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Enhancing Non-Linear PDE Solver Convergence with Learnable Models

AMS Seminar Series

Speaker: Jennifer Abras, Bowhead Total Enterprise Solutions LLC

Presentation

Seminar Slide Deck (PDF-3.2MB)

Abstract

Production non-linear PDE solvers typically utilize a framework consisting of a transformation of the PDEs into a linear system and the use of an implicit iterative method to solve the linear system. This is typical of production solvers where real applications usually have a large range of grid cell sizes, especially in the boundary layers, that make explicit solution methods unrealistically expensive. However, in a breakdown of the time spent at various stages of production solver execution, most of the time is spent solving the linear system. Methods that focus on reducing the time spent solving the linear system can potentially save a significant amount of overall simulation execution time.

The present effort describes a fully encapsulated graph neural network (GNN) methodology that learns the residual to solution mappings as the solver executes and applies the trained model predictions to warm start the solver iterations. Both the non-linear and linear solver stages utilize an independently trained GNN, and all stages of the data curation and training are executed as the simulation runs. This method is applied to a variety of 1D and 2D cases of increasing complexity and demonstrates that in all cases the GNN-based warm-start reduces the initial residual magnitudes; thus, reducing the number of linear iterations required to reach an equivalent solver tolerance at each time step, saving overall time spent in the solver.

Biography

Photo of Jennifer Abras
Jennifer Abras obtained her Ph.D. in aerospace engineering from Georgia Tech in 2009 in the area of rotary wing CFD and CFD/CSD coupling. She joined NAVAIR in 2007 as part of the rotary wing aerodynamics group where she supported various Navy applied and research efforts until 2018. In 2013, she also joined the HPCMP CREATETM-AV Helios team, transitioning to a full-time roll in 2019. Her efforts with the Helios team have covered a combination of quality assurance, development, and research tasking. Recent research has mostly focused on a variety of machine learning related efforts to investigate how machine learning can be used to improve internal and external workflows.