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Inductive Spatio-Temporal Kriging with Physics-Guided Increment Training Strategy for Air Quality Inference

Songlin Yang, Tao Yang, Bo Hu

TL;DR

The paper tackles sparse urban air quality inference by addressing the graph gap between training virtual nodes and real unobserved nodes in inductive spatio-temporal kriging. It introduces Physics-Guided Increment Training Strategy (PGITS), which embeds advection and diffusion physics into a Dynamic Graph Generation module and enforces physical continuity through Node-Aware Cycle Regulation, enabling robust semi-supervised kriging. The framework combines a physics-informed dynamic graph with Spatio-Temporal Graph Convolution and a physics-aware loss, achieving superior accuracy on the AQI-36 Beijing dataset compared with strong baselines. This approach enhances applicability of fine-grained air quality inference in dynamic sensor networks and supports more accurate urban environmental monitoring.

Abstract

The deployment of sensors for air quality monitoring is constrained by high costs, leading to inadequate network coverage and data deficits in some areas. Utilizing existing observations, spatio-temporal kriging is a method for estimating air quality at unobserved locations during a specific period. Inductive spatio-temporal kriging with increment training strategy has demonstrated its effectiveness using virtual nodes to simulate unobserved nodes. However, a disparity between virtual and real nodes persists, complicating the application of learning patterns derived from virtual nodes to actual unobserved ones. To address these limitations, this paper presents a Physics-Guided Increment Training Strategy (PGITS). Specifically, we design a dynamic graph generation module to incorporate the advection and diffusion processes of airborne particles as physical knowledge into the graph structure, dynamically adjusting the adjacency matrix to reflect physical interactions between nodes. By using physics principles as a bridge between virtual and real nodes, this strategy ensures the features of virtual nodes and their pseudo labels are closer to actual nodes. Consequently, the learned patterns of virtual nodes can be applied to actual unobserved nodes for effective kriging.

Inductive Spatio-Temporal Kriging with Physics-Guided Increment Training Strategy for Air Quality Inference

TL;DR

The paper tackles sparse urban air quality inference by addressing the graph gap between training virtual nodes and real unobserved nodes in inductive spatio-temporal kriging. It introduces Physics-Guided Increment Training Strategy (PGITS), which embeds advection and diffusion physics into a Dynamic Graph Generation module and enforces physical continuity through Node-Aware Cycle Regulation, enabling robust semi-supervised kriging. The framework combines a physics-informed dynamic graph with Spatio-Temporal Graph Convolution and a physics-aware loss, achieving superior accuracy on the AQI-36 Beijing dataset compared with strong baselines. This approach enhances applicability of fine-grained air quality inference in dynamic sensor networks and supports more accurate urban environmental monitoring.

Abstract

The deployment of sensors for air quality monitoring is constrained by high costs, leading to inadequate network coverage and data deficits in some areas. Utilizing existing observations, spatio-temporal kriging is a method for estimating air quality at unobserved locations during a specific period. Inductive spatio-temporal kriging with increment training strategy has demonstrated its effectiveness using virtual nodes to simulate unobserved nodes. However, a disparity between virtual and real nodes persists, complicating the application of learning patterns derived from virtual nodes to actual unobserved ones. To address these limitations, this paper presents a Physics-Guided Increment Training Strategy (PGITS). Specifically, we design a dynamic graph generation module to incorporate the advection and diffusion processes of airborne particles as physical knowledge into the graph structure, dynamically adjusting the adjacency matrix to reflect physical interactions between nodes. By using physics principles as a bridge between virtual and real nodes, this strategy ensures the features of virtual nodes and their pseudo labels are closer to actual nodes. Consequently, the learned patterns of virtual nodes can be applied to actual unobserved nodes for effective kriging.

Paper Structure

This paper contains 26 sections, 27 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Air Quality Inference
  4. Spatio-Temporal Kriging
  5. PRELIMINARIES
  6. Inductive Spatio-temporal Kriging for Air Quality Inference
  7. Inductive Spatio-temporal Kriging with Increment Training Strategy
  8. METHODOLOGY
  9. Physics Principles of Airborne Particles Movement
  10. Advection and diffusion processes of airborne particles
  11. Advection and diffusion processes on the graph
  12. Dynamic Graph Generation (DGG)
  13. The diffusion-based graph
  14. The advection-based graph
  15. Dynamic graph generation process
  16. ...and 11 more sections

Figures (3)

  • Figure 1: Training and testing strategies of inductive spatio-temporal kriging.
  • Figure 2: Training and testing strategies of inductive spatio-temporal kriging with increment training strategy.
  • Figure 3: Overview of PGITS. (a) Increment Training Strategy for Inductive Spatio-temporal Kriging (b) Kriging Model with Dynamic Graph Generation (DGG), Spatio-Temporal Graph Convolution (STGC), and Node-Aware Cycle Regulation (NCR) Modules. (c) Dynamic Graph Generation Module Based on the Advection and Diffusion Processes of Airborne Particles. The heatmap represents the PM$_{2.5}$ concentrations at various nodes, and the arrows indicate the transport of PM$_{2.5}$ between nodes facilitated by advection and diffusion processes of airborne particles.