  Multiscale models allow for the treatment of complex phenomena involving
different scales, such as remodeling and growth of tissues, muscular
activation, and cardiac electrophysiology. Numerous numerical approaches have
been developed to simulate multiscale problems. However, compared to the
well-established methods for classical problems, many questions have yet to be
answered. Here, we give an overview of existing models and methods, with
particular emphasis on mechanical and bio-mechanical applications. Moreover, we
discuss state-of-the-art techniques for multilevel and multifidelity
uncertainty quantification. In particular, we focus on the similarities that
can be found across multiscale models, discretizations, solvers, and
statistical methods for uncertainty quantification. Similarly to the current
trend of removing the segregation between discretizations and solution methods
in scientific computing, we anticipate that the future of multiscale simulation
will provide a closer interaction with also the models and the statistical
methods. This will yield better strategies for transferring the information
across different scales and for a more seamless transition in selecting and
adapting the level of details in the models. Finally, we note that machine
learning and Bayesian techniques have shown a promising capability to capture
complex model dependencies and enrich the results with statistical information;
therefore, they can complement traditional physics-based and numerical analysis
approaches.
