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International Journal for Uncertainty Quantification
IF: 3.259 5-Year IF: 2.547 SJR: 0.417 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2014008154
pages 171-184

INFERENCE AND UNCERTAINTY PROPAGATION OF ATOMISTICALLY INFORMED CONTINUUM CONSTITUTIVE LAWS, PART 2: GENERALIZED CONTINUUM MODELS BASED ON GAUSSIAN PROCESSES

Maher Salloum
Sandia National Laboratories, 7011 East Avenue, MS 9158, Livermore, California 94550, USA
Jeremy A. Templeton
Sandia National Laboratories, 7011 East Avenue, MS 9409, Livermore, California 94550, USA

ABSTRACT

Constitutive models in nanoscience and engineering often poorly represent the physics due to significant deviations in model form from their macroscale counterparts. In Part 1 of this study, this problem was explored by considering a continuum scale heat conduction constitutive law inferred directly from molecular dynamics (MD) simulations. In contrast, this work uses Bayesian inference based on the MD data to construct a Gaussian process emulator of the heat flux as a function of temperature and temperature gradient. No assumption of Fourier-like behavior is made, requiring alternative approaches to assess the well-posedness and accuracy of the emulator. Validation is provided by comparing continuum scale predictions using the emulator model against a larger all-MD simulation representing the true solution. The results show that a Gaussian process emulator of the heat conduction constitutive law produces an empirically unbiased prediction of the continuum scale temperature field for a variety of time scales, which was not observed when Fourier's law is assumed to hold. Finally, uncertainty is propagated in the continuum model and quantified in the temperature field so the impact of errors in the model on continuum quantities can be determined.


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