Scientific machine learning (SciML) is an emerging interdisciplinary field of research that integrates traditional scientific disciplines with machine learning methods to solve complex scientific problems. The primary goal of SciML is to enable researchers to leverage the power of machine learning to accelerate scientific discovery and to build predictive models that can simulate and optimize complex scientific systems. Scientific machine learning methods can be applied to a wide range of scientific fields, including applied mathematics, physics, chemistry, biology, geoscience, climate science, and materials science, among others. In this summer course, we aim to introduce the latest advances in scientific machine learning. Specifically, we will introduce fast algorithms in evaluating multivariate normal distributions and the transformer model; compressed representations of layer and volume potentials using algebraic variety; random Fourier features in machine learning; operator learning in PDE problems. We hope to provide new perspectives and directions for scholars and academics to study machine learning in science.

Date: 7/17

Title: Fast algorithm for computing the expectations of high dimensional truncated multivariate normal distributions

 

Date: 7/18

Title: Frequency domain statistical analysis

 

Date: 7/31

Title: Fast algorithm for speeding up transformer computations

 

Date: 8/1

Title: Compressed representations of layer and volume potentials using algebraic variety

Topic 2: Machine learning methods for PDEsSpeaker: Petr Plechac (University of Delaware, USA)

 

Date: 7/24, 7/25

Title: Random Fourier features and connections to neural networks and approximations of differential equations

 

Date: 8/7, 8/8

Title: Diffusion probabilistic models and their application to operator learning in parametric or random coefficient PDE problems.