用保结构机器学习构建数字孪生,实时优化传感器布局以精确定位污染源。
Physics-informed sensor coverage through structure preserving machine learning
- 基于条件神经惠特尼形式,融合有限元外微分与变压器架构
- 实测数据驱动下实现物理守恒与源场重建的实时自适应
- 适合需要高精度环境溯源的智能监测系统设计者
我们提出一种自适应源定位的机器学习框架,代理通过保结构的数字孪生模型进行实时轨迹规划与数据同化。该孪生模型基于条件神经惠特尼形式(CNWF),结合有限元外微分计算(FEEC)的数值保证与基于变压器的算子学习能力,确保离散守恒性,并能实时响应流式传感器数据。模型采用条件注意力机制识别:约化惠特尼基、约化积分平衡方程及与传感器测量兼容的源场。由此生成的低阶环境模型保持标准有限元模拟的稳定性和一致性,从传感器数据到源场映射具有物理可实现性。我们提出交错方案,交替评估数字孪生与应用洛夫勒算法指导传感器部署,并提供覆盖率函数单调提升的条件。利用预测源场作为最优恢复中的重要性函数,在连续性假设下实现点源恢复,凸显正则性作为定位充分条件的作用。实验对比显示,引入物理约束的模型在复杂几何中优于无物理先验的变压器架构,证明结构保持是源识别的有效归纳偏置。
原文摘要 · Abstract (English)
We present a machine learning framework for adaptive source localization in which agents use a structure-preserving digital twin of a coupled hydrodynamic-transport system for real-time trajectory planning and data assimilation. The twin is constructed with conditional neural Whitney forms (CNWF), coupling the numerical guarantees of finite element exterior calculus (FEEC) with transformer-based operator learning. The resulting model preserves discrete conservation, and adapts in real time to streaming sensor data. It employs a conditional attention mechanism to identify: a reduced Whitney-form basis; reduced integral balance equations; and a source field, each compatible with given sensor measurements. The induced reduced-order environmental model retains the stability and consistency of standard finite-element simulation, yielding a physically realizable, regular mapping from sensor data to the source field. We propose a staggered scheme that alternates between evaluating the digital twin and applying Lloyd's algorithm to guide sensor placement, with analysis providing conditions for monotone improvement of a coverage functional. Using the predicted source field as an importance function within an optimal-recovery scheme, we demonstrate recovery of point sources under continuity assumptions, highlighting the role of regularity as a sufficient condition for localization. Experimental comparisons with physics-agnostic transformer architectures show improved accuracy in complex geometries when physical constraints are enforced, indicating that structure preservation provides an effective inductive bias for source identification.
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