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When deformation gradients act on the scale of the microstructure of a part due to geometry and loading, spatial correlations and finite-size effects in simulation cells cannot be neglected. We propose a multiscale method that accounts for these effects using a variational autoencoder to encode the structure–property map of the stochastic volume elements making up the statistical description of the part. In this paradigm the autoencoder can be used to directly encode the microstructure or, alternatively, its latent space can be sampled to provide likely realizations. We demonstrate the method on three examples using the common additively manufactured material AlSi 10 Mg in: (a) a comparison with direct numerical simulation of the part microstructure, (b) a push forward of microstructural uncertainty to performance quantities of interest, and (c) a simulation of functional gradation of a part with stochastic microstructure. • Focus is on multiscale simulation where spatial correlations and finite-size effects cannot be neglected. • A multiscale method with a variational autoencoder to encode the structure-property map is proposed. • The autoencoder can directly encode microstructure or its latent space can be sampled. • Demonstrations: comparison to full-scale simulation, push forward of microstructural uncertainty, simulation of functional gradation. [ABSTRACT FROM AUTHOR]

Predictive modeling typically relies on Bayesian model calibration to provide uncertainty quantification. Variational inference utilizing fully independent ("mean-field") Gaussian distributions are often used as approximate probability density functions. This simplification is attractive since the number of variational parameters grows only linearly with the number of unknown model parameters. However, the resulting diagonal covariance structure and unimodal behavior can be too restrictive to provide useful approximations of intractable Bayesian posteriors that exhibit highly non-Gaussian behavior, including multimodality. High-fidelity surrogate posteriors for these problems can be obtained by considering the family of Gaussian mixtures. Gaussian mixtures are capable of capturing multiple modes and approximating any distribution to an arbitrary degree of accuracy, while maintaining some analytical tractability. Unfortunately, variational inference using Gaussian mixtures with full-covariance structures suffers from a quadratic growth in variational parameters with the number of model parameters. The existence of multiple local minima due to strong nonconvex trends in the loss functions often associated with variational inference present additional complications, These challenges motivate the need for robust initialization procedures to improve the performance and computational scalability of variational inference with mixture models. In this work, we propose a method for constructing an initial Gaussian mixture model approximation that can be used to warm-start the iterative solvers for variational inference. The procedure begins with a global optimization stage in model parameter space. In this step, local gradient-based optimization, globalized through multistart, is used to determine a set of local maxima, which we take to approximate the mixture component centers. Around each mode, a local Gaussian approximation is constructed via the Laplace approximation. Finally, the mixture weights are determined through constrained least squares regression. The robustness and scalability of the proposed methodology is demonstrated through application to an ensemble of synthetic tests using high-dimensional, multimodal probability density functions. The practical aspects of the approach are demonstrated with inversion problems in structural dynamics. • Developed a method for constructing Gaussian mixture model approximations. • The method relies on global optimization and Laplace approximations. • Exhibits improved scalability in comparison to variational inference. • We conduct global sensitivity analysis to measure its robustness. • The approach is demonstrated with two inversion problems in structural dynamics. [ABSTRACT FROM AUTHOR]

Abstract: The viscoelastic response of bovine corneas was characterized using in vitro inflation (bulge) experiments combined with spatially-resolved deformation mapping via digital image correlation. A complex fixture conforming to the limbal annulus was developed to hold the attached sclera rigid while allowing deformation only in the cornea. A statistical set of experiments was performed for a pressure range of 3.6–8kPa (27–60mmHg), representing nominal bovine intraocular pressure (IOP) to acute glaucoma conditions. A broader pressure range of 0–32kPa (0–240mmHg) was also examined to characterize the nonlinear finite deformation behavior of the tissue. Results showed that for pressures near and above IOP, the majority of the deformation was localized in the limbus and peripheral regions, which left the central cornea largely undeformed. This observation was consistent with the known preferred circumferential alignment of collagen fibrils outside of the central cornea. In general, the inflation experiments observed viscoelastic behavior in the form of rate-dependent hysteresis in the pressure–deformation response of the apex of the cornea, creep in the apex deformation at a constant inflation pressure, and relaxation in the pressure response at a constant inflation volume. The 3.6–8kPa (27–60mmHg) pressure range produced small viscoelastic deformations and a nearly linear pressure–deformation response, which suggests that for physiological pressure ranges, the cornea can be approximated as a linear viscoelastic or linear pseudo-elastic material. [Copyright &y& Elsevier]