On spike-and-slab priors for Bayesian equation discovery of nonlinear dynamical systems via sparse linear regression

Nayek, Rajdip; Fuentes, Ramón; Worden, Keith; Cross, Elizabeth

doi:10.1016/j.ymssp.2021.107986

Cited by 31 publications

(9 citation statements)

References 57 publications

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“…The Gibbs sampling procedure requires knowledge of the conditional posterior distributions for all the random variables. Nayek et al (2021) derived analytical expressions for all the conditional posterior distributions which we briefly summarize here.…”

Section: Model Discovery Via Posterior Estimationmentioning

confidence: 99%

“…The physical constraint of linear momentum conservation leads to a residual which defines the likelihood. We use a hierarchical Bayesian model with sparsity-promoting spikeslab priors (Nayek et al, 2021) and Monte Carlo sampling to efficiently solve the parsimonious model selection task and discover constitutive models in the form of multivariate multi-modal posterior probability distributions. Figure 1 summarizes the schematic of the method.…”

Section: Introductionmentioning

confidence: 99%

“…While other priors such as horseshoe(Carvalho et al, 2010) and Laplacian(Kabán, 2007) also promote sparsity, discontinuous spike-slab priors have been shown to be more robust and efficient in finding parsimonious solutions(Nayek et al, 2021).…”

mentioning

confidence: 99%

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Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties

Joshi,

Thakolkaran,

Zheng

et al. 2022

Preprint

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Within the scope of our recent approach for Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID), we propose an unsupervised Bayesian learning framework for discovery of parsimonious and interpretable constitutive laws with quantifiable uncertainties. As in deterministic EUCLID, we do not resort to stress data, but only to realistically measurable full-field displacement and global reaction force data; as opposed to calibration of an a priori assumed model, we start with a constitutive model ansatz based on a large catalog of candidate functional features; we leverage domain knowledge by including features based on existing, both physics-based and phenomenological, constitutive models. In the new Bayesian-EUCLID approach, we use a hierarchical Bayesian model with sparsitypromoting priors and Monte Carlo sampling to efficiently solve the parsimonious model selection task and discover physically consistent constitutive equations in the form of multivariate multi-modal probabilistic distributions. We demonstrate the ability to accurately and efficiently recover isotropic and anisotropic hyperelastic models like the Neo-Hookean, Isihara, Gent-Thomas, Arruda-Boyce, Ogden, and Holzapfel models in both elastostatics and elastodynamics. The discovered constitutive models are reliable under both epistemic uncertainties -i.e. uncertainties on the true features of the constitutive catalog -and aleatoric uncertainties -which arise from the noise in the displacement field data, and are automatically estimated by the hierarchical Bayesian model.

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Section: Model Discovery Via Posterior Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties

Joshi,

Thakolkaran,

Zheng

et al. 2022

Preprint

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“…The measurement matrix can be defined as

, where

is the sensing design matrix and

is a proper sparsifying basis. There exist various approaches to solve for

in ( 1 ) including greedy-based, convex-based, thresholding-based and sparse Bayesian learning (SBL) algorithms [ 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 ]. Typically, the performance of CS reconstruction is determined in terms of the mean-squared reconstruction error.…”

Section: Introductionmentioning

confidence: 99%

Compressive Sensing via Variational Bayesian Inference under Two Widely Used Priors: Modeling, Comparison and Discussion

Shekaramiz

Moon

2023

Entropy

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Compressive sensing is a sub-Nyquist sampling technique for efficient signal acquisition and reconstruction of sparse or compressible signals. In order to account for the sparsity of the underlying signal of interest, it is common to use sparsifying priors such as Bernoulli–Gaussian-inverse Gamma (BGiG) and Gaussian-inverse Gamma (GiG) priors on the components of the signal. With the introduction of variational Bayesian inference, the sparse Bayesian learning (SBL) methods for solving the inverse problem of compressive sensing have received significant interest as the SBL methods become more efficient in terms of execution time. In this paper, we consider the sparse signal recovery problem using compressive sensing and the variational Bayesian (VB) inference framework. More specifically, we consider two widely used Bayesian models of BGiG and GiG for modeling the underlying sparse signal for this problem. Although these two models have been widely used for sparse recovery problems under various signal structures, the question of which model can outperform the other for sparse signal recovery under no specific structure has yet to be fully addressed under the VB inference setting. Here, we study these two models specifically under VB inference in detail, provide some motivating examples regarding the issues in signal reconstruction that may occur under each model, perform comparisons and provide suggestions on how to improve the performance of each model.

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“…Further, SINDy is computationally efficient and scalable with an increase in the dimension of the measurement states. The Bayesian approach for discovering governing physics from data can also be found in [25,26,27]. These approaches, although robust to noise, are computationally demanding as compared to SINDy.…”

Section: Introductionmentioning

confidence: 99%

Discovering interpretable Lagrangian of dynamical systems from data

Tripura¹,

Chakraborty²

2023

Preprint

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A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing equations of motion. The generalization of equation discovery techniques has huge potential; however, existing Lagrangian discovery frameworks are black-box in nature. This raises a concern about the reusability of the discovered Lagrangian. In this article, we propose a novel data-driven machine-learning algorithm to automate the discovery of interpretable Lagrangian from data. The Lagrangian are derived in interpretable forms, which also allows the automated discovery of conservation laws and governing equations of motion. The architecture of the proposed framework is designed in such a way that it allows learning the Lagrangian from a subset of the underlying domain and then generalizing for an infinite-dimensional system. The fidelity of the proposed framework is exemplified using examples described by systems of ordinary differential equations and partial differential equations where the Lagrangian and conserved quantities are known.

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On spike-and-slab priors for Bayesian equation discovery of nonlinear dynamical systems via sparse linear regression

Cited by 31 publications

References 57 publications

Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties

Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties

Compressive Sensing via Variational Bayesian Inference under Two Widely Used Priors: Modeling, Comparison and Discussion

Discovering interpretable Lagrangian of dynamical systems from data

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