Bi-HYCO：碎片化观测下偏微分方程参数识别的双目标协同学习

中文摘要 AI 辅助

物理模型和合成模型可能描述同一偏微分方程控制系统的互补方面，同时接收不同的、可能碎片化的观测。我们提出双目标HYCO（Bi-HYCO），这是一个协同框架，保留两种表示及其局部观测目标，同时在其预测状态在未标记的交互点处耦合。这些点不包含测量值，也不增加数据；它们在共同状态空间中提供了一种通信机制。这两个准则形成一个向量值目标，加权标量化提供计算实现。对于具有固定交互点的确定性共享观测算法，我们证明了整个交替序列的充分下降和有限长度，该序列在所述Kurdyka-Lojasiewicz型假设下收敛到混合临界点。椭圆传输和二维Navier-Stokes实验评估了参数和状态重建、噪声和标量化效应，以及PINN/XPINN参考。消融研究表明，在测试配置中，移除状态交互同时保留聚合会恶化参数恢复，特别是对于Navier-Stokes。

英文摘要

Physical and synthetic models may describe complementary aspects of the same PDE-governed system while receiving different, possibly fragmented, observations. We propose Bi-Objective HYCO (Bi-HYCO), a cooperative framework that retains both representations and their local observational objectives while coupling their predicted states at unlabeled interaction points. These points contain no measurements and do not augment the data; they provide a communication mechanism in the common state space. The two criteria form a vector-valued objective, and weighted scalarizations provide computational realizations. For the deterministic shared-observation algorithm with fixed interaction points, we prove sufficient decrease and finite length of the whole alternating sequence, which converges to a mixed critical point under the stated Kurdyka-Lojasiewicz-type assumptions. Elliptic transmission and two-dimensional Navier-Stokes experiments assess parameter and state reconstruction, noise and scalarization effects, and PINN/XPINN references. Ablations show that removing state interaction while retaining aggregation deteriorates parameter recovery in the tested configurations, particularly for Navier-Stokes.

发表机构

• University of Deusto（德乌斯托大学）

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