Learning Only on Boundaries: A Physics-Informed Neural Operator for Solving Parametric Partial Differential Equations in Complex Geometries.
Neural Comput
; 36(3): 475-498, 2024 Feb 16.
Article
en En
| MEDLINE
| ID: mdl-38363659
ABSTRACT
Recently, deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we present a novel physics-informed neural operator method to solve parameterized boundary value problems without labeled data. By reformulating the PDEs into boundary integral equations (BIEs), we can train the operator network solely on the boundary of the domain. This approach reduces the number of required sample points from O(Nd) to O(Nd-1), where d is the domain's dimension, leading to a significant acceleration of the training process. Additionally, our method can handle unbounded problems, which are unattainable for existing physics-informed neural networks (PINNs) and neural operators. Our numerical experiments show the effectiveness of parameterized complex geometries and unbounded problems.
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1
Colección:
01-internacional
Banco de datos:
MEDLINE
Idioma:
En
Revista:
Neural Comput
Asunto de la revista:
INFORMATICA MEDICA
Año:
2024
Tipo del documento:
Article
País de afiliación:
Estados Unidos