Nonlinear sparse Bayesian learning for physics-based models
[3];
- Carleton Univ., Ottawa, ON (Canada). Dept. of Civil & Environmental Engineering
- Sandia National Lab. (SNL-CA), Livermore, CA (United States). Quantitative Modeling & Analysis Dept.
- United States Naval Academy, Annapolis, MD (United States). Dept. of Aerospace Engineering
- Royal Military College of Canada, Kingston, ON (Canada). Dept. of Mechanical & Aerospace Engineering
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 is 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.
- Research Organization:
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- AC04-94AL85000; NA0003525
- OSTI ID:
- 1670717
- Report Number(s):
- SAND-2019-14718J; 682468; TRN: US2203877
- Journal Information:
- Journal of Computational Physics, Vol. 426; ISSN 0021-9991
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Similar Records
Encoding nonlinear and unsteady aerodynamics of limit cycle oscillations using nonlinear sparse Bayesian learning
Approximate Bayesian Model Inversion for PDEs with Heterogeneous and State-Dependent Coefficients