{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T16:46:26Z","timestamp":1764089186866,"version":"3.45.0"},"reference-count":49,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T00:00:00Z","timestamp":1763942400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Committee of Science of the Ministry of Science and Higher Education of the Republic of Kazakhstan","award":["BR21882366","AP19175328"],"award-info":[{"award-number":["BR21882366","AP19175328"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Developing a high-precision regional geoid model is a key element in modernizing Kazakhstan\u2019s vertical reference framework and ensuring consistent GNSS-based height determination. However, the mountainous terrain of southeastern Kazakhstan, characterized by strong topographic gradients and sparse terrestrial gravity coverage, poses significant modelling challenges. This study presents the first AI-enhanced hybrid geoid model developed for the Almaty region, integrating classical gravimetric modelling with modern machine-learning simulation. The baseline solution was computed using the Least-Squares Modification of Stokes\u2019 Formula with Additive Corrections, combining digitized Soviet-era terrestrial gravity data, the global geopotential model XGM2019e_2159, and the FABDEM 30 m digital elevation model. Validation using GNSS\/levelling benchmarks revealed a systematic bias of \u22120.06 m and an RMS of 0.08 m. To improve the fit between modelled and observed undulations, three machine-learning regressors\u2014Gaussian Process Regression (GPR), Support Vector Regression (SVR), and LSBoost\u2014were applied to model the residual correction surface. Among them, SVR provided the best held-out performance (RMSE = 0.04 m), while LOOCV, 10-fold and spatial CV confirmed stable generalization across terrain regimes. The resulting hybrid model, designated NALM2025, achieved centimetre-level consistency with GNSS\/levelling data. The results demonstrate that integrating classical geoid computation with AI-based residual modelling provides an efficient computational framework for high-precision geoid determination in complex mountainous environments.<\/jats:p>","DOI":"10.3390\/a18120737","type":"journal-article","created":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T16:31:54Z","timestamp":1764088314000},"page":"737","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hybrid Geoid Modelling with AI Enhancements: A Case Study for Almaty, Kazakhstan"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7444-2897","authenticated-orcid":false,"given":"Asset","family":"Urazaliyev","sequence":"first","affiliation":[{"name":"Institute of Ionosphere, Almaty 050000, Kazakhstan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6825-4774","authenticated-orcid":false,"given":"Daniya","family":"Shoganbekova","sequence":"additional","affiliation":[{"name":"Institute of Ionosphere, Almaty 050000, Kazakhstan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9735-7820","authenticated-orcid":false,"given":"Serik","family":"Nurakynov","sequence":"additional","affiliation":[{"name":"Institute of Ionosphere, Almaty 050000, Kazakhstan"}]},{"given":"Magzhan","family":"Kozhakhmetov","sequence":"additional","affiliation":[{"name":"Institute of Ionosphere, Almaty 050000, Kazakhstan"}]},{"given":"Nailya","family":"Zhaksygul","sequence":"additional","affiliation":[{"name":"Institute of Ionosphere, Almaty 050000, Kazakhstan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2938-0444","authenticated-orcid":false,"given":"Roman","family":"Sermiagin","sequence":"additional","affiliation":[{"name":"RSE National Centre of Geodesy and Spatial Information, Astana 010000, Kazakhstan"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,24]]},"reference":[{"key":"ref_1","first-page":"656","article-title":"A Novel Approach for Optimizing Regional Geoid Modeling over Rugged Terrains Based on Global Geopotential Models and Artificial Intelligence Algorithms","volume":"27","author":"Elshewy","year":"2024","journal-title":"Egypt. 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