{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/non-stationary-spatio-temporal-modeling-using","title":"Non-stationary Spatio-Temporal Modeling Using the Stochastic Advection-Diffusion Equation","arxiv_id":"2406.03400","date":"2024-06-05","proceeding":null,"authors":["Martin Outzen Berild","Geir-Arne Fuglstad"],"abstract":"We construct flexible spatio-temporal models through stochastic partial differential equations (SPDEs) where both diffusion and advection can be spatially varying. Computations are done through a Gaussian Markov random field approximation of the solution of the SPDE, which is constructed through a finite volume method. The new flexible non-separable model is compared to a flexible separable model both for reconstruction and forecasting, and evaluated in terms of root mean square errors and continuous rank probability scores. A simulation study demonstrates that the non-separable model performs better when the data is simulated from a non-separable model with diffusion and advection. Further, we estimate surrogate models for emulating the output of a ocean model in Trondheimsfjorden, Norway, and simulate observations of autonomous underwater vehicles. The results show that the flexible non-separable model outperforms the flexible separable model for real-time prediction of unobserved locations.","url_abs":"https://arxiv.org/abs/2406.03400v2","url_pdf":"https://arxiv.org/pdf/2406.03400v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"non-stationary-spatio-temporal-modeling-using","repo_url":"https://github.com/berild/spdepy","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}