HotCSE Seminar: Conlain Kelly

Name: School of CSE Ph.D. Candidate Conlain Kelly

Date: Wednesday, Oct. 30, 2024, at 12:00 p.m.

Location: Coda Building, Room 230 (Google Maps link)

Lunch provided!

Title: Embedding Thermodynamics into Neural Operators for Variable-Coefficient PDEs

Abstract: We propose a new class of data-driven models which predict local deformations over heterogeneous material microstructures. This problem -- termed the localization problem -- is a core component of numerous open challenges in multiscale materials design. The inherent stochasticity of manufacturing means that conducting forward (process -> property) or inverse (property -> process) uncertainty quantification requires solving a variable-coefficient PDE repeatedly for many microstructure instantiations. Moreover, the discontinuity and disorder of the PDE coefficients leads to a high-dimensional, poorly-conditioned system of equations. Our work combines traditional numerical solvers and data-driven methods to construct a hybrid approximation for the coefficient-to-solution map. In particular, we utilize the Lippmann-Schwinger formulation of localization to guide the design of a thermodynamically-informed implicit (Deep Equilibrium) neural operator. Applied to both two-phase composites and polycrystalline materials, our methodology shows improved accuracy and stability compared to existing machine learning methods. Finally, we find that embedding thermodynamic encodings into the architecture provides improved data efficiency and generalizability. 

Bio: Conlain completed their undergraduate studies at the University of Wisconsin — Madison, pursuing a double major in Applied Math, Engineering, & Physics and Computer Science. They are currently a Ph.D. candidate in Computational Science and Engineering at Georgia Tech. Their research focuses on hybrid physics-centric data-driven models for statistical continuum mechanics and materials design. More broadly, they are interested in the intersection of deep learning and traditional numerical methods, as well as decision-making under uncertainty.

About HotCSE

HotCSE is an academic seminar series to bring Ph.D. students in Computational Science and Engineering together to discuss interesting topics. The topics consist of high-performance computing, machine learning, data analysis, simulation, computational sustainability, medical informatics, etc.

The talks have always been enjoyable and have ranged from quite informal to formal conference style talks. Either chalks or slides can be used to help people understand your talk. It is also a great forum to practice conference talks and bounce around new ideas.

Currently the talks are sponsored by the School of Computational Science and Engineering. The goal of CSE is slightly broader than that of these talks - we want to bring more people outside CSE to discuss their related work here.