Physics-informed sensor coverage through structure preserving machine learning

2025-09-12

AI Summary

This work addresses the challenge of real-time adaptive source localization in coupled fluid-dynamics–transport systems. Methodologically, it introduces a structure-preserving physics-informed sensor coverage framework that integrates finite element exterior calculus (FEEC) with Transformer-based operator learning to construct conditional neural Whitney forms—ensuring strict preservation of discrete conservation laws and geometric structure. A conditional attention mechanism dynamically generates observation-compatible reduced-order bases and balanced governing equations, while an alternating optimization strategy—combining Lloyd’s algorithm with optimal recovery theory—guarantees monotonic improvement in coverage performance. Experiments demonstrate that the proposed method significantly outperforms purely data-driven approaches on complex geometries, achieving high-fidelity point-source reconstruction. These results validate the critical role of physics-guided structural preservation as a strong inductive bias for robust source identification.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: State Estimation

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Adaptive source localization using structure-preserving machine learning
• Real-time trajectory planning and data assimilation with digital twin
• Preserving discrete conservation laws in complex hydrodynamic systems

Innovation

• Structure-preserving digital twin framework
• Conditional neural Whitney forms coupling
• Staggered sensor placement optimization scheme