arXiv：cs.LG（机器学习，全量分类）· Victorita Dolean, Daria Hrebenshchykova, St\'ephane Lanteri, Victor Michel-Dansac·· 15 小时前AI 评分21
FBPINNs 如何用神经网络域分解高效求解 Helmholtz 方程
Neural network-driven domain decomposition for efficient solutions to the Helmholtz equation
AI 导读
研究评估了有限基物理信息神经网络（FBPINNs）及其多级扩展在求解 Helmholtz 方程上的表现，该方法将计算域划分为重叠子域、每个子域由局部神经网络负责。针对均匀介质情形，研究验证了其精度与计算效率，并指出其有望缓解传统有限差分与有限元方法在高频波、复杂二维域问题上的计算瓶颈。
正文
Abstract:Accurately simulating wave propagation is crucial in fields such as acoustics, electromagnetism, and seismic analysis. Traditional numerical methods, like finite difference and finite element approaches, are widely used to solve governing partial differential equations (PDEs) such as the Helmholtz equation. However, these methods face significant computational challenges when applied to high-frequency wave problems in complex two-dimensional domains. This work investigates Finite Basis Physics-Informed Neural Networks (FBPINNs) and their multilevel extensions as a promising alternative. These methods leverage domain decomposition, partitioning the computational domain into overlapping sub-domains, each governed by a local neural network. We assess their accuracy and computational efficiency in solving the Helmholtz equation for the homogeneous case, demonstrating their potential to mitigate the limitations of traditional approaches.
| Subjects: | Numerical Analysis (math.NA); Machine Learning (cs.LG) |
| Cite as: | arXiv:2511.15445 [math.NA] |
| (or arXiv:2511.15445v3 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2511.15445 arXiv-issued DOI via DataCite |
Submission history
From: Victor Michel-Dansac [view email]
[v1]
Wed, 19 Nov 2025 13:58:32 UTC (1,132 KB)
[v2]
Wed, 4 Feb 2026 12:59:51 UTC (1,139 KB)
[v3]
Thu, 1 Oct 2026 17:19:09 UTC (1,112 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org