发表机构
Sun Yat-sen University; Great Bay University; Shanghai Jiao Tong University（中山大学; 大湾区大学; 上海交通大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种基于交叉注意力编码器和傅里叶神经算子解码器的机器学习框架，用于从单个物理场的稀疏观测中重建耦合系统全部物理场并识别未知参数，在多个流体和磁流体动力学问题上验证了有效性。
AI 中文摘要
给定一个含未知参数的耦合系统中单个物理场的不完整测量，我们能否推断其完整的物理状态并识别潜在参数？这一问题具有挑战性，因为必须从仅一个场的有限观测中同时重建多个耦合场，而系统参数是未知的。在这项工作中，我们提出了一种机器学习框架，用于从单个物理场的稀疏观测中进行全场重建和未知物理系统的参数识别。具体而言，交叉注意力编码器将稀疏传感器观测传播到规则网格上，以构建传感器条件潜在表示，而傅里叶神经算子（FNO）解码器捕获全局空间依赖性以重建所有耦合物理场。网络参数和未知物理参数通过最小化观测损失、控制方程残差以及边界/初始条件约束来联合优化。所提出的方法在二维和三维顶盖驱动腔流、二维圆柱尾流以及二维非理想磁流体动力学问题上得到验证，展示了从不完整观测中恢复未观测场和物理参数的性能。
英文摘要
Given incomplete measurements of a single physical field in a coupled system with unknown parameters, can we infer its full physical state and identify the underlying parameters? This problem is challenging because multiple coupled fields must be reconstructed simultaneously from limited observations of only one, while the system parameters are unknown. In this work, we propose a machine learning framework for full-field reconstruction and parameter identification of unknown physical systems from sparse observations of a single physical field. Specifically, the cross-attention encoder propagates sparse sensor observations onto a regular grid to construct a sensor-conditioned latent representation, while a Fourier neural operator (FNO) decoder captures global spatial dependencies to reconstruct all coupled physical fields. The network parameters and unknown physical parameters are jointly optimized by minimizing observation losses, governing equation residuals, and boundary/initial condition constraints. The proposed approach is validated on two- and three-dimensional lid-driven cavity flows, a two-dimensional cylinder wake, and a two-dimensional non-ideal magnetohydrodynamics problem, demonstrating the recovery performance of unobserved fields and physical parameters from incomplete observations.
