Multiscale modeling: recent progress and open questions

Abstract

Many important scientific problems are inherently multi scale. This is, for instance, the case in models in material science or environmental science. A big challenge is to formulate generic frameworks for multiscale modeling and simulation. Despite its importance, the scientific community still lacks a well-accepted generic methodology to address multiscale computating. We review a recent theoretical framework which aims at filling this gap. We also present new results and extension in relation with scale bridging methods and execution multiscale simulation on HPC systems, and discuss open questions related to this topic.

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References

  1. Alowayyed S, Groen D, Coveney PV, Hoekstra A (2017) Multiscale computing in the exascale era. J Comput Sci 22:15–25. https://doi.org/10.1016/j.jocs.2017.07.004

    Article  Google Scholar 

  2. Alowayyed S, Piontek T, Suter JL, Hoenen O, Groen D, Luk OO, Bosak B, Kopta P, Kurowski K, Perks O, Brabazon K, Jancauskas V, Coster D, Coveney PV, Hoekstra AG (2017) Patterns for high performance multiscale computing. Future Gener Comput Syst

  3. Blegacem MB, Chopard B (2015) A hybrid HPC/cloud distributed infrastructure: coupling EC2 cloud resources with HPC clusters to run large tightly coupled multiscale applications. Future Gener Comput Syst. https://doi.org/10.1016/j.future.2014.08.003

  4. Belgacem MB, Chopard B (2016) Muscle-hpc: a new high performance api to couple multiscale parallel applications. Future Gener Comput Syst 67:72–82. https://doi.org/10.1016/j.future.2016.08.009

    Article  Google Scholar 

  5. Belgacem M Ben, Chopard B, Borgdorff J, Mamonski M, Rycerz K, Harezlak D (2013a) Distributed multiscale computations using the MAPPER framework. Procedia Comput Sci 18:1106–1115. https://doi.org/10.1016/j.procs.2013.05.276

    Article  Google Scholar 

  6. Borgdorf J, Falcone JL, Lorenz E, Bona-Casas C, Chopard B, Hoekstra AG (2013b) Foundations of distributed multiscale computing: formalization, specification, analysis and execution. J Parallel Distrib Comput 73:465–483

    Article  MATH  Google Scholar 

  7. Borgdorff J, Mamonski M, Bosak B, Groen D, Belgacem MB, Kurowski K, Hoekstra AG (2013c) Distributed multiscale computing with the multiscale modeling library and runtime environment. Procedia Comput Sci 18:1097–1105

    Article  Google Scholar 

  8. Borgdorff J, Mamonski M, Bosak B, Groen D, Belgacem MB, Kurowski K, Hoekstra AG (2013) Multiscale computing with the multiscale modeling library and runtime environment. Procedia Comput Sci 18(0):1097–1105. https://doi.org/10.1016/j.procs.2013.05.275. http://www.sciencedirect.com/science/article/pii/S1877050913004183

  9. Borgdorff J, Belgacem MB, Bona-Casas C, Fazendeiro L, Groen D, Hoenen O, Mizeranschi A, Suter JL, Coster D, Coveney PV, Dubitzky W, Hoekstra AG, Strand P, Chopard B (2014) Performance of distributed multiscale simulations. Philos Trans A 372(2021):20130407

  10. Caiazzo A, Falcone JL, Chopard B, Hoekstra AG (2009) Asymptotic analysis of complex automata models for reaction-diffusion systems. Appl Numer Math 59(8):2023–2034

    MathSciNet  Article  MATH  Google Scholar 

  11. Chopard B, Borgdorff J, Hoekstra AG (2014) A framework for multiscale modeling. Philos Trans A 372:20130,376

  12. Dada JO, Mendes P (2011) Multi-scale modelling and simulation in systems biology. Integr Biol 3(2):86–96

  13. Evans D, Lawford PV, Gunn J, Walker D, Hose DR, Smallwood R, Chopard B, Krafczyk M, Bernsdorf J, Hoekstra A (2008) The application of multi-scale modelling to the process of development and prevention of stenosis in a stented coronary artery. Philos Trans R Soc 366:3343–3360

    Article  Google Scholar 

  14. Falcone JL, Chopard B, Hoekstra A (2010) MML: towards a multiscale modeling language. Procedia Comput Sci 1(11):819–826

    Article  Google Scholar 

  15. Groen D, Borgdorff J, Bona-Casas C, Hetherington J, Nash RW, Zasada SJ, Saverchenko I, Mamonski M, Kurowski K, Bernabeu MO, Hoekstra AG, Coveney PV (2013) Flexible composition and execution of high performance, high fidelity multiscale biomedical simulations. Interface Focus 3(2):20120087

  16. Groen D, nad James Suter APB, Hetherington J, Zasada SJ, Coveney PV (2016) Fabsim: facilitating computational research through automation on large-scale and distributed e-infrastructures. Comput Phys Commun. https://doi.org/10.1016/j.cpc.2016.05.020

  17. Hoekstra AG et al (2016) Towards the virtual artery: a multiscale model for vascular physiology at the pcb interface. Philos Trans R Soc A 374(0160):146. https://doi.org/10.1098/rsta.2016.0146

  18. Hoekstra AG, Caiazzo A, Lorenz E, Falcone JL, Chopard B (2010) Modelling complex systems by cellular automata, chap. 3. Springer, Berlin

  19. Hoekstra AG, Coveney P, Chopard B (2014) Position a paper on multiscale modeling and computing. Philos Trans A 372:20130377

  20. Ingram G, Cameron I, Hangos K (2004) Classification and analysis of integrating frameworks in multiscale modelling. Chem Eng Sci 59:2171–2187

    Article  Google Scholar 

  21. Künzli P, Tsunematsu K, Albuquerque P, Falcone JL, Chopard B, Bonadonna C (2016) Parallel simulation of particle transport in an advection field applied to tephra dispersal. Comput GeoSci 89:174–185

    Article  Google Scholar 

  22. Lorenz E, Hoekstra A (2011) Heterogeneous multiscale simulations of suspension flow. Multiscale Model Simul 9:1301–1326

  23. Malaspinas O, Turjman A, de Souza DR, Garcia-Cardena G, Raes M, Nguyen PTT, Zhang Y, Courbebaisse G, Lelubre C, Boudjelti KZ, Chopard B (2016) A spatio-temporal model for spontaneous thrombus formation in cerebral aneurysms. J Theor Biol 394:68–76

    Article  MATH  Google Scholar 

  24. Merks RMH, Hoekstra AG, Kaandorp JA, Sloot PMA (2003) Models of coral growth: spontaneous branching, compactification and the laplacian growth assumption. J Theor Biol 224:153–166

    MathSciNet  Article  Google Scholar 

  25. Nikishovay A, Hoekstra A (2017) Semi-intrusive uncertainty quantification for multiscale models. SIAM J. Uncertain Quantif

  26. Piontek T, Bosak B, Cinicki M, Grabowski P, Kopta P, Kulczewski M, Szejnfeld D, Kurowski K (2016) Development of science gateways using qcglessons learned from the deployment on large scale distributed and hpc infrastructures. J Grid Comput 14:559–573

  27. Tahir H, Hoekstra A, Lorenz E, Lawford P, Hose D, Gunn J, Evans D (2011) Multiscale simulations of the dynamics of in-stent restenosis: impact of stent deployment and design. Interface Focus 1:365–367

    Article  Google Scholar 

  28. Tahir H, Casas CB, Hoekstra A (2013) Modelling the effect of a functional endothelium on the development of in-stent restenosis. PLoS ONE 8(e66):138

  29. Weinan E, Li X, Ren W, Vanden-Eijnden E (2007) Heterogeneous multiscale methods. A review. Commun Comput Phys 2:367–450

  30. Yang A, Marquardt W (2009) An ontological conceptualizatin of multiscale models. Comput. Chem. Eng. 33:822–837

    Article  Google Scholar 

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Acknowledgements

The authors acknowledge financial support from the Swiss Initiative PASC, from CADMOS, and from the COMPAT EU Project. BC, JLF, and PK thank Constanza Bonadonna for the collaboration on the model for volcanic ashes. BC thanks Alireza Yasdani for stimulating discussions on the amplification scale bridging techniques. On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Correspondence to Bastien Chopard.

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Chopard, B., Falcone, JL., Kunzli, P. et al. Multiscale modeling: recent progress and open questions. Multiscale and Multidiscip. Model. Exp. and Des. 1, 57–68 (2018). https://doi.org/10.1007/s41939-017-0006-4

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Keywords

  • Mutiscale modeling
  • High Perfomance multiscale computing
  • Theoretical framework
  • Coupling middleware (MUSCLE)
  • Scale bridging techniques