Title: Nonlinear sparse Bayesian learning for physics-based models

Abstract

This paper addresses the issue of overfitting while calibrating unknown parameters of over-parameterized physics-based models with noisy and incomplete observations. Here, a semi-analytical Bayesian framework of nonlinear sparse Bayesian learning (NSBL) is proposed to identify sparsity among model parameters during Bayesian inversion. NSBL offers significant advantages over machine learning algorithm of sparse Bayesian learning (SBL) for physics-based models, such as 1) the likelihood function or the posterior parameter distribution is not required to be Gaussian, and 2) prior parameter knowledge is incorporated into sparse learning (i.e. not all parameters are treated as questionable). NSBL employs the concept of automatic relevance determination (ARD) to facilitate sparsity among questionable parameters through parameterized prior distributions. The analytical tractability of NSBL is enabled by employing Gaussian ARD priors and by building a Gaussian mixture-model approximation of the posterior parameter distribution that excludes the contribution of ARD priors. Subsequently, type-II maximum likelihood is executed using Newton's method whereby the evidence and its gradient and Hessian information are computed in a semi-analytical fashion. We show numerically and analytically that SBL is a special case of NSBL for linear regression models. Subsequently, a linear regression example involving multimodality in both parameter posterior pdf and model evidence ismore » considered to demonstrate the performance of NSBL in cases where SBL is inapplicable. Next, NSBL is applied to identify sparsity among the damping coefficients of a mass-spring-damper model of a shear building frame. These numerical studies demonstrate the robustness and efficiency of NSBL in alleviating overfitting during Bayesian inversion of nonlinear physics-based models.« less

Authors:

Sandhu, Rimple ^[1]; Khalil, Mohammad ^[2]; Pettit, Chris  ^[3];

• Search DOE PAGES for author "Pettit, Chris"
• Search DOE PAGES for ORCID "0000-0003-3559-7612"

Poirel, Dominique ^[4]; Sarkar, Abhijit ^[1]

---

+ Show Author Affiliations

1. Carleton Univ., Ottawa, ON (Canada). Dept. of Civil & Environmental Engineering
2. Sandia National Lab. (SNL-CA), Livermore, CA (United States). Quantitative Modeling & Analysis Dept.
3. United States Naval Academy, Annapolis, MD (United States). Dept. of Aerospace Engineering
4. Royal Military College of Canada, Kingston, ON (Canada). Dept. of Mechanical & Aerospace Engineering

Publication Date:

Wed Jul 29 00:00:00 EDT 2020

Research Org.:

Sandia National Lab. (SNL-CA), Livermore, CA (United States)

Sponsoring Org.:

USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:

1670717

Report Number(s):

SAND-2019-14718J
Journal ID: ISSN 0021-9991; 682468; TRN: US2203877

Grant/Contract Number:  

AC04-94AL85000; NA0003525

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Computational Physics

Additional Journal Information:

Journal Volume: 426; Journal ID: ISSN 0021-9991

Publisher:

Elsevier

Country of Publication:

United States

Language:

English

Subject:

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; automatic relevance determination; Bayesian inference; Bayesian model selection; Gaussian mixture-model; inverse problems; physics-based modelling; sparse learning