A nonconcurrent multiscale homogenization method is proposed to compute the response of structures made of heterogeneous hyperelastic materials. The method uses a database describing the effective strain energy density function (potential) in the macroscopic right Cauchy-Green strain tensor space. Each value of the database is computed numerically by means of the finite element method on a representative volume element, the corresponding macroscopic strains being prescribed as boundary conditions. An interpolation scheme is then introduced to provide a continuous representation of the potential, from which the macroscopic stress and elastic tangent tensors can be derived during macroscopic structures calculations. To efficiently compute the interpolations at the macroscopic scale, the full database is reduced by a tensor product approximation. Several extensions are provided to handle issues related to finite strains. The accuracy of the method is tested through different numerical tests involving composites at finite strains with isotropic or anisotropic microstructures. Second-order accuracy is achieved during the macroscopic Newton-Raphson iterations.

The presence of defects like gas bubble in fabricated parts is inherent in the selective laser sintering process and the prediction of bubble shrinkage dynamics is crucial. In this paper, two artificial intelligence (AI) models based on Decision Trees algorithm were constructed in order to predict bubble dissolution time, namely the Ensemble Bagged Trees (EDT Bagged) and Ensemble Boosted Trees (EDT Boosted). A metadata including 68644 data were generated with the help of our previously developed numerical tool. The AI models used the initial bubble size, external domain size, diffusion coefficient, surface tension, viscosity, initial concentration, and chamber pressure as input parameters, whereas bubble dissolution time was considered as output variable. Evaluation of the models’ performance was achieved by criteria such as Mean Absolute Error (MAE), Root Mean Squared Error (RMSE) and coefficient of determination (R²). The results showed that EDT Bagged outperformed EDT Boosted. Sensitivity analysis was then conducted thanks to the Monte Carlo approach and it was found that three most important inputs for the problem were the diffusion coefficient, initial concentration, and bubble initial size. This study might help in quick prediction of bubble dissolution time to improve the production quality from industry.

This article offers an extensive survey of one of the fundamental aspects of the trustworthiness of AI in healthcare, namely uncertainty, focusing on the large panoply of recent studies addressing the connection between uncertainty, AI, and healthcare. The concept of uncertainty is a recurring theme across multiple disciplines, with varying focuses and approaches. Here, we focus on the diverse nature of uncertainty in medical applications, emphasizing the importance of quantifying uncertainty in model predictions and its advantages in specific clinical settings. Questions that emerge in this context range from the guidelines for AI integration in the healthcare domain to the ethical deliberations and their compatibility with cutting-edge AI research. Together with a description of the main specific works in this context, we also discuss that, as medicine evolves and introduces novel sources of uncertainty, there is a need for more versatile uncertainty quantification methods to be developed collaboratively by researchers and healthcare professionals. Finally, we acknowledge the limitations of current uncertainty quantification methods in addressing the different facets of uncertainty within the medical domain. In particular, we identify from this survey a relative paucity of approaches that focus on the user’s perception of uncertainty and accordingly of trustworthiness.