Multiscale modelling: approaches and challenges.

Abstract

You have accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Karabasov Sergey, Nerukh Dmitry, Hoekstra Alfons, Chopard Bastien and Coveney Peter V. 2014Multiscale modelling: approaches and challengesPhil. Trans. R. Soc. A.3722013039020130390http://doi.org/10.1098/rsta.2013.0390SectionYou have accessIntroductionMultiscale modelling: approaches and challenges Sergey Karabasov Sergey Karabasov Department of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London E1 4NS, UK [email protected] Google Scholar Find this author on PubMed Search for more papers by this author , Dmitry Nerukh Dmitry Nerukh Department of Engineering and Applied Science, Aston University, Aston Triangle, Birmingham B4 7ET, UK Google Scholar Find this author on PubMed Search for more papers by this author , Alfons Hoekstra Alfons Hoekstra Computational Science, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands National Research University ITMO, Kronverkskiy Prospekt 49, 197101 St Petersburg, Russia Google Scholar Find this author on PubMed Search for more papers by this author , Bastien Chopard Bastien Chopard Computer Science Department, University of Geneva, 1211 Geneva 4, Switzerland Google Scholar Find this author on PubMed Search for more papers by this author and Peter V. Coveney Peter V. Coveney Centre for Computational Science, University College London, 20 Gordon Street, London WC1H OAJ, UK Google Scholar Find this author on PubMed Search for more papers by this author Sergey Karabasov Sergey Karabasov Department of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London E1 4NS, UK [email protected] Google Scholar Find this author on PubMed Search for more papers by this author , Dmitry Nerukh Dmitry Nerukh Department of Engineering and Applied Science, Aston University, Aston Triangle, Birmingham B4 7ET, UK Google Scholar Find this author on PubMed Search for more papers by this author , Alfons Hoekstra Alfons Hoekstra Computational Science, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands National Research University ITMO, Kronverkskiy Prospekt 49, 197101 St Petersburg, Russia Google Scholar Find this author on PubMed Search for more papers by this author , Bastien Chopard Bastien Chopard Computer Science Department, University of Geneva, 1211 Geneva 4, Switzerland Google Scholar Find this author on PubMed Search for more papers by this author and Peter V. Coveney Peter V. Coveney Centre for Computational Science, University College London, 20 Gordon Street, London WC1H OAJ, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:06 August 2014https://doi.org/10.1098/rsta.2013.0390Multiscale systems that are characterized by a great range of spatial–temporal scales arise widely in many scientific domains. These range from the study of protein conformational dynamics to multiphase processes in, for example, granular media or haemodynamics, and from nuclear reactor physics to astrophysics. Despite the diversity in subject areas and terminology, there are many common challenges in multiscale modelling, including validation and design of tools for programming and executing multiscale simulations. This Theme Issue seeks to establish common frameworks for theoretical modelling, computing and validation, and to help practical applications to benefit from the modelling results. This Theme Issue has been inspired by discussions held during two recent workshops in 2013: ‘Multiscale modelling and simulation’ at the Lorentz Center, Leiden (http://www.lorentzcenter.nl/lc/web/2013/569/info.php3?wsid=569&venue=Snellius), and ‘Multiscale systems: linking quantum chemistry, molecular dynamics and microfluidic hydrodynamics’ at the Royal Society Kavli Centre. The objective of both meetings was to identify common approaches for dealing with multiscale problems across different applications in fluid and soft matter systems. This was achieved by bringing together experts from several diverse communities.As discussed in the contribution by Hoekstra et al. [1] (which opens this issue), one of the first questions that arise is what exactly constitutes the multiscale modelling that is inherent in multiscale systems and the issues that it involves. For example, it can be observed that multiscale problems do not typically have a closed solution (except for some idealized situations when a single-scale model at the finest level, e.g. a solution of the time-dependent Schrödinger equation in quantum mechanics, can be used as a first-principles direct solution method). To simulate a large enough system with multiple scales at the level of detail required, one has to combine models at various scale resolutions and invariably deal with different physics. Multiscale systems can be characterized by the fact that there is a form of approximation or coarse graining involved in the multiscale modelling, corresponding to an error below some threshold scale of interest. The specific terminology used for coarse graining and scale bridging in multiscale systems varies in different subject areas. For instance, terms such as projection, upscaling, model reduction and physical analogy could be used to describe the procedure of reducing the full complexity of the multiscale problem to an insightful, but tractable, representation. Coarse graining is implemented in order to reproduce interesting quantities at longer length and time scales. This, in turn, extends the modelling to a wider scale range at an affordable computational cost. On the other hand, it is not possible to coarse grain everything, as it incurs a loss of information at each step. Coarse graining also involves the exchange of information between the fine scale and the coarse scale. In some cases, this can be approximated as a one-way coupling between the scales, but, in others, a fully two-way coupling framework is required.Despite the differences in the application methods, there is a good deal of similarity found in the application of scale separation and computational implementations in many multiscale problems. These can be analysed at the abstract level, as discussed in the contribution by Chopard et al. [2]. The exchange of information between multiple scales leads to error propagation within the multiscale model, thus affecting the stability and accuracy of the solution. Furthermore, it probes the question as to whether any mutual approaches for careful error analysis can be carried out at a theoretical level. Some examples of possible a priori estimates are discussed in the contribution by Abdulle & Bai [3] in applications to continuum fluid dynamics equations with multiscale coefficients based on homogenization theory.Without thorough analysis or a priori guidance for computational modelling, it is necessary to make a comparison by empirical validation, or with a high-fidelity single-scale model, if that is computationally tractable. In numerous multiscale systems, a sequential approach is adopted when building a hierarchy of models. These begin with a high-fidelity model at a single scale well established with regard to the experiment or observation, which sequentially transfers information to a more coarse-grained level. For example, Booth et al. [4] discuss a ‘boxed dynamics’ approach to accelerate atomistic simulations for capturing the thermodynamics and kinetics of complex molecular-dynamics systems. In the area of biological fluid flows, examples of multiscale models are discussed in the contribution by Li et al. [5] in application to multicomponent blood cell interactions in small capillary vessels. Validation is also discussed in the contribution by Wu et al. [6], who consider the interactions of platelets, blood flow and vessel walls that occur during blood clotting. In the area of coupling continuum flow and discrete particle dynamics, Srivastava et al. [7] provide an example of a multiscale model for two-phase granular systems and Markesteijn et al. [8] discuss a hybrid method for bridging continuum and molecular dynamics representations of liquids.In addition to the physical and mathematical complexity at the conceptual level, another issue present in many domains is how to implement multiscale models in practice at the computational level. For example, there is the issue of coupling different codes written for single-scale single-physics simulation in a unified framework. It is necessary for the latter to be flexible enough to accommodate new codes written in an object-oriented environment in addition to legacy ones used in different communities for many years and based on more traditional data structures. These issues are discussed by van Elteren et al. [9] in the context of astrophysics and by Mahadevan et al. [10] in nuclear engineering applications. The scalability of such heterogeneous computational frameworks becomes important as the size of the multiscale system increases and requires the development of specialized custom-made software as discussed by Borgdorff et al. [11]. For efficient modelling of complex systems such as large biomolecular systems, including software optimization, it can be beneficial to implement custom-made hardware accelerators, such as those where the molecular interactions are implemented at the chip level, as discussed by Ohmura et al. [12].To summarize, the contributions within this Theme Issue discuss the different aspects (conceptual, theoretical, algorithmic, applied) of various multiscale and multiphysics problems. Although this issue illustrates the diversity of the underlying scientific challenges, the solutions share common methodologies that can potentially be re-used and may possibly constitute the basis of a general theory of multiscale modelling and simulation.FootnotesOne contribution of 13 to a Theme Issue ‘Multi-scale systems in fluids and soft matter: approaches, numerics and applications’.© 2014 The Author(s) Published by the Royal Society. All rights reserved.References1Hoekstra A, Chopard B& Coveney PV. 2014Multiscale modelling and simulation: a position paper. Phil. Trans. R. Soc. A 372, 20130377. (doi:10.1098/rsta.2013.0377). Link, ISI, Google Scholar2Chopard B, Borgdorff J& Hoekstra AG. 2014A framework for multi-scale modelling. Phil. Trans. R. Soc. A 372, 20130378. (doi:10.1098/rsta.2013.0378). Link, ISI, Google Scholar3Abdulle A& Bai Y. 2014Reduced-order modelling numerical homogenization. Phil. Trans. R. Soc. A 372, 20130388. (doi:10.1098/rsta.2013.0388). Link, ISI, Google Scholar4Booth J, Vazquez S, Martinez-Nunez E, Marks A, Rodgers J, Glowacki DR& Shalashilin DV. 2014Recent applications of boxed molecular dynamics: a simple multiscale technique for atomistic simulations. Phil. Trans. R. Soc. A 372, 20130384. (doi:10.1098/rsta.2013.0384). Link, ISI, Google Scholar5Li X, Peng Z, Lei H, Dao M& Karniadakis GE. 2014Probing red blood cell mechanics, rheology and dynamics with a two-component multi-scale model. Phil. Trans. R. Soc. A 372, 20130389. (doi:10.1098/rsta.2013.0389). Link, ISI, Google Scholar6Wu Z, Xu Z, Kim O& Alber M. 2014Three-dimensional multi-scale model of deformable platelets adhesion to vessel wall in blood flow. Phil. Trans. R. Soc. A 372, 20130380. (doi:10.1098/rsta.2013.0380). Link, ISI, Google Scholar7Srivastava S, Yazdchi K& Luding S. 2014Mesoscale dynamic coupling of finite- and discrete-element methods for fluid–particle interactions. Phil. Trans. R. Soc. A 372, 20130386. (doi:10.1098/rsta.2013.0386). Link, ISI, Google Scholar8Markesteijn A, Karabasov S, Scukins A, Nerukh D, Glotov V& Goloviznin V. 2014Concurrent multiscale modelling of atomistic and hydrodynamic processes in liquids. Phil. Trans. R. Soc. A 372, 20130379. (doi:10.1098/rsta.2013.0379). Link, ISI, Google Scholar9van Elteren A, Pelupessy I& Portegies Zwart S. 2014Multi-scale and multi-domain computational astrophysics. Phil. Trans. R. Soc. A 372, 20130385. (doi:10.1098/rsta.2013.0385). Link, ISI, Google Scholar10Mahadevan VS, Merzari E, Tautges T, Jain R, Obabko A, Smith M& Fischer P. 2014High-resolution coupled physics solvers for analysing fine-scale nuclear reactor design problems. Phil. Trans. R. Soc. A 372, 20130381. (doi:10.1098/rsta.2013.0381). Link, ISI, Google Scholar11Borgdorff J, et al.2014Performance of distributed multiscale simulations. Phil. Trans. R. Soc. A 372, 20130407. (doi:10.1098/rsta.2013.0407). Link, ISI, Google Scholar12Ohmura I, Morimoto G, Ohno Y, Hasegawa A& Taiji M. 2014MDGRAPE-4: a special-purpose computer system for molecular dynamics simulations. Phil. Trans. R. Soc. A 372, 20130387. (doi:10.1098/rsta.2013.0387). Link, ISI, Google Scholar Next Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited byYe D, Veen L, Nikishova A, Lakhlili J, Edeling W, Luk O, Krzhizhanovskaya V and Hoekstra A (2021) Uncertainty quantification patterns for multiscale models, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 379:2197, Online publication date: 17-May-2021.Coveney P and Highfield R (2021) When we can trust computers (and when we can't), Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 379:2197, Online publication date: 17-May-2021. 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Hoekstra A, Chopard B, Coster D, Portegies Zwart S and Coveney P (2019) Multiscale computing for science and engineering in the era of exascale performance, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 377:2142, Online publication date: 8-Apr-2019.van Elteren A, Bédorf J and Portegies Zwart S (2019) Multi-scale high-performance computing in astrophysics: simulating clusters with stars, binaries and planets, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 377:2142, Online publication date: 8-Apr-2019.Hoekstra A, Portegies Zwart S and Coveney P (2019) Multiscale modelling, simulation and computing: from the desktop to the exascale, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 377:2142, Online publication date: 8-Apr-2019. Durbhakula K, Chatterjee D and Hassan A An Efficient Algorithm for Locating TE and TM Poles for a Class of Multiscale Inhomogeneous Media Problems, IEEE Journal on Multiscale and Multiphysics Computational Techniques, 10.1109/JMMCT.2020.2965108, 4, (364-373) Naghibi S, Karabasov S, Jalali M and Sadati S (2019) Fast spectral solutions of the double-gyre problem in a turbulent flow regime, Applied Mathematical Modelling, 10.1016/j.apm.2018.09.026, 66, (745-767), Online publication date: 1-Feb-2019. Little J, Hester E, Elsawah S, Filz G, Sandu A, Carey C, Iwanaga T and Jakeman A (2019) A tiered, system-of-systems modeling framework for resolving complex socio-environmental policy issues, Environmental Modelling & Software, 10.1016/j.envsoft.2018.11.011, 112, (82-94), Online publication date: 1-Feb-2019. Nikishova A and Hoekstra A (2019) Semi-intrusive uncertainty propagation for multiscale models, Journal of Computational Science, 10.1016/j.jocs.2019.06.007, 35, (80-90), Online publication date: 1-Jul-2019. Zheng Z, Chen J and Luo X (2019) Parallel computational building-chain model for rapid urban-scale energy simulation, Energy and Buildings, 10.1016/j.enbuild.2019.07.034, 201, (37-52), Online publication date: 1-Oct-2019. Ivanović M, Kaplarević-Mališić A, Stojanović B, Svičević M and Mijailovich S (2019) Machine learned domain decomposition scheme applied to parallel multi-scale muscle simulation, The International Journal of High Performance Computing Applications, 10.1177/1094342019833151, 33:5, (885-896), Online publication date: 1-Sep-2019. Fedosov D (2018) Hemostasis is a highly multiscale process, Physics of Life Reviews, 10.1016/j.plrev.2018.06.017, 26-27, (108-109), Online publication date: 1-Nov-2018. Korotkin I and Karabasov S (2018) A generalised Landau-Lifshitz fluctuating hydrodynamics model for concurrent simulations of liquids at atomistic and continuum resolution, The Journal of Chemical Physics, 10.1063/1.5058804, 149:24, (244101), Online publication date: 28-Dec-2018. Alowayyed S, Groen D, Coveney P and Hoekstra A (2017) Multiscale computing in the exascale era, Journal of Computational Science, 10.1016/j.jocs.2017.07.004, 22, (15-25), Online publication date: 1-Sep-2017. Tarasova E, Korotkin I, Farafonov V, Karabasov S and Nerukh D (2017) Complete virus capsid at all-atom resolution: Simulations using molecular dynamics and hybrid molecular dynamics/hydrodynamics methods reveal semipermeable membrane function, Journal of Molecular Liquids, 10.1016/j.molliq.2017.06.124, 245, (109-114), Online publication date: 1-Nov-2017. Kyaw S, Rouse J, Lu J and Sun W (2016) Determination of material parameters for a unified viscoplasticity-damage model for a P91 power plant steel, International Journal of Mechanical Sciences, 10.1016/j.ijmecsci.2016.06.014, 115-116, (168-179), Online publication date: 1-Sep-2016. Viceconti M, Hunter P and Hose R Big Data, Big Knowledge: Big Data for Personalized Healthcare, IEEE Journal of Biomedical and Health Informatics, 10.1109/JBHI.2015.2406883, 19:4, (1209-1215) Korotkin I, Karabasov S, Nerukh D, Markesteijn A, Scukins A, Farafonov V and Pavlov E (2015) A hybrid molecular dynamics/fluctuating hydrodynamics method for modelling liquids at multiple scales in space and time, The Journal of Chemical Physics, 10.1063/1.4923011, 143:1, (014110), Online publication date: 7-Jul-2015. Kampis G, Kantelhardt J, Kloch K and Lukowicz P (2015) Analytical and simulation models for collaborative localization, Journal of Computational Science, 10.1016/j.jocs.2014.09.001, 6, (1-10), Online publication date: 1-Jan-2015. Suter J, Groen D and Coveney P (2014) Chemically Specific Multiscale Modeling of Clay-Polymer Nanocomposites Reveals Intercalation Dynamics, Tactoid Self-Assembly and Emergent Materials Properties, Advanced Materials, 10.1002/adma.201403361, 27:6, (966-984), Online publication date: 1-Feb-2015. Suter J, Groen D and Coveney P (2015) Mechanism of Exfoliation and Prediction of Materials Properties of Clay–Polymer Nanocomposites from Multiscale Modeling, Nano Letters, 10.1021/acs.nanolett.5b03547, 15:12, (8108-8113), Online publication date: 9-Dec-2015. Read M, Alden K, Timmis J and Andrews P (2018) Strategies for calibrating models of biology, Briefings in Bioinformatics, 10.1093/bib/bby092 This Issue06 August 2014Volume 372Issue 2021Theme Issue ‘Multi-scale systems in fluids and soft matter: approaches, numerics and applications’ organised and edited by Sergey Karabasov, Dmitry Nerukh, Alfons Hoekstra, Bastien Chopard and Peter Coveney Article InformationDOI:https://doi.org/10.1098/rsta.2013.0390Published by:Royal SocietyPrint ISSN:1364-503XOnline ISSN:1471-2962History: Published online06/08/2014Published in print06/08/2014 License:© 2014 The Author(s) Published by the Royal Society. All rights reserved. Citations and impact Subjectsapplied mathematics