---
title: "Adaptive Domain Decomposition for Finite Basis Physics-Informed Neural Networks"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.05659v1"
permalink: "https://feed.astralor.com/items/itm_7641a90fa0e9d35efbff469a"
published: "2026-11-03T21:46:19.000Z"
score: 56
channel: "tech"
tags: ["多模态","Adaptive Domain Decomposition","Finite Basis Physics-Informed","Neural Networks","ADD-FBPINNs","Partition","Unity Networks","POUNets"]
---

# Adaptive Domain Decomposition for Finite Basis Physics-Informed Neural Networks

## At a glance

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 learni…

## Key points

- 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 …
- FBPINNs improve upon the accuracy of standard physics-informed neural networks (PINNs) through user-defined subdivisions of the computational domain.

## Full text

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.

---

Verify against the original before citing; curated by Astral Feed: https://feed.astralor.com/items/itm_7641a90fa0e9d35efbff469a