2018/03/02 by Lukas Bruder, Bruder, Lukas, Phaedon‐Stelios Koutsourelakis +1
Computer Science · Decision Sciences · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1803.00930
openalex publication_date 2018/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The present paper is motivated by one of the most fundamental challenges in\ninverse problems, that of quantifying model discrepancies and errors. While\nsignificant strides have been made in calibrating model parameters, the\noverwhelming majority of pertinent methods is based on the assumption of a\nperfect model. Motivated by problems in solid mechanics which, as all problems\nin continuum thermodynamics, are described by conservation laws and\nphenomenological constitutive closures, we argue that in order to quantify\nmodel uncertainty in a physically meaningful manner, one should break open the\nblack-box forward model. In particular we propose formulating an undirected\nprobabilistic model that explicitly accounts for the governing equations and\ntheir validity. This recasts the solution of both forward and inverse problems\nas probabilistic inference tasks where the problem's state variables should not\nonly be compatible with the data but also with the governing equations as well.\nEven though the probability densities involved do not contain any black-box\nterms, they live in much higher-dimensional spaces. In combination with the\nintractability of the normalization constant of the undirected model employed,\nthis poses significant challenges which we propose to address with a\nlinearly-scaling, double-layer of Stochastic Variational Inference. We\ndemonstrate the capabilities and efficacy of the proposed model in synthetic\nforward and inverse problems (with and without model error) in elastography.\n