Spatio-Temporal Fluid Dynamics Modeling via Physical-Awareness and Parameter Diffusion Guidance

TL;DR

Extensive experiments have verified the effectiveness and robustness of the ST-PAD framework, which showcase that ST-PAD outperforms current mainstream models in fluid dynamics modeling and prediction, especially in effectively capturing local representations and maintaining significant advantages in OOD generations.

Abstract

This paper proposes a two-stage framework named ST-PAD for spatio-temporal fluid dynamics modeling in the field of earth sciences, aiming to achieve high-precision simulation and prediction of fluid dynamics through spatio-temporal physics awareness and parameter diffusion guidance. In the upstream stage, we design a vector quantization reconstruction module with temporal evolution characteristics, ensuring balanced and resilient parameter distribution by introducing general physical constraints. In the downstream stage, a diffusion probability network involving parameters is utilized to generate high-quality future states of fluids, while enhancing the model's generalization ability by perceiving parameters in various physical setups. Extensive experiments on multiple benchmark datasets have verified the effectiveness and robustness of the ST-PAD framework, which showcase that ST-PAD outperforms current mainstream models in fluid dynamics modeling and prediction, especially in effectively capturing local representations and maintaining significant advantages in OOD generations.

Figures (7)

• Figure 1: We observe that a model trained under scenario 1 does not perform well when directly transferred to scenario 2.
• Figure 2: Overview of the ST-PAD framework: The upper half demonstrates the upstream model, which locks in a reasonable range of model parameter distributions through self-supervision. The lower half of the model utilizes a parameter-involved diffusion model to enhance the model's generalization capabilities across different environmental settings.
• Figure 3: Diagram illustrating the front-door adjustment strategy in causal inference, with $\mathcal{X}$ representing the input, $\tilde{\mathcal{X}}_{\mathcal{C}}^*$, ${\mathcal{X}}_{\mathcal{C}}$ act as the surrogate variable of ${ {\mathcal{X}}_{\mathcal{C}}}$ and the causal part of $\mathcal{X}$, ${\mathcal{D}}$ denoting as a confounder.
• Figure 4: Visualization on TaxiBJ+. For simplicity, we display the results of the last 10 frames.
• Figure 5: The figure shows input frames from 8 to 24 hours, along with their actual conditions and future frame predictions. The left side compares the performance of three models: ST-PAD, Earthforeseer, and SimVP. Red boxes highlight the local details that both models and the actual conditions successfully predicted. The bottom displays the error distribution of predictions made by the ST-PAD and TAU models.