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Generalized Swift–Hohenberg and phase-field-crystal equations based on a second-gradient phase-field theory (2020)
Journal Article
Espath, L., Calo, V. M., & Fried, E. (2020). Generalized Swift–Hohenberg and phase-field-crystal equations based on a second-gradient phase-field theory. Meccanica, 55(10), 1853-1868. https://doi.org/10.1007/s11012-020-01228-9

The principle of virtual power is used derive a microforce balance for a second-gradient phase-field theory. In conjunction with constitutive relations consistent with a free-energy imbalance, this balance yields a broad generalization of the Swift–H... Read More about Generalized Swift–Hohenberg and phase-field-crystal equations based on a second-gradient phase-field theory.

Multilevel double loop Monte Carlo and stochastic collocation methods with importance sampling for Bayesian optimal experimental design (2020)
Journal Article
Beck, J., Mansour Dia, B., Espath, L., & Tempone, R. (2020). Multilevel double loop Monte Carlo and stochastic collocation methods with importance sampling for Bayesian optimal experimental design. International Journal for Numerical Methods in Engineering, 121(15), 3482-3503. https://doi.org/10.1002/nme.6367

An optimal experimental set-up maximizes the value of data for statistical inferences. The efficiency of strategies for finding optimal experimental set-ups is particularly important for experiments that are time-consuming or expensive to perform. In... Read More about Multilevel double loop Monte Carlo and stochastic collocation methods with importance sampling for Bayesian optimal experimental design.

Nesterov-aided stochastic gradient methods using Laplace approximation for Bayesian design optimization (2020)
Journal Article
Gustavo Carlon, A., Mansour Dia, B., Espath, L., Holdorf Lopez, R., & Tempone, R. (2020). Nesterov-aided stochastic gradient methods using Laplace approximation for Bayesian design optimization. Computer Methods in Applied Mechanics and Engineering, 363, Article 112909. https://doi.org/10.1016/j.cma.2020.112909

Finding the best setup for experiments is the primary concern for Optimal Experimental Design (OED). Here, we focus on the Bayesian experimental design problem of finding the setup that maximizes the Shannon expected information gain. We use the stoc... Read More about Nesterov-aided stochastic gradient methods using Laplace approximation for Bayesian design optimization.