Multiscale modeling has become an indispensable tool in computational materials science. The properties of materials are typically governed by structures and processes on a multitude of time scales, ranging from electronic/atomic to millimeters and beyond, and from sub-picoseconds to seconds and beyond. The central element of multiscale modeling is coarse-graining, i.e., the art to describe complex systems with many degrees of freedom by a reduced set of representative degrees of freedom. Even though this idea has a long history, many fundamental aspects of coarse-graining and scale bridging are still poorly understood. Soft materials present a particular challenge, because different scales are not well separated quasi by definition. The characteristic feature of such complex systems is to respond strongly to small changes in the environment. This involves an interplay of processes on multiple scales, that cannot be disentangled easily [e.g., Weiss 2016, Hafner 2019] and often require multiresolution approaches [Kreis 2016, Wildman 2018, Stalter 2018, Kolli 2018, Lagardere 2018, Ciccotti 2019].

For many years, multiscale techniques have evolved in parallel and often independently in different communities, i.e., chemistry, physics, applied mathematics, and engineering. In chemistry and condensed matter physics, the focus has traditionally been on developing particle-based coarse-grained models and coarse-graining methods, often targeting structural properties of equilibrium systems [e.g., Uhlig 2018]. In recent years, dynamiccoarse-graining techniques [Zhang 2016, Izvekov 2017, Jung 2017, Bereau 2018] and multiscale models for nonequilibrium systems [Knoch 2017] are also attracting growing interest. In applied mathematics, the focus in multiscale modelling has traditionally been on multiscale methods for continuum models. Several techniques to model and approximate multiple scale phenomena have been developed, such as Fourier analysis, multigrid and wavelet analysis, heterogenous and/or variational multiscale methods, stochastic homogenization to name a few [e.g., Pavliotis 2008, E 2011, Malqvist 2014, Harbrecht 2016, Abdulle 2017, Otto 2017]. Nevertheless, bridging the enormous range of dynamically coupled scales as they arise in soft matter systems remains a
challenge.

Although rigorous numerical analyses for traditional particle- and or continuum-based multiscale methods are available in many cases [Lubich 2008, Ghanemn 2017], similar analyses for the recently developed multiscale methods for soft matter systems are still at the beginning [Hanke 2018]. Another recent development is a shift from traditional deterministic model-building and coarse-graining schemes to data based [Angelikopoulos 2013, Law 2015, Stalter 2018, Zdeborova 2016] and machine learning based schemes [Hruska 2018, Adorf 2018, Browning 2017, Chen 2019], which is in particular benefitting from recent advances in deep learning algorithms [Noe 2019].

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