Multiscale and multiphysics applications are now commonplace, and many researchers focus on combining existing models to construct combined multiscale models. Here we present a concise review of multiscale applications and their source communities. We investigate the prevalence of multiscale projects in the EU and the US, review a range of coupling toolkits they use to construct multiscale models and identify areas where collaboration between disciplines could be particularly beneficial. We conclude that multiscale computing has become increasingly popular in recent years, that different communities adopt very different approaches to constructing multiscale simulations, and that simulations on a length scale of a few metres and a time scale of a few hours can be found in many of the multiscale research domains. Communities may receive additional benefit from sharing methods that are geared towards these scales.
Aside from numerous publications, project websites and domain-specific reviews, we have identified a few sources which provide information on multiscale simulations in various scientific domains. One such source of information is the Journal of Multiscale Modeling and Simulation (epubs.siam.org mms), which defines itself as an interdisciplinary journal focusing on the fundamental modeling and computational principles underlying various multiscale methods. The Journal of Multiscale Modeling (www.worldscinet.com jmm ) is also targeted at multiscale modeling in general. There are also several books which present multiscale research in a range of domains @cite_17 @cite_12 , as well as dozens of multiscale modeling workshops such as the Multiscale Materials Meeting (www.mrs.org.sg mmm2012) or the Modelling and Computing Multiscale Systems workshop (www.computationalscience.nl MCMS2013). There are several articles which focus on the theoretical aspects of multiscale modelling across domains. @cite_3 present a thorough and systematic review of the computational and (especially) the conceptual toolkits for multiscale modelling. In addition, @cite_13 investigate the modeling aspects of multiscale simulations, emphasizing simulations using Cellular Automata.
@cite_3 @cite_13 @cite_12 @cite_17
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Small scale features and processes occurring at a nanometer and femtoseconds scales have a profound impact on what happens at a larger scale and over extensive period of time. The primary objective of this volume is to reflect the-state-of-the art in multiscale mathematics, modeling and simulations and to address the following barriers: What is the information that needs to be transferred from one model or scale to another and what physical principles must be satisfied during the transfer of information? What are the optimal ways to achieve such transfer of information? How to quantify variability of physical parameters at multiple scales and how to account for it to ensure design robustness? Various multiscale approaches in space and time presented in this Volume are grouped into two main categories: information-passing and concurrent. In the concurrent approaches, various scales are simultaneously resolved, whereas in the information-passing methods, the fine scale is modeled and its gross response is infused into the continuum scale. The issue of reliability of multiscale modeling and simulation tools is discussed in several, which focus on hierarchy of multiscale models and a posterior model error estimation including uncertainty quantification. Component software that can be effectively combined to address a wide range of multiscale simulations is described as well. Applications range from advanced materials, to nanoelectromechanical systems (NEMS), to biological systems, and nanoporous catalysts where physical phenomena operate across 12 orders of magnitude in time scales and 10 orders of magnitude in spatial scales. A valuable reference book for scientists, engineers and graduate students practicing in traditional engineering and science disciplines as well as in emerging fields of nanotechnology, biotechnology, microelectronics and energy. Multi-level simulation models, i.e., models where different components are simulated using sub-models of varying levels of complexity, belong to the current state-of-the-art in simulation. The existing analysis practice for multi-level simulation results is to manually compare results from different levels of complexity, amounting to a very tedious and error-prone, trial-and-error exploration process. In this paper, we introduce hierarchical visual steering, a new approach to the exploration and design of complex systems. Hierarchical visual steering makes it possible to explore and analyze hierarchical simulation ensembles at different levels of complexity. At each level, we deal with a dynamic simulation ensemble — the ensemble grows during the exploration process. There is at least one such ensemble per simulation level, resulting in a collection of dynamic ensembles, analyzed simultaneously. The key challenge is to map the multi-dimensional parameter space of one ensemble to the multi-dimensional parameter space of another ensemble (from another level). In order to support the interactive visual analysis of such complex data we propose a novel approach to interactive and semi-automatic parameter space segmentation and comparison. The approach combines a novel interaction technique and automatic, computational methods — clustering, concave hull computation, and concave polygon overlapping — to support the analysts in the cross-ensemble parameter space mapping. In addition to the novel parameter space segmentation we also deploy coordinated multiple views with standard plots. We describe the abstract analysis tasks, identified during a case study, i.e., the design of a variable valve actuation system of a car engine. The study is conducted in cooperation with experts from the automotive industry. Very positive feedback indicates the usefulness and efficiency of the newly proposed approach. In this paper we propose a general framework for the uncertainty quantification of quantities of interest for high-contrast single-phase flow problems. It is based on the generalized multiscale finite element method (GMsFEM) and multilevel Monte Carlo (MLMC) methods. The former provides a hierarchy of approximations of different resolution, whereas the latter gives an efficient way to estimate quantities of interest using samples on different levels. The number of basis functions in the online GMsFEM stage can be varied to determine the solution resolution and the computational cost, and to efficiently generate samples at different levels. In particular, it is cheap to generate samples on coarse grids but with low resolution, and it is expensive to generate samples on fine grids with high accuracy. By suitably choosing the number of samples at different levels, one can leverage the expensive computation in larger fine-grid spaces toward smaller coarse-grid spaces, while retaining the accuracy of the final Monte Carlo estimate. Further, we describe a multilevel Markov chain Monte Carlo method, which sequentially screens the proposal with different levels of approximations and reduces the number of evaluations required on fine grids, while combining the samples at different levels to arrive at an accurate estimate. The framework seamlessly integrates the multiscale features of the GMsFEM with the multilevel feature of the MLMC methods following the work in [26], and our numerical experiments illustrate its efficiency and accuracy in comparison with standard Monte Carlo estimates. We explore multi-scale convolutional neural nets (CNNs) for image classification. Contemporary approaches extract features from a single output layer. By extracting features from multiple layers, one can simultaneously reason about high, mid, and low-level features during classification. The resulting multi-scale architecture can itself be seen as a feed-forward model that is structured as a directed acyclic graph (DAG-CNNs). We use DAG-CNNs to learn a set of multi-scale features that can be effectively shared between coarse and fine-grained classification tasks. While fine-tuning such models helps performance, we show that even "off-the-self" multi-scale features perform quite well. We present extensive analysis and demonstrate state-of-the-art classification performance on three standard scene benchmarks (SUN397, MIT67, and Scene15). In terms of the heavily benchmarked MIT67 and Scene15 datasets, our results reduce the lowest previously-reported error by 23.9 and 9.5 , respectively.