{"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/adversarial-uncertainty-quantification-in","title":"Adversarial Uncertainty Quantification in Physics-Informed Neural Networks","arxiv_id":"1811.04026","date":"2018-11-09","proceeding":null,"authors":["Yibo Yang","Paris Perdikaris"],"abstract":"We present a deep learning framework for quantifying and propagating\nuncertainty in systems governed by non-linear differential equations using\nphysics-informed neural networks. Specifically, we employ latent variable\nmodels to construct probabilistic representations for the system states, and\nput forth an adversarial inference procedure for training them on data, while\nconstraining their predictions to satisfy given physical laws expressed by\npartial differential equations. Such physics-informed constraints provide a\nregularization mechanism for effectively training deep generative models as\nsurrogates of physical systems in which the cost of data acquisition is high,\nand training data-sets are typically small. This provides a flexible framework\nfor characterizing uncertainty in the outputs of physical systems due to\nrandomness in their inputs or noise in their observations that entirely\nbypasses the need for repeatedly sampling expensive experiments or numerical\nsimulators. We demonstrate the effectiveness of our approach through a series\nof examples involving uncertainty propagation in non-linear conservation laws,\nand the discovery of constitutive laws for flow through porous media directly\nfrom noisy data.","url_abs":"http://arxiv.org/abs/1811.04026v1","url_pdf":"http://arxiv.org/pdf/1811.04026v1.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":"adversarial-uncertainty-quantification-in","repo_url":"https://github.com/PredictiveIntelligenceLab/UQPINNs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"adversarial-uncertainty-quantification-in","repo_url":"https://github.com/tenokonda/gan-pi","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[{"task_slug":"uncertainty-quantification","task_name":"Uncertainty Quantification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1811.04026","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}