Distill-Belief: Closed-Loop Inverse Source Localization and Characterization in Physical Fields

• URL: http://arxiv.org/abs/2604.26095v1
• Date: Tue, 28 Apr 2026 20:18:29 GMT
• Title: Distill-Belief: Closed-Loop Inverse Source Localization and Characterization in Physical Fields
• Abstract summary: We propose textbfDistill-Belief, a teacher-student framework that decouples correctness from efficiency.<n>Experiments show that Distill-Belief consistently reduces sensing cost and improves success, posterior contraction, and estimation accuracy over baselines.
• Score: 19.32007397161956
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: {Closed-loop inverse source localization and characterization (ISLC) requires a mobile agent to select measurements that localize sources and infer latent field parameters under strict time constraints.} {The core challenge lies in the belief-space objective: valid uncertainty estimation requires expensive Bayesian inference, whereas using fast learned belief model leads to reward hacking, in which the policy exploits approximation errors rather than actually reducing uncertainty.} {We propose \textbf{Distill-Belief}, a teacher--student framework that decouples correctness from efficiency. A Bayes-correct particle-filter teacher maintains the posterior and supplies a dense information-gain signal, while a compact student distills the posterior into belief statistics for control and an uncertainty certificate for stopping. At deployment, only the student is used, yielding constant per-step cost.} {Experiments on seven field modalities and two stress tests show that Distill-Belief consistently reduces sensing cost and improves success, posterior contraction, and estimation accuracy over baselines, while mitigating reward hacking.}

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