Widely Applied Mathematics Seminars

Machine Learning Surrogates for Problems with Moving Interfaces

George Biros, W. A. "Tex" Moncrief Chair in Simulation-Based Engineering Sciences, Oden Institute for Computational Engineering and Sciences, University of Texas at Austin

Thursday, Apr 4, 2024

I will present two vignettes on accelerating the solution of partial differential equations with moving interfaces. Surrogate models are low-accuracy PDE solvers that can be orders of magnitude faster than high-fidelity solvers while capturing the essential dynamics/statistics of the underlying PDE. The first vignette is on surrogates for Stokesian flows with deformable capsules. The surrogate blends several regression neural networks and an operator time-stepping scheme. The key idea here is that instead of approximating the overall input-output operator, we approximate components of the underlying dynamic system and combine them with traditional discretization schemes. The second vignette is on a surrogate for phase field models for crystal formation and growth during alloy solidification.  I will present GrainGNN, a sequence-to-sequence long-short-term-memory graph neural network that evolves the dynamics of manually crafted features. The key idea here is to combine a regression and classification network, along with scalings that minimize the training costs.  GrainGNN can be orders of magnitude faster than phase field simulations, while delivering 5%–15% pointwise error. 

References: (capsules) (GrainGNN)

Location: Maxwell Dworkin G115 & Zoom

Speaker Bio

George Biros is the W. A. "Tex" Moncrief Chair in Simulation-Based Engineering Sciences in the Oden Institute for Computational Engineering and Sciences and has Full Professor appointments with the departments of Mechanical Engineering and Computer Science (by courtesy) at The University of Texas at Austin. From 2008 to 2011, he was an Associate Professor in the School of Computational Science and Engineering at Georgia Tech and The Wallace H. Coulter Department of Biomedical Engineering at Georgia Tech and Emory University. From 2003 to 2008, he was an Assistant professor in Mechanical Engineering and Applied Mechanics at the University of Pennsylvania.  He received his BS in Mechanical Engineering from Aristotle University in Greece (1995), his MS in Biomedical Engineering from Carnegie Mellon (1996), and his PhD in Computational Science and Engineering also from Carnegie Mellon (2000).  He was a postdoctoral associate at the Courant Institute of Mathematical Sciences from 2000 to 2003. With collaborators, he received the ACM Gordon Bell Prize in 2003 and in 2010. He is a 2023 SIAM Fellow.


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