Bounded Spatial Residual Adaptation for Multi-Station GNSS Displacement-Residual Forecasting

Multi-station global navigation satellite system (GNSS) displacement-residual forecasting may benefit from neighbouring stations, yet unrestricted spatial aggregation can obscure station-local temporal dynamics and the independent value of spatial information. Whether neighbouring stations provide additional predictive information after a strong station-local forecast has been established remains unclear. Here, we propose the Multi-Scale Graph Residual Adaptation Network (MS-GRAN), a local-first framework that learns bounded spatial residual corrections rather than an unrestricted graph forecast. MS-GRAN first establishes a station-local NLinear forecast and then learns only an incremental residual correction through a training-only correlation–distance graph. The spatial branch integrates causal multi-scale high-frequency residual summaries, sparse non-negative adjacency constraints, neighbour-minus-own residual contrast, and a zero-output-initialized residual head with a gate initialized near zero to ensure a controlled spatial contribution. Experiments on a 90-station Cascadia GNSS benchmark with a fixed 2010–2019/2020–2021/2022–2024 chronological split showed that MS-GRAN achieved a 2.9158 ± 0.0033 mm one-day frozen-test RMSE, compared with 2.9579 ± 0.0006 mm for the matched frozen NLinear backbone. The resulting 1.422% reduction is modest but reproducible: 82-84 out of 90 stations improved across three random seeds, paired station-bootstrap confidence intervals were positive, upper-tail errors decreased more than mean RMSE, and gains remained positive across forecast horizons, network densities, seasons, and missingness strata. Additional controls showed gains of 0.635% for self-only adaptation, 1.265% for rewired placebo graphs, −0.343% for a validation-selected causal pre-local common-mode baseline, and 1.335% for an alternative frozen DLinear backbone. These results support conservative spatial residual adaptation in sparse GNSS networks while showing that residual-adaptation capacity contributes substantially, that simple causal common-mode preprocessing does not reproduce the gain, and that training-only graph topology provides a smaller additional benefit. They do not establish universal spatial transfer, physical event attribution, or earthquake-precursor detection.