Towards Physics-informed Diffusion for Anomaly Detection in Trajectories: A Summary of Results

Arun Sharma, Mingzhou Yang, Majid Farhadloo, Subhankar Ghosh, Bharat Jayaprakash, Shashi Shekhar

Published: 03 Nov 2025, Last Modified: 04 Dec 2025CrossrefEveryoneRevisionsCC BY-SA 4.0
Abstract: Given a dataset of moving object trajectories, a domain-specific study area, and a user-defined error threshold, we aim to identify anomalous trajectories indicative of possible GPS spoofing (e.g., broadcasting fake signals). The problem is societally important to curb illegal activities such as unauthorized fishing and illicit oil transfers in international waters. The problem is challenging due to advances in AI-generated deep fakes (e.g., additive noise, fake trajectories) and the scarcity of labeled samples for ground-truth verification. Current state-of-the-art methods ignore fine-scale spatiotemporal dependencies and prior physical knowledge, resulting in lower accuracy. In this paper, we propose a physics-informed anomaly detection framework based on an encoder-decoder architecture that incorporates kinematic constraints to identify trajectories that violate physical laws. Experimental results on maritime and urban domains demonstrate that the proposed approach yields higher solution quality and lower estimation error for anomaly detection and trajectory reconstruction tasks, respectively.
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