{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T04:48:34Z","timestamp":1791953314640,"version":"4.3.4"},"reference-count":38,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T00:00:00Z","timestamp":1791331200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T00:00:00Z","timestamp":1791331200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guilin University","id":[{"id":"https:\/\/ror.org\/00jbpxw47","id-type":"ROR","asserted-by":"crossref"}]},{"id":[{"id":"https:\/\/ror.org\/00jbpxw47","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Guilin Culture and Tourism Industry\u2013Education Consortium","award":["2026CJLHT52"],"award-info":[{"award-number":["2026CJLHT52"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Accurate multi-step traffic forecasting requires models to respond to genuine traffic-state transitions while resisting deviations caused by missing or noisy observations. Existing deviation-aware methods characterize departures from recurrent patterns, but deviation magnitude alone does not indicate whether the resulting correction will improve a node-wise forecast. Guided by the insight that correction strength should depend on forecast gain rather than deviation magnitude, we propose Spatiotemporal Traffic Forecasting with Forecast-Gain-Guided Deviation\u2013Invariance Routing (ST-FGDIR). ST-FGDIR constructs an anchor-conditioned stable endpoint and a deviation-corrected candidate through weight-shared current\u2013anchor graph encoding and multi-view deviation evidence. Signed candidate-error differences provide soft forecast-gain targets for a node-wise continuous router, while selective risk extrapolation and a false-activation loss control stable-endpoint risk across perturbation environments and suppress perturbation-induced increases in residual injection. Experiments on METR-LA, PEMS-BAY, PEMS04, and PEMS08 show competitive forecasting performance relative to published baseline results. The inference gates exhibited Spearman correlations of 0.49\u20130.53 with realized correction gain, and the complete model yielded an average relative MAE increase of 9.38% across 12 controlled dataset\u2013perturbation conditions. These results demonstrate that forecast-gain-guided routing coordinates stable periodic prediction with adaptive deviation correction under both clean and perturbed inputs.<\/jats:p>","DOI":"10.3390\/s26196319","type":"journal-article","created":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T08:28:57Z","timestamp":1791361737000},"page":"6319","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["ST-FGDIR: Spatiotemporal Traffic Forecasting with Forecast-Gain-Guided Deviation\u2013Invariance Routing"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-3603-4516","authenticated-orcid":false,"given":"Qianxin","family":"Xie","sequence":"first","affiliation":[{"name":"School of Information Engineering, Guilin University, Guilin 541006, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-0439-5663","authenticated-orcid":false,"given":"Yancun","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Guilin University, Guilin 541006, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"conceptualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-5698-1332","authenticated-orcid":false,"given":"Jinfeng","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Guilin University, Guilin 541006, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8617-0435","authenticated-orcid":false,"given":"Yuxuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Intelligent Science and Engineering, Beijing University of Agriculture, Beijing 102206, China"},{"name":"Department of Computer and Electrical Engineering, Mid Sweden University, 85170 Sundsvall, Sweden"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"conceptualization","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,10,7]]},"reference":[{"key":"ref_1","unstructured":"Li, Y., Yu, R., Shahabi, C., and Liu, Y. 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