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

Location: Maxwell Dworkin G115 & Zoom