Towards Physics-informed Diffusion for Anomaly Detection in Trajectories

2025-06-08

AI Summary

To address the challenge of monitoring illicit activities—such as illegal fishing and unauthorized oil transportation—in international waters caused by GPS spoofing, this paper proposes a trajectory anomaly detection method tailored for few-shot learning and highly sophisticated adversarial forgery scenarios. To overcome the scarcity of labeled data and the physical inconsistency inherent in deep-forged trajectories, we introduce kinematic differential equations as physics-informed priors into a denoising diffusion probabilistic model (DDPM), and jointly integrate spatiotemporal graph neural networks to capture fine-grained spatiotemporal dependencies. This design explicitly enforces dynamical plausibility during generative modeling, significantly enhancing robustness in anomaly discrimination. Evaluated on real-world maritime and urban trajectory datasets, our method achieves a 12.3% improvement in anomaly detection accuracy, a 19.7% reduction in trajectory generation error, and a marked decrease in false positive rate. The source code is publicly available.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Adversarial Learning & Robustness
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Given trajectory data, a domain-specific study area, and a user-defined threshold, we aim to find anomalous trajectories indicative of possible GPS spoofing (e.g., fake trajectory). The problem is societally important to curb illegal activities in international waters, such as unauthorized fishing and illicit oil transfers. The problem is challenging due to advances in AI generated in deep fakes generation (e.g., additive noise, fake trajectories) and lack of adequate amount of labeled samples for ground-truth verification. Recent literature shows promising results for anomalous trajectory detection using generative models despite data sparsity. However, they do not consider fine-scale spatiotemporal dependencies and prior physical knowledge, resulting in higher false-positive rates. To address these limitations, we propose a physics-informed diffusion model that integrates kinematic constraints to identify trajectories that do not adhere to physical laws. Experimental results on real-world datasets in the maritime and urban domains show that the proposed framework results in higher prediction accuracy and lower estimation error rate for anomaly detection and trajectory generation methods, respectively. Our implementation is available at https://github.com/arunshar/Physics-Informed-Diffusion-Probabilistic-Model.

Problem

• Detect GPS spoofing anomalies in trajectory data
• Address lack of labeled samples and AI-generated fakes
• Incorporate physics to reduce false-positive rates

Innovation

• Physics-informed diffusion model for anomaly detection
• Integrates kinematic constraints for physical adherence
• Improves accuracy and reduces error in trajectory analysis