Physics-informed sensor coverage through structure preserving machine learning

• URL: http://arxiv.org/abs/2509.10363v1
• Date: Fri, 12 Sep 2025 15:54:13 GMT
• Title: Physics-informed sensor coverage through structure preserving machine learning
• Authors: Benjamin David Shaffer, Brooks Kinch, Joseph Klobusicky, M. Ani Hsieh, Nathaniel Trask,
• Abstract summary: We present a machine learning framework for adaptive source localization.<n>Agents use a structure-preserving digital twin of a coupled hydrodynamic-transport system for real-time trajectory planning and data assimilation.
• Score: 8.009940044669191
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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