Prof. Dongbin Xiu | Ohio State University | United States
One of the central tasks in scientific computing is to accurately approximate unknown target functions. This is typically done with the help of data — samples of the unknown functions. The emergence of Big Data presents both opportunities and challenges. On one hand, big data introduces more information about the unknowns and, in principle, allows us to create more accurate models. On the other hand, data storage and processing become highly challenging. In this talk, we present a set of sequential algorithms for function approximation with extraordinarily large data sets. The algorithms are of iterative nature
and involve only vector operations. They use one data sample at each step and can handle dynamic/stream data. We present both the numerical algorithms, which are easy to implement, as well as rigorous analysis for their theoretical foundation.
The Role of Stochastic Simulation in Mechanics of Materials at Multiple Scales
Prof. Lori Graham-Brady | Johns Hopkins University | United States
Design of materials requires a common understanding between those who make materials (processors), those who test and characterize materials (experimentalists) and those who analyze and predict material behavior (modelers). The intrinsic requirement is for the team to understand how smaller-scale features, or actors, lead to specific failure and deformation mechanisms, and how these mechanisms compete in determining larger-scale failure. This entire process is further challenged by the many uncertainties that pervade materials by design, from the randomly occurring microstructural actors that drive localization of failure, to the characterization and testing errors introduced by inexact measurements, to the environmental uncertainties that affect the formation of the material during processing. All of these challenges present significant opportunities for the stochastic mechanics community. Probabilistic evaluation of materials characterization data highlights microstructural features that may or may not be properly introduced into models based on that characterization. Assessment of the degree to which localized material response varies within a given structure requires novel stochastic simulation tools. Surrogate models offer a potential alternative to efficiently upscale micro-scale features into macro-scale structural models, based on spatial variations of physical parameters that are directly related to materials processing.
This talk will discuss these tools, highlighting a particular example in brittle materials under high-rate compression, but with some reference to other material classes and loading conditions.