When
Where
Speaker: Ben Stilin, Program in Applied Mathematics
Title: Conditioning on Sets of Measure Zero
Abstract: For many common applications of probability it is clear how to interpret the objects manipulated in practice, such as probability density functions and expectations, using the measure theoretic formulation of probability. However, this connection is a bit more opaque in the case of conditional probabilities, especially conditional probability densities of continuous random variables. What does it mean to condition on a set of measure zero? In this short talk, we will introduce problems raised by conditional probabilities and discuss how disintegration of measure provides a partial resolution.
Speaker: Sheila Whitman, Program in Applied Mathematics
Title: Computer Vision for Accelerated Design and Development of Materials
Abstract: Machine learning is rapidly emerging as a powerful approach to establishing microstructure-property relationships in structural materials. Most existing machine learning efforts focus on the development of task-specific models for each individual class of materials and individual properties. We propose utilizing pre-trained foundational vision transformers for the extraction of task-agnostic microstructure features and subsequent light-weight machine learning. We demonstrate our approach on two case studies: (i) stiffness of two-phase microstructures learned from simulation data; and (ii) Vicker's hardness of superalloys based on experimental data published in literature. Our results show the potential of foundational vision transformers for robust microstructure representation and efficient machine learning of microstructure-property relationships without the need for expensive task-specific training or fine-tuning.