose computational cost is significantly smaller than the existing algorithms for higher dimensional search space $\X$. Furthermore, high probability bounds on a measure of discrepancy between the estimated level set and the true level set for the the proposed algorithm are obtained, which are shown to be strictly better than the existing guarantees for a large class of GPs. In the process, a tighter characterization of the information gain of the proposed algorithm is obtained which takes into account the structured nature of the evaluation points. This approach improves upon the existing technique of bounding the information gain with maximum information gain.
Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems
ShanghaiTech University（上海科技大学）；University of Notre Dame（圣母大学）；Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences（中国科学院上海微系统与信息技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Scale-Adaptive Generative Flows for Multiscale Scientific Data
Department of Mathematics, University of California, Los Angeles（加州大学洛杉矶分校数学系）；Machine Learning Lab, Capital Fund Management（资本基金管理有限公司机器学习实验室）；Courant Institute, New York University（纽约大学柯朗研究所）
Operator-Informed Gaussian Processes for Complex Helmholtz Wavefields: From Synthetic Benchmarks to In Vivo Brain Elastography
Department of Civil and Systems Engineering, Johns Hopkins University（约翰霍普金斯大学土木与系统工程系）；Department of Aerospace Engineering and Mechanics, University of Minnesota（明尼苏达大学航空航天工程与力学系）
Robust Parameter and State Estimation in Multiscale Neuronal Systems Using Physics-Informed Neural Networks
Department of Mathematics, University of Iowa（数学系，爱荷华大学）；Department of Mathematics, Volen National Center for Complex Systems, Brandeis University（数学系，布兰迪大学复杂系统国家中心）
