# Physics-Refined Spatiotemporal Forecasting on Open-Boundary Hydrologic Graphs

arXiv: https://arxiv.org/abs/2610.01765 · HTML: https://mlsanity.com/paper/2610.01765/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 36 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 16 of 16)

- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Towards Stability of Autoregressive Neural Operators](https://mlsanity.com/paper/2306.10619/) (2023)
- [Graph Classification via Deep Learning with Virtual Nodes](https://mlsanity.com/paper/1708.04357/) (2017)
- [Long Range Propagation on Continuous-Time Dynamic Graphs](https://mlsanity.com/paper/2406.02740/) (2024)
- [PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems](https://mlsanity.com/paper/2410.01337/) (2024)
- [Conditionally Parameterized, Discretization-Aware Neural Networks for Mesh-Based Modeling of Physical Systems](https://mlsanity.com/paper/2109.09510/) (2021)
- [State Space Models on Temporal Graphs: A First-Principles Study](https://mlsanity.com/paper/2406.00943/) (2024)
- [The Merit of River Network Topology for Neural Flood Forecasting](https://mlsanity.com/paper/2405.19836/) (2024)
- [PhysicsCorrect: A Training-Free Approach for Stable Neural PDE Simulations](https://mlsanity.com/paper/2507.02227/) (2025)
- [Mixture of neural operator experts for learning boundary conditions and model selection](https://mlsanity.com/paper/2502.04562/) (2025)
- [Topology-aware Neural Flux Prediction Guided by Physics](https://mlsanity.com/paper/2506.05676/) (2025)
- [DUALFloodGNN: Physics-informed Graph Neural Network for Operational Flood Modeling](https://mlsanity.com/paper/2512.23964/) (2025)
- [HydroGAT: Distributed Heterogeneous Graph Attention Transformer for Spatiotemporal Flood Prediction](https://mlsanity.com/paper/2509.02481/) (2025)

## Abstract (arXiv)

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.