Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayesian-EUCLID: discovering hyperelastic material laws with
  uncertainties   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
sparsity-promoting 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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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: math
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph