{"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/a-data-driven-and-model-based-accelerated","title":"A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems","arxiv_id":"2104.13070","date":"2021-04-27","proceeding":null,"authors":["Sijing Li","Cheng Zhang","Zhiwen Zhang","Hongkai Zhao"],"abstract":"In this paper, we consider a Bayesian inverse problem modeled by elliptic partial differential equations (PDEs). Specifically, we propose a data-driven and model-based approach to accelerate the Hamiltonian Monte Carlo (HMC) method in solving large-scale Bayesian inverse problems. The key idea is to exploit (model-based) and construct (data-based) the intrinsic approximate low-dimensional structure of the underlying problem which consists of two components - a training component that computes a set of data-driven basis to achieve significant dimension reduction in the solution space, and a fast solving component that computes the solution and its derivatives for a newly sampled elliptic PDE with the constructed data-driven basis. Hence we achieve an effective data and model-based approach for the Bayesian inverse problem and overcome the typical computational bottleneck of HMC - repeated evaluation of the Hamiltonian involving the solution (and its derivatives) modeled by a complex system, a multiscale elliptic PDE in our case. We present numerical examples to demonstrate the accuracy and efficiency of the proposed method.","url_abs":"https://arxiv.org/abs/2104.13070v1","url_pdf":"https://arxiv.org/pdf/2104.13070v1.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":"a-data-driven-and-model-based-accelerated","repo_url":"https://github.com/LSijing/Bayesian-pde-inverse-problem","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","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}