Physics-Refined Spatiotemporal Forecasting on Open-Boundary Hydrologic Graphs

2026-10-01

AI Summary

This study addresses the issues of autoregressive error accumulation and long-term instability in open-boundary hydrograph prediction caused by missing external forcings. To this end, we propose a physics-guided spatiotemporal graph neural network framework. The core innovation lies in designing a ghost node proxy compensation mechanism to bridge the gap from missing boundary information, coupled with a dual physical refinement strategy that enforces both local consistency and global stability to constrain error propagation. Experiments on real-world hydrological datasets demonstrate that the proposed approach significantly improves predictive accuracy and long-term stability, comprehensively outperforming existing baseline models.

Abstract

Spatiotemporal forecasting on hydrologic graphs is especially prone to instability in open-boundary systems, where the forecast domain exchanges fluxes with an unobserved exterior. In such systems, boundary nodes receive external forcing, e.g., upstream inflows in rivers or tidal signals in coastal regions, that is typically unavailable at prediction time. The absence of this information can compound errors as forecasts unfold in an autoregressive fashion, leading to inferior long-horizon performance. This paper dissects this instability issue by exploring two questions. 1) What boundary forcing enters the forecast domain when information beyond the boundary is missing? 2) How should this forcing propagate through the domain without incurring error amplification under autoregressive rollout? To address both, we propose a new computing framework comprising two key components. First, to compensate for the boundary forcing, our framework learns ghost node proxies from the boundary and interior nodes, striving to approximate unobserved external inputs. Second, to control error accumulation from these learned proxies, we leverage two physics refiners. In particular, one refiner enforces local consistency by aligning ghost proxies with their two-hop neighbors (i.e., boundary nodes and their immediate interiors). The other refiner enhances global stability by correcting the model forecasts through a physics-guided graph neural operator, reducing long-horizon numerical drift. Two real-world hydrologic graphs are employed for empirical evaluation. Comparative results show that our proposal enjoys higher prediction accuracy and long-horizon stability over both learning-based and physics-informed model competitors.

Problem

• spatiotemporal forecasting
• open-boundary systems
• hydrologic graphs
• error accumulation
• autoregressive rollout

Innovation

• Spatiotemporal forecasting
• Open-boundary hydrologic graphs
• Ghost node proxies
• Physics refiners
• Graph neural operator