Publications – Mauro Maggioni's personal home page

2024

Yin, Minglang; Charon, Nicolas; Brody, Ryan; Lu, Lu; Trayanova, Natalia; Maggioni, Mauro

A scalable framework for learning the geometry-dependent solution operators of partial differential equations Journal Article

In: Nature Computational Science, 2024.

Abstract | Links | BibTeX | Tags: digital twins, Machine learning, model reduction, neural networks, PDEs, precision medicine

@article{DIMON2024,

title = {A scalable framework for learning the geometry-dependent solution operators of partial differential equations},

author = {Minglang Yin and Nicolas Charon and Ryan Brody and Lu Lu and Natalia Trayanova and Mauro Maggioni},

url = {https://arxiv.org/pdf/2402.07250.pdf

https://www.nature.com/articles/s43588-024-00732-2

https://rdcu.be/d2UPp

https://github.com/MinglangYin/DIMON},

doi = {10.1038/s43588-024-00732-2},

year  = {2024},

date = {2024-02-13},

urldate = {2024-02-13},

journal = {Nature Computational Science},

abstract = {The solution of a PDE over varying initial/boundary conditions on multiple domains is needed in a wide variety of applications, but it is computationally expensive if the solution is computed de novo whenever the initial/boundary conditions of the domain change. We introduce a general operator learning framework, called DIffeomorphic Mapping Operator learNing (DIMON) to learn approximate PDE solutions over a family of domains ${Omega_{theta}}_theta$, that learns the map from initial/boundary conditions and domain $Omega_theta$ to the solution of the PDE, or to specified functionals thereof. DIMON is based on transporting a given problem (initial/boundary conditions and domain $Omega_theta$) to a problem on a reference domain $Omega_0$, where training data from multiple problems is used to learn the map to the solution on $Omega_0$, which is then re-mapped to the original domain $Omega_theta$. We consider several problems to demonstrate the performance of the framework in learning both static and time-dependent PDEs on non-rigid geometries; these include solving the Laplace equation, reaction-diffusion equations, and a multiscale PDE that characterizes the electrical propagation on the left ventricle. This work paves the way toward the fast prediction of PDE solutions on a family of domains and the application of neural operators in engineering and precision medicine.},

keywords = {digital twins, Machine learning, model reduction, neural networks, PDEs, precision medicine},

pubstate = {published},

tppubtype = {article}

}