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Machine Learning Surrogates for Problems with Moving Interfaces

Thursday, April 4, 2024 3pm to 4pm

Image of Machine Learning Surrogates for Problems with Moving Interfaces

33 Oxford Street, Cambridge, MA 02138

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:
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.99.063313 (capsules)
https://arxiv.org/abs/2401.03661 (GrainGNN)

Location: Maxwell Dworkin G115 & Zoom


Topic: Widely Applied Math Seminar
Time: Apr 4, 2024 03:00 PM Eastern Time (US and Canada)

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