Learning-Based Multiscale Modelling: Computing, Data Science, and Uncertainty Quantification

Explore a comprehensive lecture on learning-based multiscale modeling, focusing on computing, data science, and uncertainty quantification in materials science. Delve into the complex interactions between physics at multiple lengths and time scales that determine macroscopic properties of materials. Discover how multiscale modeling leverages inherent hierarchies to understand these interactions. Learn about machine learning frameworks addressing challenges in multi-scale modeling, including Fourier neural operators (FNOs) for accelerating fine-scale model solutions and recurrent neural operators (RNOs) for bridging scales and providing insights into history dependence and macroscopic internal variables. Conclude with a discussion on quantifying uncertainty propagation through length scales in materials modeling.