{"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/operator-learning-for-continuous-spatial","title":"Neural Dynamical Operator: Continuous Spatial-Temporal Model with Gradient-Based and Derivative-Free Optimization Methods","arxiv_id":"2311.11798","date":"2023-11-20","proceeding":null,"authors":["Chuanqi Chen","Jin-Long Wu"],"abstract":"Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different types of data, e.g., with different spatial and temporal resolutions, and the combined use of short-term trajectories and long-term statistics. In this work, we build on the recent progress of neural operator and present a data-driven modeling framework called neural dynamical operator that is continuous in both space and time. A key feature of the neural dynamical operator is the resolution-invariance with respect to both spatial and temporal discretizations, without demanding abundant training data in different temporal resolutions. To improve the long-term performance of the calibrated model, we further propose a hybrid optimization scheme that leverages both gradient-based and derivative-free optimization methods and efficiently trains on both short-term time series and long-term statistics. We investigate the performance of the neural dynamical operator with three numerical examples, including the viscous Burgers' equation, the Navier-Stokes equations, and the Kuramoto-Sivashinsky equation. The results confirm the resolution-invariance of the proposed modeling framework and also demonstrate stable long-term simulations with only short-term time series data. In addition, we show that the proposed model can better predict long-term statistics via the hybrid optimization scheme with a combined use of short-term and long-term data.","url_abs":"https://arxiv.org/abs/2311.11798v4","url_pdf":"https://arxiv.org/pdf/2311.11798v4.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":"abstracts"},"code_links":[{"paper_slug":"operator-learning-for-continuous-spatial","repo_url":"https://github.com/aims-madison/neural-dynamical-operator","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"operator-learning-for-continuous-spatial","repo_url":"https://github.com/chuanqichencc/continous-spatial-temporal-model","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"operator-learning","task_name":"Operator learning"},{"task_slug":"time-series-1","task_name":"Time Series"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}