← 研踪 PaperTrailarXiv:2611.05659 · v1
Adaptive Domain Decomposition for Finite Basis Physics-Informed Neural Networks
首次提交 2026-11-04 05:46
版本更新 2026-11-04 05:46
雷达观测 2026-11-05 10:08
摘要
In this work, we present adaptive domain decomposition finite basis physics-informed neural networks (ADD-FBPINNs). The proposed method integrates Partition of Unity Networks (POUNets), a data-driven approach for learning domain partitions, with finite Basis physics-informed neural networks (FBPINNs) to perform more efficient domain decomposition and achieve more accurate approximations. FBPINNs improve upon the accuracy of standard physics-informed neural networks (PINNs) through user-defined subdivisions of the computational domain. By adapting the domain decomposition based on the solution's features using a separable POUNet, the framework can automatically learn partitions that are stable and can be geometrically interpretable. We test this approach on the two-dimensional Helmholtz equation, two-dimensional Poisson equation with multiscale features, and viscous Burgers equation and observe improved accuracy compared with FBPINNs with fixed domain decomposition.
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v1 · 2026-11-04 05:46 · 最新观测版本
Adaptive Domain Decomposition for Finite Basis Physics-Informed Neural Networks
In this work, we present adaptive domain decomposition finite basis physics-informed neural networks (ADD-FBPINNs). The proposed method integrates Partition of Unity Networks (POUNets), a data-driven approach for learning domain partitions, with finite Basis physics-informed neural networks (FBPINNs) to perform more efficient domain decomposition and achieve more accurate approximations. FBPINNs improve upon the accuracy of standard physics-informed neural networks (PINNs) through user-defined subdivisions of the computational domain. By adapting the domain decomposition based on the solution's features using a separable POUNet, the framework can automatically learn partitions that are stable and can be geometrically interpretable. We test this approach on the two-dimensional Helmholtz equation, two-dimensional Poisson equation with multiscale features, and viscous Burgers equation and observe improved accuracy compared with FBPINNs with fixed domain decomposition.
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