PINN based on multi-scale strategy for solving Navier–Stokes equation
Neural networks combined with automatic differentiation technology provide a fundamental framework for the numerical solution of partial differential equations. This framework constitutes a loss function driven by both data and physical models, significantly enhancing generalization capabilities. Co...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-02-01
|
| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037424000967 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Neural networks combined with automatic differentiation technology provide a fundamental framework for the numerical solution of partial differential equations. This framework constitutes a loss function driven by both data and physical models, significantly enhancing generalization capabilities. Combining the framework and the idea of multi-scale methods in traditional numerical methods, such as domain decomposition and collocation self-adaption, we construct a method of the Physics-Informed Neural Networks (PINNs) based on multi-scale strategy to solve Navier–Stokes equations, and the results are more effective than XPINNs and SAPINNs. The computational efficiency of the proposed method is verified by solving two-dimensional and three-dimensional Navier–Stokes equations. |
|---|---|
| ISSN: | 2590-0374 |