OmniST: Topology-Invariant Spatiotemporal Forecasting with Guaranteed-Coverage Uncertainty at Unseen Sensor Locations

Abstract

Standard spatiotemporal graph convolutional networks need a fixed-size adjacency matrix, coupling model weights to a specific sensor count N; they cannot produce any output at a sensor absent from training. We present OmniST, a topology-invariant forecaster whose computation has zero structural dependency on the number of nodes, and which, composed with inductive split-conformal calibration, gives distribution-free, coverage-guaranteed prediction intervals at arbitrary (including never-seen) sensor locations, preserving that guarantee as sensors are added or removed. Topology invariance follows from coordinate-based tokenization, k-nearest-neighbor attention from geographic coordinates at each forward pass, and per-node temporal processing via a bidirectional GRU. On real Delhi air-quality data (37 stations, 2019-2023), OmniST attains a 30-day PM2.5 MAE of 31.0 ug/m3 and degrades at most 1.1 percent when 40 percent of stations are removed. Its inductive forecasts at unseen stations beat nearest-neighbor interpolation (about 12 percent) and a learned kriging GNN (IGNNK, about 21 percent), and, unlike either, carry a finite-sample coverage guarantee. The guarantee holds at 90 percent or above under 30-50 percent node dropout across four real datasets over three domains (Delhi and Beijing air quality, NOAA GHCN weather, Caltrans PeMSD7-M traffic), and still holds at 325 real sensors (full PeMS-BAY). We also fix a temporal-drift failure: static conformal under-covers over time (about 0.50 late), but a rolling adaptive-conformal estimator restores target coverage (0.89 overall, 0.96 late) at the cost of wider intervals.