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Multiscale Modeling Meets Machine Learning: What Can We Learn?

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Abstract

Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate applications in diagnostics including electrophysiology, radiology, or pathology, where we have access to massive amounts of annotated data. However, machine learning often performs poorly in prognosis, especially when dealing with sparse data. This is a field where classical physics-based simulation seems to remain irreplaceable. In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data; multiscale modeling can integrate machine learning to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. With a view towards applications in the life sciences, we discuss the state of the art of combining machine learning and multiscale modeling, identify applications and opportunities, raise open questions, and address potential challenges and limitations. We anticipate that it will stimulate discussion within the community of computational mechanics and reach out to other disciplines including mathematics, statistics, computer science, artificial intelligence, biomedicine, systems biology, and precision medicine to join forces towards creating robust and efficient models for biological systems.

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References

  1. Ahmed OJ, Sudhakar SK (2019) High frequency activity during stereotyped low frequency events might help to identify the seizure onset zone. Epilepsy Curr 19(3):184–186

    Google Scholar 

  2. Ahmed OJ, John TT (2019) A straw can break a neural network’s back and lead to seizures but only when delivered at the right time. Epilepsy Currents 19(2):115–116

    Google Scholar 

  3. Alber M, Buganza Tepole A, Cannon W, De S, Dura-Bernal S, Garikipati K, Karniadakis G, Lytton WW, Perdikaris P, Petzold L, Kuhl E (2019) Integrating machine learning and multiscale modeling: perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences. NPJ Digit Med 2:115

    Google Scholar 

  4. Ambrosi D, Ateshian GA, Arruda EM, Cowin SC, Dumais J, Goriely A, Holzapfel GA, Humphrey JD, Kemkemer R, Kuhl E, Olberding JE, Taber LA, Garikipati K (2011) Perspectives on biological growth and remodeling. J Mech Phys Solids 59:863–883

    MathSciNet  MATH  Google Scholar 

  5. Ambrosi D, BenAmar M, Cyron CJ, DeSimone A, Goriely A, Humphrey JD, Kuhl E (2019) Growth and remodelling of living tissues: perspectives, challenges, and opportunities. J R Soc Interface 16:20190233

    Google Scholar 

  6. Anderson B, Hy TS, Kondor R (2019) ArXiv preprint arXiv:1906.04015

  7. Athreya AP, Neavin D, Carrillo-Roa T, Skime M, Biernacka J, Frye MA, Rush AJ, Wang L, Binder EB, Iyer RK, Weinshilboum RM, Bobo WV (2019) Pharmacogenomics-driven prediction of antidepressant treatment outcomes: a machine learning approach with multi-trial replication. Clin Pharmacol Thera 106:855–865. https://doi.org/10.1002/cpt.1482

    Article  Google Scholar 

  8. Baillargeon B, Rebelo N, Fox DD, Taylor RL, Kuhl E (2014) The living heart project: a robust and integrative simulator for human heart function. Eur J Mech A/Solids 48:38–47

    MathSciNet  MATH  Google Scholar 

  9. Baydin AG, Pearlmutter BA, Radul AA, Siskind JM (2018) Automatic differentiation in machine learning: a survey. J Mach Learn Res 18:153

    MathSciNet  MATH  Google Scholar 

  10. Bennett BD, Kimball EH, Gao M, Osterhout R, Van Dien SJ, Rabinowitz JD (2009) Absolute metabolite concentrations and implied enzyme active site occupancy in Escherichia coli. Nat Chem Biol 5(8):593–539

    Google Scholar 

  11. Booth V, Xique IJ, Diniz Behn CG (2017) One-dimensional map for the circadian modulation of sleep in a sleep-wake regulatory network model for human sleep. SIAM J Appl Dyn Syst 16:1089–1112

    MathSciNet  MATH  Google Scholar 

  12. Botvinick M, Ritter S, Wang JX, Kurth-Nelson Z, Blundell C, Hassabis D (2019) Reinforcement learning, fast and slow. Trends Cognit Sci 23:408–422

    Google Scholar 

  13. Brunton SL, Proctor JL, Kutz JN (2016) Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc Natl Acad Sci 113:3932–3937

    MathSciNet  MATH  Google Scholar 

  14. Bruynseels K, Santoni de Sio F, van den Hoven J (2018) Digital Twins in health care: ethical implications of an emerging engineering paradigm. Front Genet 9:31

    Google Scholar 

  15. Buehler MJ (2006) Atomistic and continuum modeling of mechanical properties of collagen: elasticity, fracture, and self-assembly. J Mater Res 21:19471961

    Google Scholar 

  16. Carlson KD, Nageswaran JM, Dutt N, Krichmar JL (2014) An efficient automated parameter tuning framework for spiking neural networks. Front Neurosci 8(10):00010

    Google Scholar 

  17. Cao YH, Eisenberg MC (2018) Practical unidentifiability of a simple vector-borne disease model: implications for parameter estimation and intervention assessment. Epidemics 25:89–100

    Google Scholar 

  18. Chabiniok R, Wang V, Hadjicharalambous M, Asner L, Lee J, Sermesant M, Kuhl E, Young A, Moireau P, Nash M, Chapelle D, Nordsletten DA (2016) Multiphysics and multiscale modeling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics. Interface Focus 6:20150083

    Google Scholar 

  19. Champion KP, Brunton SL, Kutz JN (2019) Discovery of nonlinear multiscale systems: sampling strategies and embeddings. SIAM J Appl Dyn Syst 18:312–333

    MathSciNet  MATH  Google Scholar 

  20. Chandran PL, Barocas VH (2007) Deterministic material-based averaging theory model of collagen gel micromechanics. J Biomech Eng 129:137147

    Google Scholar 

  21. Chen TQ, Rubanova Y, Bettencourt J, Duvenaud DK (2018) Neural ordinary differential equations. In: Advances in neural information processing systems, pp 6571–6583

  22. Conti S, Müller S, Ortiz M (2018) Data-driven problems in elasticity. Arch Ration Mech Anal 229:79–123

    MathSciNet  MATH  Google Scholar 

  23. Costello Z, Martin HG (2018) A machine learning approach to predict metabolic pathway dynamics from time-series multiomics data. NPJ Syst Biol Appl 4:19

    Google Scholar 

  24. Cuperlovic-Culf M (2018) Machine learning methods for analysis of metabolic data and metabolic pathway modeling. Metabolites 8:4

    Google Scholar 

  25. De S, Wongmuk H, Kuhl E (eds) (2014) Multiscale modeling in biomechanics and mechanobiology. Springer, Berlin

    MATH  Google Scholar 

  26. Deist TM, Patti A, Wang Z, Krane D, Sorenson T, Craft D (2019) Simulation assisted machine learning. Bioinformatics 35:4072–4080. https://doi.org/10.1093/bioinformatics/btz199

    Article  Google Scholar 

  27. Deo RC (2015) Machine learning in medicine. Circulation 132:1920–1930

    Google Scholar 

  28. DeWoskin D, Myung J, Belle MD, Piggins HD, Takumi T, Forger DB (2015) Distinct roles for GABA across multiple timescales in mammalian circadian timekeeping. Proc Natl Acad Sci 112:E2911

    Google Scholar 

  29. Dura-Bernal S, Neymotin SA, Kerr CC, Sivagnanam S, Majumdar A, Francis JT, Lytton WW (2017) Evolutionary algorithm optimization of biological learning parameters in a biomimetic neuroprosthesis. IBM J Res Dev 61(6):114

    Google Scholar 

  30. Dura-Bernal S, Suter BA, Gleeson P, Cantarelli M, Quintana A, Rodriguez F, Lytton WW (2019) NetPyNE, a tool for data-driven multiscale modeling of brain circuits. Elife 8:e44494. https://doi.org/10.7554/eLife.44494.001

    Article  Google Scholar 

  31. Esteva A, Kuprel B, Novoa RA, Ko J, Swetter SM, Blau HM, Thrun S (2017) Dermatologist-level classification of skin cancer with deep neural networks. Nature 542:115–118

    Google Scholar 

  32. Fritzen F, Hodapp M (2016) The finite element square reduced (FE2R) method with GPU acceleration: towards three-dimensional two-scale simulations. Int J Numer Methods Eng 107:853881

    MATH  Google Scholar 

  33. Geers MGD, Kouznetsova VG, Brekelmans WAM (2010) Multi-scale computational homogenization: trends and challenges. J Comput Appl Math 234:21752182

    MATH  Google Scholar 

  34. Gerlee P, Kim E, Anderson ARA (2015) Bridging scales in cancer progression: mapping genotype to phenotype using neural networks. Semin Cancer Biol 30:3041

    Google Scholar 

  35. Gillespie DT (2007) Stochastic simulation of chemical kinetics. Ann Rev Phys Chem 58:3555

    Google Scholar 

  36. Hagge T, Stinis P, Yeung E, Tartakovsky AM (2017) Solving differential equations with unknown constitutive relations as recurrent neural networks. arXiv:1710.02242

  37. Han J, Jentzen A, Weinan E (2018) Solving high-dimensional partial differential equations using deep learning. Proc Natl Acad Sci 115(34):8505–8510

    MathSciNet  MATH  Google Scholar 

  38. Hannun AY, Rajpurkar P, Haghpanahi M, Tison GH, Bourn C, Turakhia MP, Ng AY (2019) Cardiologist-level arrhythmia detection and classification in ambulatory electrocardiograms using a deep neural network. Nat Med 25:65–69

    Google Scholar 

  39. Hassabis D, Kumaran D, Summerfield C, Botvinick M (2017) Neuroscience-inspired artificial intelligence. Neuron 95(2):245258

    Google Scholar 

  40. Hicks JL, Althoff T, Sosic R, Kuhar P, Bostjancic B, King AC, Leskovec J, Delp SL (2019) Best practices for analyzing large-scale health data from wearables and smartphone apps. NPJ Digit Med 2:45

    Google Scholar 

  41. Huan X, Marzouk YM (2013) Simulation-based optimal experimental design for nonlinear systems. J Comput Phys 232:288–317

    MathSciNet  Google Scholar 

  42. Hunt CA, Erdemir A, Lytton WW, Mac Gabhann F, Sander EA, Transtrum MK, Mulugeta L (2018) The spectrum of mechanism-oriented models and methods for explanations of biological phenomena. Processes 6(5):56

    Google Scholar 

  43. Hunter PJ, Borg TK (2003) Integration from proteins to organs: the physiome project. Processes 4:237–243

    Google Scholar 

  44. Kennedy M, O’Hagan A (2001) Bayesian calibration of computer models (with discussion). J Roy Stat Soc B 63:425–464

    MATH  Google Scholar 

  45. Kim R, Li Y, Sejnowski TJ (2019) Simple framework for constructing functional spiking recurrent neural networks. Proc Natl Acad Sci 116:22811–22820. https://doi.org/10.1101/579706

    Article  Google Scholar 

  46. Kissas G, Yang Y, Hwuang E, Witschey WR, Detre JA, Perdikaris P (2019) Machine learning in cardiovascular flows modeling: predicting pulse wave propagation from non-invasive clinical measurements using physics-informed deep learning. ArXiv preprint arXiv:1905.04817

  47. Kitano H (2002) Systems biology: a brief overview. Science 295:16621664

    Google Scholar 

  48. Kouznetsova V, Brekelmans WAM, Baaijens FPT (2001) Approach to micro-macro modeling of heterogeneous materials. Comput Mech 27:3748

    MATH  Google Scholar 

  49. Kouznetsova VG, Geers MGD, Brekelmans WAM (2004) Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy. Comput Methods Appl Mech Eng 193:55255550

    MATH  Google Scholar 

  50. Lange V, Picotti P, Domon B, Aebersold R (2008) Selected reaction monitoring for quantitative proteomics: a tutorial. Mol Syst Biol 4:222

    Google Scholar 

  51. Le BA, Yvonnet J, He QC (2015) Computational homogenization of nonlinear elastic materials using neural networks. Int J Numer Methods Eng 104:10611084

    MathSciNet  MATH  Google Scholar 

  52. Leal LG, David A, Jarvelin M-R, Sebert S, Ruddock M, Karhunen V, Sternberg MJE (2019) Identification of disease-associated loci using machine learning for genotype and network data integration. Bioinformatics 35:5182–5190. https://doi.org/10.1093/bioinformatics/btz310

    Article  Google Scholar 

  53. Leary SJ, Bhaskar A, Keane AJ (2003) A knowledge-based approach to response surface modelling in multifidelity optimization. J Glob Optim 26(3):297319

    MathSciNet  MATH  Google Scholar 

  54. LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521:436–444

    Google Scholar 

  55. Lee T, Turin SY, Gosain AK, Bilionis I, Buganza Tepole A (2018) Propagation of material behavior uncertainty in a nonlinear finite element model of reconstructive surgery. Biomech Model Mechanobiol 17(6):1857–18731

    Google Scholar 

  56. Lee T, Gosain AK, Bilionis I, Buganza Tepole A (2019) Predicting the effect of aging and defect size on the stress profiles of skin from advancement, rotation and transposition flap surgeries. J Mech Phys Solids 125:572590

    MathSciNet  Google Scholar 

  57. Lee T, Bilionis I, Buganza Tepole A (2020) Propagation of uncertainty in the mechanical and biological response of growing tissues using multi-fidelity Gaussian process regression. Comput Methods Appl Mech Eng 359:112724

    MathSciNet  MATH  Google Scholar 

  58. Liang G, Chandrashekhara K (2008) Neural network based constitutive model for elastomeric foams. Eng Struct 30:20022011

    Google Scholar 

  59. Lin C-L, Choi S, Haghighi B, Choi J, Hoffman EA (2018) Cluster-guided multiscale lung modeling via machine learning. In: Handbook of materials modeling, vol 120. https://doi.org/10.1007/978-3-319-50257-1_98-1

  60. Liu Y, Zhang L, Yang Y, Zhou L, Ren L, Liu R, Pang Z, Deen MJ (2019) A novel cloud-based framework for the elderly healthcare services using Digital Twin. IEEE Access 7:49088–49101

    Google Scholar 

  61. Liu Z, Wu CT, Koishi M (2019) A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials. Comput Methods Appl Mech Eng 345:11381168

    MathSciNet  MATH  Google Scholar 

  62. Lu W, Su X, Klein MS, Lewis IA, Fiehn O, Rabinowitz JD (2017) Metabolite measurement: pitfalls to avoid and practices to follow. Ann Rev Biochem 86:277–304

    Google Scholar 

  63. Luebberding S, Krueger N, Kerscher M (2014) Mechanical properties of human skin in vivo: a comparative evaluation in 300 men and women. Skin Res Technol 20:127135

    Google Scholar 

  64. Lytton WW, Arle J, Bobashev G, Ji S, Klassen TL, Marmarelis VZ, Sanger TD (2017) Multiscale modeling in the clinic: diseases of the brain and nervous system. Brain Inform 4(4):219230

    Google Scholar 

  65. Lytton WW (2017) Computers, causality and cure in epilepsy. Brain 140(3):516–526

    Google Scholar 

  66. Madireddy S, Sista B, Vemaganti K (2015) A Bayesian approach to selecting hyperelastic constitutive models of soft tissue. Comput Methods Appl Mech Eng 291:102122

    MathSciNet  MATH  Google Scholar 

  67. Madni AM, Madni CC, Lucerno SD (2019) Leveraging Digital Twin technology in model-based systems enginereering. Systems 7:1–13

    Google Scholar 

  68. Mangan NM, Brunton SL, Proctor JL, Kutz JN (2016) Inferring biological networks by sparse identification of nonlinear dynamics. IEEE Trans Mol Biol Multi-Scale Commun 2:52–63

    Google Scholar 

  69. Mangan NM, Askham T, Brunton SL, Kutz NN, Proctor JL (2019) Model selection for hybrid dynamical systems via sparse regression. Proceedings R Soc A Math Phys Eng Sci 475:20180534

    MathSciNet  MATH  Google Scholar 

  70. Marino M, Vairo G (2012) Stress and strain localization in stretched collagenous tissues via a multiscale modelling approach. Comput Methods Biomech Biomed Eng 17:1130

    Google Scholar 

  71. McCammon JA, Gelin BR, Karplus M (1977) Dynamics of folded proteins. Nature 267:585–590

    Google Scholar 

  72. Mihai LA, Woolley TE, Goriely A (2018) Stochastic isotropic hyperelastic materials: constitutive calibration and model selection. Proc R Soc A/Math Phys Eng Sci 474:0858

    MathSciNet  MATH  Google Scholar 

  73. Myung J, Hong S, DeWoskin D, De Schutter E, Forger DB, Takumi T (2015) GABA-mediated repulsive coupling between circadian clock neurons encodes seasonal time. Proc Natl Acad Sci 112:E2920

    Google Scholar 

  74. Nazari F, Pearson AT, Nor JE, Jackson TL (2018) A mathematical model for IL-6-mediated, stem cell driven tumor growth and targeted treatment. PLOS Comput Biol 14:e1005920. https://doi.org/10.1371/journal.pcbi.1005920

    Article  Google Scholar 

  75. Neftci EO, Averbeck BB (2019) Reinforcement learning in artificial and biological systems. Nat Mach Intell 1:133–143

    Google Scholar 

  76. Neymotin SA, Dura-Bernal S, Moreno H, Lytton WW (2016) Computer modeling for pharmacological treatments for dystonia. Drug Discov Today Disease Models 19:5157

    Google Scholar 

  77. Neymotin SA, Suter BA, Dura-Bernal S, Shepherd GMG, Migliore M, Lytton WW (2016) Optimizing computer models of corticospinal neurons to replicate in vitro dynamics. J Neurophysiol 117:148–162

    Google Scholar 

  78. Nguyen A, Yosinski J, Clune J (2015) Deep neural networks are easily fooled: high confidence predictions for unrecognizable images. In: 2015 IEEE conference on computer vision and pattern recognition

  79. Ognjanovski N, Broussard C, Zochowski M, Aton SJ (2018) Hippocampal network oscillations drive memory consolidation in the absence of sleep. Cereb Cortex 28(10):1–13

    Google Scholar 

  80. Park JO, Rubin SA, Amador-Noguz D, Fan J, Shlomi T, Rabinowitz JD (2016) Metabolite concentrations, fluxes and free energies imply efficient enzyme usage. Nat Chem Biol 12(7):482–489

    Google Scholar 

  81. Peirlinck M, Sahli Costabal F, Sack KL, Choy JS, Kassab GS, Guccione JM, De Beule M, Segers P, Kuhl E (2019) Using machine learning to characterize heart failure across the scales. Biomech Model Mechanobiol 18:1987–2001. https://doi.org/10.1007/s10237-019-01190-w

    Article  Google Scholar 

  82. Peng GCY (2016) Moving toward model reproducibility and reusability. IEEE Trans Biomed Eng 63:1997–1998

    Google Scholar 

  83. Perdikaris P, Karniadakis GE (2016) Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond. J R Soc Interface 13(118):20151107

    Google Scholar 

  84. Perdikaris P, Raissi M, Damianou A, Lawrence ND, Karniadakis GE (2016) Nonlinear information fusion algorithms for robust multi-fidelity modeling. Proc R Soc A/Math Phys Eng Sci 473:0751

    Google Scholar 

  85. Poggio T, Mhaskar H, Rosasco L, Miranda B, Liao Q (2017) Why and when can deep-but not shallow-networks avoid the curse of dimensionality: a review. Int J Autom Comput 14:503–519

    Google Scholar 

  86. Proix T, Bartolomei F, Guye M, Jirsa VK (2017) Individual brain structure and modeling predict seizure propagation. Brain 140:651–654

    Google Scholar 

  87. Puentes-Mestril C, Roach J, Niethard N, Zochowski M, Aton SJ (2019) How rhythms of the sleeping brain tune memory and synaptic plasticity. Sleep zsz42:095. https://doi.org/10.1093/sleep/zsz095

    Article  Google Scholar 

  88. Quade M, Abel M, Kutz JN, Brunton SL (2018) Sparse identification of nonlinear dynamics for rapid model recovery. Chaos 28:063116

    MathSciNet  Google Scholar 

  89. Raina A, Linder C (2014) A homogenization approach for nonwoven materials based on fiber undulations and reorientation. J Mech Phys Solids 65:1234

    MathSciNet  Google Scholar 

  90. Raissi M, Perdikaris P, Karniadakis GE (2017) Inferring solutions of differential equations using noisy multi-fidelity data. J Comput Phys 335:736746

    MathSciNet  MATH  Google Scholar 

  91. Raissi M, Perdikaris P, Karniadakis GE (2017) Machine learning of linear differential equations using Gaussian processes. J Comput Phys 348:683–693

    MathSciNet  MATH  Google Scholar 

  92. Raissi M, Perdikaris P, Karniadakis GE (2017) Physics informed deep learning (Part I): data-driven solutions of nonlinear partial differential equations. ArXiv preprint arXiv:171110561

  93. Raissi M, Perdikaris P, Karniadakis GE (2017) Physics informed deep learning (Part II): data-driven discovery of nonlinear partial differential equations. ArXiv preprint arXiv:171110566

  94. Raissi M, Karniadakis GE (2018) Hidden physics models: machine learning of nonlinear partial differential equations. J Comput Phys 357:125–141

    MathSciNet  MATH  Google Scholar 

  95. Raissi M, Yazdani A, Karniadakis GE (2018) Hidden fluid mechanics: a Navier-Stokes informed deep learning framework for assimilating flow visualization data. ArXiv preprint arXiv:1808.04327

  96. Raissi M, Perdikaris P, Karniadakis GE (2019) Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys 378:686707

    MathSciNet  MATH  Google Scholar 

  97. Rhodes SJ, Knight GM, Kirschner DE, White RG, Evans TG (2019) Dose finding for new vaccines: the role for immunostimulation/immunodynamic modelling. J Theor Biol 465:51–55

    Google Scholar 

  98. Riley P (2019) Three pitfalls to avoid in machine learning. Nature 572:27–28

    Google Scholar 

  99. Rubanova Y, Chen RTQ, Duvenaud D (2019) Latent odes for irregularly-sampled time series. ArXiv preprint arXiv:1907.03907

  100. Rudy SH, Brunton SL, Proctor JL, Kutz JN (2017) Data-driven discovery of partial differential equations. Sci Adv 3(4):e1602614

    Google Scholar 

  101. Sahli Costabal F, Choy JS, Sack KL, Guccione JM, Kassab GS, Kuhl E (2019) Multiscale characterization of heart failure. Acta Biomater 86:66–76

    Google Scholar 

  102. Sahli Costabal F, Matsuno K, Yao J, Perdikaris P, Kuhl E (2019) Machine learning in drug development: characterizing the effect of 30 drugs on the QT interval using Gaussian process regression, sensitivity analysis, and uncertainty quantification. Comput Methods Appl Mech Eng 348:313–333

    MathSciNet  MATH  Google Scholar 

  103. Sahli Costabal F, Perdikaris P, Kuhl E, Hurtado DE (2019) Multi-fidelity classification using Gaussian processes: accelerating the prediction of large-scale computational models. Comput Methods Appl Mech Eng 357:112602

    MathSciNet  MATH  Google Scholar 

  104. Sahli Costabal F, Seo K, Ashley E, Kuhl E (2020) Classifying drugs by their arrhythmogenic risk using machine learning. Biophys J 118:1–12

    Google Scholar 

  105. Sahli Costabal F, Yang Y, Perdikaris P, Hurtado DE, Kuhl E (2020) Physics-informed neural networks for cardiac activation mapping. Front Phys. https://doi.org/10.3389/fphy.2020.00042

    Article  Google Scholar 

  106. Sanchez-Lengeling B, Aspuru-Guzik A (2018) Inverse molecular design using machine learning: generative models for matter engineering. Science 361:360–365

    Google Scholar 

  107. Sander EA, Stylianopoulos T, Tranquillo RT, Barocas VH (2009) Image-based multiscale modeling predicts tissue-level and network-level fiber reorganization in stretched cell-compacted collagen gels. Proc Natl Acad Sci 106:1767517680

    Google Scholar 

  108. Sankaran S, Moghadam ME, Kahn AM, Tseng EE, Guccione JM, Marsden AL (2012) Patient-specific multiscale modeling of blood flow for coronary artery bypass graft surgery. Ann Biomed Eng 40(10):2228–2242

    Google Scholar 

  109. Schoeberl B, Eichler-Jonsson C, Gilles ED, Mller G (2002) Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. Nat Biotechnol 20:370375

    Google Scholar 

  110. Shaked I, Oberhardt MA, Atias N, Sharan R, Ruppin E (2018) Metabolic network prediction of drug side effects. Cell Systems 2:209213

    Google Scholar 

  111. Shenoy VB, Miller RE, Tadmor EB, Rodney D, Phillips R, Ortiz M (1999) An adaptive finite element approach to atomic scale mechanics-the quasicontinuum method. J Mech Phys Solids 47:611642

    MathSciNet  MATH  Google Scholar 

  112. Snowden TJ, van der Graaf PH, Tindall MJ (2017) Methods of model reduction for large-scale biological systems: a survey of current methods and trends. Bull Math Biol 79(7):14491486

    MathSciNet  MATH  Google Scholar 

  113. Song D, Hugenberg N, Oberai AA (2019) Three-dimensional traction microscopy with a fiber-based constitutive model. Comput Methods Appl Mech Eng 357:112579

    MathSciNet  MATH  Google Scholar 

  114. Southern J, Pitt-Francis J, Whiteley J, Stokeley D, Kobashi H, Nobes R, Kadooka Y, Gavaghan D (2008) Multi-scale computational modelling in biology and physiology. Prog Biophys Mol Biol 96:6089

    Google Scholar 

  115. Stelling J, Gilles ED (2004) Mathematical modeling of complex regulatory networks. NanoBioscience, IEEE Transactions 3:172179

    Google Scholar 

  116. Szegedy C, Zaremba W, Sutskever I, Bruna J, Erhan D, Goodfellow I, Fergus R (2013) Intriguing properties of neural networks. ArXiv preprint arXiv:1312.6199

  117. Tank A, Covert I, Foti N, Shojaie A, Fox E (2018) Neural Granger causality for nonlinear time series. arXiv:1802.05842

  118. Tartakovsky AM, Marrero CO, Perdikaris P, Tartakovsky GD, Barajas-Solano D (2018) Learning Parameters and constitutive relationships with physics informed deep neural networks. arXiv:1808.03398

  119. Tartakovsky G, Tartakovsky AM, Perdikaris P (2018) Physics informed deep neural networks for learning parameters with non-Gaussian non-stationary statistics. arXiv:2018agufm.h21j1791t

  120. Taylor CA, Figueroa CA (2009) Patient-specific modeling of cardiovascular mechanics. Annu Rev Biomed Eng 11:109134

    Google Scholar 

  121. Teichert G, Garikipati K (2019) Machine learning materials physics: surrogate optimization and multi-fidelity algorithms predict precipitate morphology in an alternative to phase field dynamics. Comput Methods Appl Mech Eng 344:666–693

    MathSciNet  MATH  Google Scholar 

  122. Teichert GH, Natarajan AR, Van der Ven A, Garikipati K (2019) Machine learning materials physics: integrable deep neural networks enable scale bridging by learning free energy functions. Comput Methods Appl Mech Eng 353:201–216

    MathSciNet  MATH  Google Scholar 

  123. Topol EJ (2019) Deep medicine: how artificial intelligence can make healthcare human again. Hachette Book Group, New York

    Google Scholar 

  124. Topol EJ (2019) High-performance medicine: the convergence of human and artificial intelligence. Nat Med 25:44–56

    Google Scholar 

  125. Topol EJ (2019) Deep learning detects impending organ injury. Nature 572:36–37

    Google Scholar 

  126. Tran JS, Schiavazzi DE, Kahn AM, Marsden AL (2019) Uncertainty quantification of simulated biomechanical simuli in coronary artery bypass grafts. Comput Methods Appl Mech Eng 345:402–428

    MATH  Google Scholar 

  127. Tremblay J, Prakash A, Acuna D, Brophy M, Jampani V, Anil C, Birchfield S (2018) Training deep networks with synthetic data: bridging the reality gap by domain randomization. arXiv:1804.06516

  128. Vu MAT, Adali T, Ba D, Buzsaki G, Carlson D, Heller K, Dzirasa K (2018) A shared vision for machine learning in neuroscience. J Neurosci 38(7):16011607

    Google Scholar 

  129. Wagner GJ, Liu WK (2003) Coupling of atomistic and continuum simulations using a bridging scale decomposition. J Comput Phys 190:249274

    Google Scholar 

  130. Wang Z, Huan X, Garikipati K (2019) Variational system identification of the partial differential equations governing the physics of pattern-formation: inference under varying fidelity and noise. Comput Methods Appl Mech Eng 356:44–74

    MathSciNet  MATH  Google Scholar 

  131. Warshel A, Levitt M (1976) Theoretical studies of enzymic reactions–dielectric, electrostatic and steric stabilization of carbonium-ion in reaction of lysozyme. J Mol Biol 103:227–249

    Google Scholar 

  132. Weickenmeier J, Kuhl E, Goriely A (2018) The multiphysics of prion-like diseases: progression and atrophy. Phys Rev Lett 121:158101

    Google Scholar 

  133. Weickenmeier J, Jucker M, Goriely A, Kuhl E (2019) A physics-based model explains the prion-like features of neurodegeneration in Alzheimers disease, Parkinsons disease, and amyotrophic lateral sclerosis. J Mech Phys Solids 124:264–281

    Google Scholar 

  134. Weinan E, Han J, Jentzen A (2017) Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Commun Math Stat 5(4):349–380

    MathSciNet  MATH  Google Scholar 

  135. Weinan E, Yu B (2018) The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems. Commun Math Stat 6(1):1–12

    MathSciNet  MATH  Google Scholar 

  136. White R, Peng G, Demir S (2009) Multiscale modeling of biomedical, biological, and behavioral systems. IEEE Eng Med 28:12–13

    Google Scholar 

  137. Wiechert W (2001) 13C metabolic flux analysis. Metab Eng 2:195–206

    Google Scholar 

  138. Wiering M, van Otterlo M (2013) Reinforcement learning and Markov decision processes. In: Reinforcement learning, pp 3–39

  139. Wolters DA, Washburn MP, Yates JR III (2001) An automated multidimensional protein identification technology for shotgun proteomics. Anal Chem 73(23):5683–5090

    Google Scholar 

  140. Yang L, Zhang D, Karniadakis GE (2018) Physics-informed generative adversarial networks for. arXiv:181102033 [StatML]

  141. Yang Y, Perdikaris P (2019) Adversarial uncertainty quantification in physics-informed neural networks. J Comput Phys 394:136–152

    MathSciNet  MATH  Google Scholar 

  142. Zangooei MH, Habibi J (2017) Hybrid multiscale modeling and prediction of cancer cell behavior. PLoS ONE 12(8):e0183810

    Google Scholar 

  143. Zhao L, Li Z, Caswell B, Ouyang J, Karniadakis GE (2018) Active learning of constitutive relation from mesoscopic dynamics for macroscopic modeling of non-Newtonian flows. J Comput Phys 363:116–127

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors acknowledge support of the National Institutes of Health Grants U01 HL116330 (Alber), R01 AR074525 (Buganza Tepole), U01 EB022546 (Cannon), R01 CA197491 (De), U24 EB028998 (Dura-Bernal), U01 HL116323 and U01 HL142518 (Karniadakis), U01 EB017695 (Lytton), R01 EB014877 (Petzold) and U01 HL119578 (Kuhl), as well as DARPA Grant HR0011199002 and Toyota Research Institute Grant 849910, (both Garikipati). This work was inspired by the 2019 Symposium on Integrating Machine Learning with Multiscale Modeling for Biological, Biomedical, and Behavioral Systems (ML-MSM) as part of the Interagency Modeling and Analysis Group (IMAG), and is endorsed by the Multiscale Modeling (MSM) Consortium, by the U.S. Association for Computational Mechanics (USACM) Technical Trust Area Biological Systems, and by the U.S. National Committee on Biomechanics (USNCB). The authors acknowledge the active discussions within these communities.

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Authors and Affiliations

  1. National Institutes of Health, Bethesda, MD, USA

    Grace C. Y. Peng

  2. University of California, Riverside, USA

    Mark Alber

  3. Purdue University, Lafayette, IN, USA

    Adrian Buganza Tepole

  4. Pacific Northwest National Laboratory, Richland, WA, USA

    William R. Cannon

  5. Rensselaer Polytechnic Institute, Troy, NY, USA

    Suvranu De

  6. State University of New York, New York, USA

    Savador Dura-Bernal & William W. Lytton

  7. University of Michigan, Ann Arbor, MI, USA

    Krishna Garikipati

  8. Brown University, Providence, RI, USA

    George Karniadakis

  9. University of Pennsylvania, Philadelphia, PA, USA

    Paris Perdikaris

  10. University of California, Santa Barbara, CA, USA

    Linda Petzold

  11. Stanford University, Stanford, CA, USA

    Ellen Kuhl

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  1. Grace C. Y. Peng
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Correspondence to Ellen Kuhl.

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Peng, G.C.Y., Alber, M., Buganza Tepole, A. et al. Multiscale Modeling Meets Machine Learning: What Can We Learn?. Arch Computat Methods Eng 28, 1017–1037 (2021). https://doi.org/10.1007/s11831-020-09405-5

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