{"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/inverse-modeling-of-viscoelasticity-materials","title":"Inverse Modeling of Viscoelasticity Materials using Physics Constrained Learning","arxiv_id":"2005.04384","date":"2020-05-09","proceeding":null,"authors":["Kailai Xu","Alexandre M. Tartakovsky","Jeff Burghardt","Eric Darve"],"abstract":"We propose a novel approach to model viscoelasticity materials using neural networks, which capture rate-dependent and nonlinear constitutive relations. However, inputs and outputs of the neural networks are not directly observable, and therefore common training techniques with input-output pairs for the neural networks are inapplicable. To that end, we develop a novel computational approach to both calibrate parametric and learn neural-network-based constitutive relations of viscoelasticity materials from indirect displacement data in the context of multi-physics interactions. We show that limited displacement data hold sufficient information to quantify the viscoelasticity behavior. We formulate the inverse computation---modeling viscoelasticity properties from observed displacement data---as a PDE-constrained optimization problem and minimize the error functional using a gradient-based optimization method. The gradients are computed by a combination of automatic differentiation and physics constrained learning. The effectiveness of our method is demonstrated through numerous benchmark problems in geomechanics and porous media transport.","url_abs":"https://arxiv.org/abs/2005.04384v1","url_pdf":"https://arxiv.org/pdf/2005.04384v1.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":"inverse-modeling-of-viscoelasticity-materials","repo_url":"https://github.com/kailaix/PoreFlow.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"inverse-modeling-of-viscoelasticity-materials","repo_url":"https://github.com/kailaix/ADCME.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"inverse-modeling-of-viscoelasticity-materials","repo_url":"https://github.com/kailaix/AdFem.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}