Neural PDE Solvers for Irregular Domains

Biswajit Khara, Ethan Herron, Aditya Balu, Dhruv Gamdha, Chih-Hsuan Yang, Kumar Saurabh, Anushrut Jignasu, Zhanhong Jiang, Soumik Sarkar, Chinmay Hegde, Baskar Ganapathysubramanian, Adarsh Krishnamurthy

Abstract: Highlights•Irregular boundary network (IBN) predicts field PDE solution over arbitrary domains.•PDE loss to learn watertight boundary conditions imposed by complex geometries.•Single trained IBN can produce solutions to a PDE across different arbitrary shapes.•Analysis of convergence and generalization error bounds of the PDE-based loss.•Illustrate the approach on Poisson’s and Navier–Stokes PDE for different geometries.