无需标注数据，自动划分物理空间并发现不同区域的物理规律。
Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts
- 用分片单位网络分解空间，每块配独立非线性参数。
- 通过物理残差损失检测物性变化，实现无监督分区。
- 适合复杂物理系统建模，如多相介质与冰盖演化。
物理信息神经网络（PINNs）常用于求解病态反问题，揭示未知物理规律。本文提出一种新型无监督学习框架，可自动识别具有特定控制物理规律的空间子域。该方法采用分片单位网络（POUs）将空间划分为若干子域，为每个子域分配独特的非线性模型参数，并将其融入物理模型。核心优势在于基于物理残差的损失函数，可在无需标签数据的情况下检测物理属性的变化。该方法能发现偏微分方程（PDEs）中的空间分解与非线性参数，通过子域划分优化解空间，提升精度。在多孔介质热消融和冰盖建模中的应用验证了其有效性，展示了应对真实物理挑战的潜力。
原文摘要 · Abstract (English)
Physics-informed neural networks (PINNs) commonly address ill-posed inverse problems by uncovering unknown physics. This study presents a novel unsupervised learning framework that identifies spatial subdomains with specific governing physics. It uses the partition of unity networks (POUs) to divide the space into subdomains, assigning unique nonlinear model parameters to each, which are integrated into the physics model. A vital feature of this method is a physics residual-based loss function that detects variations in physical properties without requiring labeled data. This approach enables the discovery of spatial decompositions and nonlinear parameters in partial differential equations (PDEs), optimizing the solution space by dividing it into subdomains and improving accuracy. Its effectiveness is demonstrated through applications in porous media thermal ablation and ice-sheet modeling, showcasing its potential for tackling real-world physics challenges.
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