融合物理模型与深度学习，提升未知系统状态估计与预测精度
Hybrid twinning using PBDW and DeepONet for the effective state estimation and prediction on partially known systems
- 用PBDW框架结合物理模型与数据，建模不确定性
- 引入DeepONet修正模型偏差，仅学习未知部分
- 适合需高精度预测的复杂系统建模与传感器设计
精确估计复杂不确定物理系统的状态，需调和理论模型（固有缺陷）与噪声实验数据之间的矛盾。本文提出一种混合方法，结合基于物理的建模与数据驱动学习，以增强状态估计并实现更优预测。该方法基于参数化背景数据弱（PBDW）框架，自然融合最优可用模型的降维表示与测量数据，以涵盖预期与非预期不确定性。为弥补降维空间未捕捉的模型偏差，并学习模型偏离的结构，引入受约束的深度算子网络（DeepONet），使其正交于已有知识流形，确保所学修正仅针对模型偏差的未知成分，保持物理模型的可解释性与保真度。同时研究了最优传感器布置策略，以最大化测量信息获取。在含多种建模误差（如边界条件、源项误差）的亥姆霍兹方程代表性问题上验证了该方法的有效性。
原文摘要 · Abstract (English)
The accurate estimation of the state of complex uncertain physical systems requires reconciling theoretical models, with inherent imperfections, with noisy experimental data. In this work, we propose an effective hybrid approach that combines physics-based modeling with data-driven learning to enhance state estimation and further prediction. Our method builds upon the Parameterized Background Data-Weak (PBDW) framework, which naturally integrates a reduced-order representation of the best-available model with measurement data to account for both anticipated and unanticipated uncertainties. To address model discrepancies not captured by the reduced-order space, and learn the structure of model deviation, we incorporate a Deep Operator Network (DeepONet) constrained to be an orthogonal complement of the best-knowledge manifold. This ensures that the learned correction targets only the unknown components of model bias, preserving the interpretability and fidelity of the physical model. An optimal sensor placement strategy is also investigated to maximize information gained from measurements. We validate the proposed approach on a representative problem involving the Helmholtz equation under various sources of modeling error, including those arising from boundary conditions and source terms.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。