🤖 AI Summary
Traditional constant-velocity advection models suffer from unphysical distortions due to perfect temporal correlation. To address this, this paper proposes a novel spatiotemporal transport stochastic modeling framework that jointly ensures interpretability and physical fidelity. Methodologically: (1) it introduces a construction paradigm combining multiscale superposition with locally varying velocity fields, relaxing the rigid advection assumption; (2) it pioneers flexible spectral-domain design to achieve controllable temporal decorrelation. Leveraging stochastic process modeling, spectral analysis, and efficient numerical simulation, the framework successfully reproduces complex dynamical behaviors—including tropical cyclone evolution and solutions of partial differential equations. Experiments demonstrate substantial improvements in fitting accuracy for real-world spatiotemporal dynamics and strong cross-scenario generalization capability. This work establishes a new pathway for interpretable, physics-informed modeling.
📝 Abstract
Stochastic models for spatio-temporal transport face a critical trade-off between physical realism and interpretability. The advection model with a single constant velocity is interpretable but physically limited by its perfect correlation over time. This work aims to bridge the gap between this simple framework and its physically realistic extensions. Our guiding principle is to introduce a spatial correlation structure that vanishes over time. To achieve this, we present two distinct approaches. The first constructs complex velocity structures, either through superpositions of advection components or by allowing the velocity to vary locally. The second is a spectral technique that replaces the singular spectrum of rigid advection with a more flexible form, introducing temporal decorrelation controlled by parameters. We accompany these models with efficient simulation algorithms and demonstrate their success in replicating complex dynamics, such as tropical cyclones and the solutions of partial differential equations.
