Towards general neural surrogate PDE solvers with specialized neural accelerators

Chenkai Mao, Robert Lupoiu, Mingkun Chen, Tianxiang Dai, Jonathan Fan

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Keywords: Surrogate Solver, Neural Operator, Domain Decomposition Methods, Nanophotonics, Maxwell's Equations, Navier Stokes Equations

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.

TL;DR: A semi-general neural surrogate PDE solver is built that solves problems with arbitrary domain size, boundary conditions and parameter maps.

Abstract: Surrogate neural network-based partial differential equation (PDE) solvers have the potential to solve PDEs in an accelerated manner, but they are largely limited to systems featuring predetermined problem sizes or fixed PDE parameters. We propose Specialized Neural Accelerator-Powered Domain Decomposition Methods (SNAP-DDM), a DDM-based approach to PDE solving in which subdomain problems containing arbitrary boundary conditions and geometric parameters are accurately solved using an ensemble of specialized neural operators. We tailor SNAP-DDM to 2D electromagnetics and fluidic flow problems and show how innovations in network architecture and loss function engineering can produce specialized surrogate subdomain solvers with near unity accuracy. We also show how these solvers can be used with standard DDM algorithms to accurately solve freeform electromagnetics and fluids problems with a wide range of domain sizes.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 4225