{"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/deep-uq-learning-deep-neural-network","title":"Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification","arxiv_id":"1802.00850","date":"2018-02-02","proceeding":null,"authors":["Rohit Tripathy","Ilias Bilionis"],"abstract":"State-of-the-art computer codes for simulating real physical systems are\noften characterized by a vast number of input parameters. Performing\nuncertainty quantification (UQ) tasks with Monte Carlo (MC) methods is almost\nalways infeasible because of the need to perform hundreds of thousands or even\nmillions of forward model evaluations in order to obtain convergent statistics.\nOne, thus, tries to construct a cheap-to-evaluate surrogate model to replace\nthe forward model solver. For systems with large numbers of input parameters,\none has to deal with the curse of dimensionality - the exponential increase in\nthe volume of the input space, as the number of parameters increases linearly.\nIn this work, we demonstrate the use of deep neural networks (DNN) to construct\nsurrogate models for numerical simulators. We parameterize the structure of the\nDNN in a manner that lends the DNN surrogate the interpretation of recovering a\nlow dimensional nonlinear manifold. The model response is a parameterized\nnonlinear function of the low dimensional projections of the input. We think of\nthis low dimensional manifold as a nonlinear generalization of the notion of\nthe active subspace. Our approach is demonstrated with a problem on uncertainty\npropagation in a stochastic elliptic partial differential equation (SPDE) with\nuncertain diffusion coefficient. We deviate from traditional formulations of\nthe SPDE problem by not imposing a specific covariance structure on the random\ndiffusion coefficient. Instead, we attempt to solve a more challenging problem\nof learning a map between an arbitrary snapshot of the diffusion field and the\nresponse.","url_abs":"http://arxiv.org/abs/1802.00850v1","url_pdf":"http://arxiv.org/pdf/1802.00850v1.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":"deep-uq-learning-deep-neural-network","repo_url":"https://github.com/rohitkt10/deep-uq-paper","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"uncertainty-quantification","task_name":"Uncertainty Quantification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1802.00850","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}