Efficient Sampling Algorithms for Complex Models

Overview

Since the invention of the first general-purpose digital computer ENIAC, sampling methods (particularly Monte Carlo methods and their variants) have become one of the pillars of modern computational mathematics. With the increasing interest in machine learning and uncertainty quantification for scientific and engineering problems, sampling methods face a set of new challenges. Firstly, the ever-increasing size of observed data in scientific discovery often requires large-scale computational models to unravel the underlying phenomena beyond the observables. Such large-scale models are often computationally expensive to solve. Secondly, the driving factors of these models are often described by some analytically intractable and high-dimensional (or infinite-dimensional) random variables to account for all available information and uncertainty in the modelling and observation processes. Typical examples include seismic imaging, numerical weather forecast, Bayesian neural networks (NN), large queueing systems, Markov decision processes (MDP), nuclear waste disposal, etc. The computational burden and the high-dimensionality pose significant challenges in designing scalable sampling methods for solving these problems.

Active research groups advancing sampling algorithms and their theoretical foundations have been formed in most top universities and research institutes. The proposed program aims to bring together a group of researchers working at the forefront of sampling methods for scientific machine learning and uncertainty quantification. We will focus on three related themes: algorithmic development, mathematical foundation, and frontier applications.