K-M LLM-pro: Physics-guided cross-modal adaptation for fine-grained spatiotemporal trajectory classification

Area of Science:

• Artificial Intelligence
• Machine Learning
• Physics-Informed AI

Background:

• Spatiotemporal trajectory classification is crucial for intelligent perception but faces challenges like weak feature separability and multimodal data conflicts.
• Existing methods struggle with limited samples and heterogeneous trajectory data, hindering robust performance.

Purpose of the Study:

• To propose K-M LLM-pro, a physics-guided cross-modal adaptation framework for improved spatiotemporal trajectory understanding.
• To address challenges in trajectory classification, including data limitations and feature representation.

Main Methods:

• Physics-informed prompt engineering using Kramers-Moyal (K-M) coefficients and reproducing kernel Hilbert space projection.
• Dynamic patching optimization incorporating variance maximization and Lyapunov stability for heterogeneous trajectory modeling.
• Dual spatiotemporal adapters with parameter-efficient expansion (optimizing 3.8% of parameters).

Main Results:

• K-M LLM-pro significantly outperforms state-of-the-art models on public datasets (Geolife, AIS).
• Achieves strong classification accuracy even in few-shot scenarios (1% training data).
• Demonstrates effective modeling of complex spatiotemporal dynamics.

Conclusions:

• K-M LLM-pro offers a lightweight and effective solution for complex spatiotemporal dynamics modeling.
• This work pioneers the integration of K-M coefficients as interpretable statistical priors into LLMs.
• The framework enhances trajectory understanding in intelligent perception systems.