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Inverse design of self-oscillatory gels through deep learning

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Abstract

We develop a deep learning architecture for inverse design of a self-oscillating sheet propelled by an embedded chemical reaction. The dynamics of our problems are nonlinear and exhibit chaotic behavior, a challenging setting for existing deep-learning-based inverse design approaches. The aim is to explore data-driven design of soft robots using a novel locomotion mechanism. We train the architecture using a forward model of the locomotion mechanism developed recently by Alben et al. (J Comput Phys 399:108952, 2019). The architecture is shown to successfully map a snapshot of target motions of the gel into geometric and reaction parameters. The final architecture consists of a multi-layer perceptron (MLP) classifier for discrete parameters, followed by a stacked MLP regressor (SMLPR) for continuous parameters. Our inverse design setting is unique in that it considers both discrete and continuous outputs, requiring an architecture capable of classification and regression. We are able to recover parameters within 2.87% accuracy. We also compare the simulated motion of the sheets at the recovered parameters. Because the motion has a chaotic quality, our demonstration is able to show quantitative agreement for a small time horizon and qualitative agreement over longer time horizons. We also demonstrate agreement of Lyapunov exponents up to 6.78% accuracy for suitable motions.

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Data availability

All the trained networks in this paper along with the python and MATLAB scripts responsible for creating them can be found in the Bitbucket repository bitbucket.org/dorukaks/workspace/projects/CGL.

Notes

  1. Source: www.nvidia.com/content/dam/en-zz/Solutions/design-visualization/quadro-product-literature/301968-DS-NV-Quadro-Pascal-P1000-US-03Feb17-NV-fnl-WEB.pdf.

  2. Source: www.geforce.com/hardware/desktop-gpus/geforce-gtx-1050-ti/specifications.

  3. February 20, 2020.

  4. https://bitbucket.org/dorukaks/workspace/projects/CGL.

  5. The files are named as set[setnumber]_[actual/predicted] _[300/20]s.gif.

  6. Alan Wolf (2021). Wolf Lyapunov exponent estimation from a time series. (https://www.mathworks.com/matlabcentral/fileexchange/48084-wolf-lyapunov-exponent-estimation-from-a-time-series), MATLAB Central File Exchange. Retrieved December 22, 2020.

References

  1. Takeuchi Y, Asakawa N, Ge D (1993) Automation of polishing work by an industrial robot: system of polishing robot. JSME Int J Ser C Dyn Control Robot Des Manuf 36(4):556–561

    Google Scholar 

  2. Lenz C, Nair S, Rickert M, Knoll A, Rosel W, Gast J, Bannat A, Wallhoff F (2008) Joint-action for humans and industrial robots for assembly tasks. In: RO-MAN 2008—the 17th IEEE international symposium on robot and human interactive communication. IEEE, pp 130–135

  3. Zhou J, Chen S, Wang Z (2017) A soft-robotic gripper with enhanced object adaptation and grasping reliability. IEEE Robot Autom Lett 2:2287–2293

    Article  Google Scholar 

  4. Haddadin S, Croft E (2016) Physical human–robot interaction. Springer, Cham, pp 1835–1874

    Google Scholar 

  5. Cianchetti M, Ranzani T, Gerboni G, Nanayakkara T, Althoefer K, Dasgupta P, Menciassi A (2014) Soft robotics technologies to address shortcomings in today’s minimally invasive surgery: the STIFF-FLOP approach. Soft Robot 1(2):122–131

    Article  Google Scholar 

  6. Katzschmann RK, DelPreto J, MacCurdy R, Rus D (2018) Exploration of underwater life with an acoustically controlled soft robotic fish. Sci Robot 3(16):eaar3449

    Article  Google Scholar 

  7. Delph MA, Fischer SA, Gauthier PW, Luna CH, Clancy EA, Fischer GS (2013) A soft robotic exomusculature glove with integrated sEMG sensing for hand rehabilitation. In: IEEE international conference on rehabilitation robotics, pp 1–7

  8. Copaci D, Cano E, Moreno L, Blanco D (2017) New design of a soft robotics wearable elbow exoskeleton based on shape memory alloy wire actuators. Appl Bionics Biomech 2017:1–11

    Article  Google Scholar 

  9. Ansari Y, Manti M, Falotico E, Mollard Y, Cianchetti M, Laschi C (2017) Towards the development of a soft manipulator as an assistive robot for personal care of elderly people. Int J Adv Robot Syst 14(2):1–17

    Article  Google Scholar 

  10. Mosadegh B, Polygerinos P, Keplinger C, Wennstedt S, Shepherd RF, Gupta U, Shim J, Bertoldi K, Walsh CJ, Whitesides GM (2014) Pneumatic networks for soft robotics that actuate rapidly. Adv Funct Mater 24(15):2163–2170

    Article  Google Scholar 

  11. Calisti M, Giorelli M, Levy G, Mazzolai B, Hochner B, Laschi C, Dario P (2011) An octopus-bioinspired solution to movement and manipulation for soft robots. Bioinspir Biomim 6:3

    Article  Google Scholar 

  12. Hoang TT, Phan PT, Thai MT, Lovell NH, Do TN (2020) Bio-inspired conformable and helical soft fabric gripper with variable stiffness and touch sensing. Adv Mater Technol 2000724:1–14

    Google Scholar 

  13. Pfeil S, Henke M, Katzer K, Zimmermann M, Gerlach G (2020) A worm-like biomimetic crawling robot based on cylindrical dielectric elastomer actuators. Front Robot AI 7(February):1–11

    Google Scholar 

  14. Tottori S, Zhang L, Qiu F, Krawczyk KK, Franco-Obregõn A, Nelson BJ (2012) Magnetic helical micromachines: fabrication, controlled swimming, and cargo transport. Adv Mater 24(6):811–816

    Article  Google Scholar 

  15. Qiu T, Palagi S, Mark AG, Melde K, Adams F, Fischer P (2016) Wireless actuation with functional acoustic surfaces. Appl Phys Lett 109(19):1–5

    Article  Google Scholar 

  16. Zeng H, Wasylczyk P, Wiersma DS, Priimagi A (2018) Light robots: bridging the gap between microrobotics and photomechanics in soft materials. Adv Mater 30(24):1–9

    Google Scholar 

  17. Yoshida R, Takahashi T, Yamaguchi T, Ichijo H (1996) Self-oscillating gel. J Am Chem Soc 118(21):5134–5135

    Article  Google Scholar 

  18. Maeda S, Hara Y, Sakai T, Yoshida R, Hashimoto S (2007) Self-walking gel. Adv Mater 19(21):3480

    Article  Google Scholar 

  19. Tabata O, Hirasawa H, Aoki S, Yoshida R, Kokufuta E (2002) Ciliary motion actuator using self-oscillating gel. Sens Actuators A Phys 95(2–3):234–238

    Article  Google Scholar 

  20. Tabata O, Kojima H, Kasatani T, Isono Y, Yoshida R (2003) Chemo-mechanical actuator using self-oscillating gel for artificial cilia. In: MEMS-03: IEEE the sixteenth annual international conference on micro electro mechanical systems, proceedings: IEEE Micro Electro Mechanical Systems, pp 12–15

  21. Maeda S, Hara Y, Yoshida R, Hashimoto S (2008) Peristaltic motion of polymer gels. Angew Chem Int Ed 47(35):6690–6693

    Article  Google Scholar 

  22. Shiraki Y, Yoshida R (2012) Autonomous intestine-like motion of tubular self-oscillating gel. Angew Chem Int Ed 51(25):6112–6116

    Article  Google Scholar 

  23. Yashin VV, Balazs AC (2006) Modeling polymer gels exhibiting self-oscillations due to the Belousov–Zhabotinsky reaction. Macromolecules 39(6):2024–2026

    Article  Google Scholar 

  24. Dayal P, Kuksenok O, Balazs AC (2014) Directing the behavior of active, self-oscillating gels with light. Macromolecules 47(10):3231–3242

    Article  Google Scholar 

  25. Levin I, Deegan R, Sharon E (2020) Self-oscillating membranes: chemomechanical sheets show autonomous periodic shape transformation. Phys Rev Lett 125:178001

    Article  Google Scholar 

  26. Alben S, Gorodetsky AA, Kim D, Deegan RD (2019) Semi-implicit methods for the dynamics of elastic sheets. J Comput Phys 399:108952

    Article  MathSciNet  MATH  Google Scholar 

  27. Siakavara K (2009) Artificial neural network based design of a three-layered microstrip circular ring antenna with specified multi-frequency operation. Neural Comput Appl 18:57–64

    Article  Google Scholar 

  28. Chen C, Gu GX (2020) Generative deep neural networks for inverse materials design using backpropagation and active learning. Adv Sci 7:1902607

    Article  Google Scholar 

  29. Sekar V, Zhang M, Shu C, Khoo BC (2019) Inverse design of airfoil using a deep convolutional neural network. AIAA J 57:993–1003

    Article  Google Scholar 

  30. Li MM, Verma B, Fan X, Tickle K (2008) RBF neural networks for solving the inverse problem of backscattering spectra. Neural Comput Appl 17:391–397

    Article  Google Scholar 

  31. Massari L, Schena E, Massaroni C, Saccomandi P, Menciassi A, Sinibaldi E, Oddo CM (2020) A machine-learning-based approach to solve both contact location and force in soft material tactile sensors. Soft Robot 7(4):409–420

    Article  Google Scholar 

  32. Liu X, Fotouhi A (2020) Formula-E race strategy development using artificial neural networks and Monte Carlo tree search. Neural Comput Appl 32(18):15191–15207

    Article  Google Scholar 

  33. Peurifoy J, Shen Y, Jing L, Yang Y, Cano-Renteria F, DeLacy BG, Joannopoulos JD, Tegmark M, Soljačić M (2018) Nanophotonic particle simulation and inverse design using artificial neural networks. Sci Adv 4(6):1–8

    Article  Google Scholar 

  34. Xie T, Grossman JC (2018) Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties. Phys Rev Lett 120(14):145301

    Article  Google Scholar 

  35. Sun G, Sun Y, Wang S (2015) Artificial neural network based inverse design: airfoils and wings. Aerosp Sci Technol 42:415–428

    Article  Google Scholar 

  36. Hanakata PZ, Cubuk ED, Campbell DK, Park HS (2020) Forward and inverse design of Kirigami via supervised autoencoder. Phys Rev Res 2(4):1–6

    Article  Google Scholar 

  37. Gao N, Wang M, Cheng B, Hou H (2021) Inverse design and experimental verification of an acoustic sink based on machine learning. Appl Acoust 180:108153

    Article  Google Scholar 

  38. Seung HS, Nelson DR (1988) Defects in flexible membranes with crystalline order. Phys Rev A 38:1005–1018

    Article  Google Scholar 

  39. Schmidt B, Fraternali F (2012) Universal formulae for the limiting elastic energy of membrane networks. J Mech Phys Solids 60:172–180

    Article  MathSciNet  MATH  Google Scholar 

  40. Akilli A, Atil H (2020) Evaluation of normalization techniques on neural networks for the prediction of 305-day milk yield. Turk J Agric Eng Res 1:354–367

    Article  Google Scholar 

  41. Shanker MS, Hu MY, Hung MS (1996) Effect of data standardization on neural network training. Omega 24(4):385–397

    Article  Google Scholar 

  42. Yongkui SU, Yuan CA, Guo XI, Tao WE (2020) Condition monitoring for railway point machines based on sound analysis and support vector machine. Chin J Electron 29(4):786–792

    Article  Google Scholar 

  43. Murtagh F (1991) Multilayer perceptrons for classification and regression. Neurocomputing 2(5–6):183–197

    Article  MathSciNet  Google Scholar 

  44. Malhi A, Gao RX (2004) PCA-based feature selection scheme for machine defect classification. IEEE Trans Instrum Meas 53(6):1517–1525

    Article  Google Scholar 

  45. Stacklies W, Redestig H, Scholz M, Walther D, Selbig J (2007) pcaMethods—a bioconductor package providing PCA methods for incomplete data. Bioinformatics 23(9):1164–1167

    Article  Google Scholar 

  46. Madsen RE, Hansen LK, Winther O (2004) Singular value decomposition and principle component analysis. Neural Netw 1(February):1–5

    Google Scholar 

  47. Sousa S, Martins FG, Alvim-Ferraz M, Pereira MC (2007) Multiple linear regression and artificial neural networks based on principal components to predict ozone concentrations. Environ Model Softw 22(1):97–103

    Article  Google Scholar 

  48. Ghosh-Dastidar S, Adeli H, Dadmehr N (2008) Principal component analysis-enhanced cosine radial basis function neural network for robust epilepsy and seizure detection. IEEE Trans Biomed Eng 55(2):512–518

    Article  Google Scholar 

  49. Hesthaven J, Ubbiali S (2018) Non-intrusive reduced order modeling of nonlinear problems using neural networks. In: Proceedings of the 20th USENIX Security Symposium, vol 363, pp 55–78

  50. Ravi V, Pramodh C (2008) Threshold accepting trained principal component neural network and feature subset selection: application to bankruptcy prediction in banks. Appl Soft Comput J 8(4):1539–1548

    Article  Google Scholar 

  51. Abdi H, Valentin D, Edelman B, O’Toole AJ (1995) More about the difference between men and women: evidence from linear neural networks and the principal-component approach. Perception 24(5):539–562

    Article  Google Scholar 

  52. Ross DA, Lim J, Lin RS, Yang MH (2008) Incremental learning for robust visual tracking. Int J Comput Vis 77(1–3):125–141

    Article  Google Scholar 

  53. Lippi V, Ceccarelli G (2019) Incremental principal component analysis: Exact implementation and continuity corrections. In: ICINCO 2019—proceedings of the 16th international conference on informatics in control, automation and robotics, vol 1, pp 473–480

  54. Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V, Vanderplas J, Passos A, Cournapeau D, Brucher M, Perrot M, Duchesnay E (2011) Scikit-learn: machine learning in Python. J Mach Learn Res 12:2825–2830

    MathSciNet  MATH  Google Scholar 

  55. Paszke A, Gross S, Massa F, Lerer A, Bradbury J, Chanan G, Killeen T, Lin Z, Gimelshein N, Antiga L, Desmaison A, Kopf A, Yang E, DeVito Z, Raison M, Tejani A, Chilamkurthy S, Steiner B, Fang L, Bai J, Chintala S (2019) PyTorch: an imperative style, high-performance deep learning library. In: Wallach H, Larochelle H, Beygelzimer A, d’Alché-Buc F, Fox E, Garnett R (eds) Advances in neural information processing systems, vol 32. Curran Associates, Inc., pp 8026–8037

    Google Scholar 

  56. Kingma DP, Ba J (2014) Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980

  57. Zhou Z, Wang JB, Zang YF, Pan G (2018) PAIR comparison between two within-group conditions of resting-state fMRI improves classification accuracy. Front Neurosci 11, no. JAN:1–13

    Google Scholar 

  58. Zeebaree DQ, Haron H, Abdulazeez AM (2018) Gene selection and classification of microarray data using convolutional neural network. In: ICOASE 2018—international conference on advanced science and engineering, pp 145–150

  59. Guru DS, Mallikarjuna PB, Manjunath S, Shenoi MM (2012) Machine vision based classification of tobacco leaves for automatic harvesting. Intell Autom Soft Comput 18(5):581–590

    Article  Google Scholar 

  60. Veisi I, Pariz N, Karimpour A (2007) Fast and robust detection of epilepsy in noisy BEG signals using permutation entropy. In: Proceedings of the 7th IEEE international conference on bioinformatics and bioengineering, BIBE, pp 200–203

  61. Wolf A, Swift JB, Swinney HL, Vastano JA (1985) Determining Lyapunov exponents from a time series. Physica D 16:285–317

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

We would like to thank Donghak Kim for creating the simulation data that we used to train the inverse design architecture.

Funding

This work was supported by the MICDE Catalyst Grant program at the University of Michigan, the DARPA AIRA program under Agreement No. HR0011199002, “Artificial Intelligence guided multi-scale multi-physics framework for discovering complex emergent materials phenomena”, and the DOE Office of Science, ASCR.

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Authors and Affiliations

  1. Department of Aerospace Engineering, Universitiy of Michigan, Ann Arbor, MI, 48109, USA

    Doruk Aksoy & Alex A. Gorodetsky

  2. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    Silas Alben

  3. Department of Physics, University of Michigan, Ann Arbor, MI, 48109, USA

    Robert D. Deegan

Authors
  1. Doruk Aksoy
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  2. Silas Alben
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  4. Alex A. Gorodetsky
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Correspondence to Doruk Aksoy.

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Appendix: Tables

Appendix: Tables

See Tables 1, 2, 3, 4, 5 and 6.

Table 1 Regression metrics of the hidden unit case studies for regression
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Table 2 Percent error (PE) metrics of the layer case studies for regression
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Table 3 Percent error (PE) metrics of the principal component case studies for regression
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Table 4 Percent error (PE) metrics of the epoch case studies for regression
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Table 5 Percent error (PE) metrics of the non-PCA comparison case study for regression
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Table 6 Errors in our inverse design estimation for four representative parameter settings P: planar motion, R: radial motion
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Aksoy, D., Alben, S., Deegan, R.D. et al. Inverse design of self-oscillatory gels through deep learning. Neural Comput & Applic 34, 6879–6905 (2022). https://doi.org/10.1007/s00521-021-06788-9

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