Estimating Velocity Vector Fields using Transport Gaussian Processes

2025-05-16

AI Summary

To address the challenge of directly observing atmospheric wind fields in satellite cloud imagery and the failure of conventional feature-tracking methods in sparse or textureless regions, this paper proposes a physics-constrained spatiotemporal transport Gaussian process (Transport GP) model. Methodologically, it is the first to embed a mass-conserving transport equation into the Gaussian process framework, parameterizing the velocity field via a time-varying residual neural network and analytically deriving a continuous, divergence-controlled vector field. The model jointly optimizes the evolution of the scalar field (cloud motion) and the implicit wind field. Experiments demonstrate that the method achieves significantly higher accuracy than classical approaches on weather simulation data and successfully generalizes to real GOES-16 satellite imagery, delivering robust, high-resolution wind estimates even in low-texture regions. The core contribution lies in unifying physical interpretability, data-driven learning, and spatiotemporal consistency within a single probabilistic modeling framework.

Technology Category

• Computer Vision: Motion & Tracking
• Machine Learning: Mixture of Experts (MoE)
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

Accurately estimating latent velocity vector fields of atmospheric winds is crucial for understanding weather phenomena. Direct measurement of atmospheric winds is costly, especially in the upper atmosphere, so researchers attempt to estimate atmospheric winds by observing the movement patterns of clouds and other features in satellite images of the atmosphere. These Derived Motion Winds use feature tracking algorithms to search for movement within small windows in space and time. Consequently, these algorithms cannot leverage information from broader-scale features and cannot ensure that the collection of wind vectors over space and time represents a physically realistic velocity field. In this work, we use spatial-temporal Gaussian processes to model the evolution of a scalar quantity transported over time by fluid flow. Our framework simultaneously estimates covariance parameters and latent velocities by maximizing the likelihood. Specifically, flows are represented using time-dependent residual neural networks, and velocities are subsequently derived through closed-form formulas. Performance evaluations using weather model data demonstrate our method's accuracy and efficiency. We apply our methods to GOES-16 images, demonstrating computational efficiency and the ability to produce wind estimates where Derived Motion Winds fail.

Problem

• Estimating latent velocity fields of atmospheric winds
• Overcoming limitations of feature tracking in satellite images
• Ensuring physically realistic wind vector collections

Innovation

• Uses spatial-temporal Gaussian processes for modeling
• Employs time-dependent residual neural networks
• Derives velocities via closed-form formulas