Accelerated Design of Architected Materials with Multifidelity Bayesian Optimization
Publication: Journal of Engineering Mechanics
Volume 149, Issue 6
Abstract
In this work, we present a multifidelity Bayesian optimization framework for designing architected materials with optimal energy absorption during compression. Data from both physical experiments (high fidelity) and numerical simulations (low fidelity) are fed in parallel to train the surrogate model, which iteratively decides the next sets of experiments and simulations to run in order to find the optimal structural parameters. We show that having multifidelity data sources allows the optimization framework to find the optimum after fewer iterations relative to using a single high-fidelity source. This saves both material costs and time in the optimization process. Finally, we also apply constraints (on relative density and stress variations) to the optimization process, finding optimal structures within the bounds of the constraints. This framework can be translated to other problems that require complex, high-fidelity, labor-intensive experiments while automating low-fidelity simulations.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
CM and JRR gratefully acknowledge support via the University of Pennsylvania Materials Research Science and Engineering Center (MRSEC) (NSF DMR-1720530), AFOSR Grant No. FA9550-22-1-0163, and by a 3M Non-Tenured Faculty Award. PP gratefully acknowledges support via DOE Grant No. DE-SC0019116.
References
Balachandran, P. V., B. Kowalski, A. Sehirlioglu, and T. Lookman. 2018. “Experimental search for high-temperature ferroelectric perovskites guided by two-step machine learning.” Nat. Commun. 9 (1): 1668. https://doi.org/10.1038/s41467-018-03821-9.
Buhl, T., C. B. W. Pedersen, and O. Sigmund. 2000. “Stiffness design of geometrically nonlinear structures using topology optimization.” Struct. Multidiscip. Optim. 19 (2): 93–104. https://doi.org/10.1007/s001580050089.
Burger, B., et al. 2020. “A mobile robotic chemist.” Nature 583 (7815): 237–241. https://doi.org/10.1038/s41586-020-2442-2.
Chen, C., Y. Zuo, W. Ye, X. Li, and S. P. Ong. 2021. “Learning properties of ordered and disordered materials from multi-fidelity data.” Nat. Comput. Sci. 1 (1): 46–53. https://doi.org/10.1038/s43588-020-00002-x.
Chen, E., S. Luan, and S. Gaitanaros. 2022. “On the strength of brittle foams with uniform and gradient densities.” Extreme Mech. Lett. 51 (Feb): 101598. https://doi.org/10.1016/j.eml.2021.101598.
Couperthwaite, R., A. Molkeri, D. Khatamsaz, A. Srivastava, D. Allaire, and R. Arròyave. 2020. “Materials design through batch bayesian optimization with multisource information fusion.” JOM 72 (12): 4431–4443. https://doi.org/10.1007/s11837-020-04396-x.
Da, D., Y.-C. Chan, L. Wang, and W. Chen. 2022. “Data-driven and topological design of structural metamaterials for fracture resistance.” Extreme Mech. Lett. 50 (Jan): 101528. https://doi.org/10.1016/j.eml.2021.101528.
Da, D., and X. Qian. 2020. “Fracture resistance design through biomimicry and topology optimization.” Extreme Mech. Lett. 40 (Oct): 100890. https://doi.org/10.1016/j.eml.2020.100890.
Dixon, P. G., and L. J. Gibson. 2014. “The structure and mechanics of moso bamboo material.” J. R. Soc. Interface 11 (99): 20140321. https://doi.org/10.1098/rsif.2014.0321.
Erps, T., M. Foshey, M. K. Luković, W. Shou, H. H. Goetzke, H. Dietsch, K. Stoll, B. von Vacano, and W. Matusik. 2021. “Accelerated discovery of 3d printing materials using data-driven multiobjective optimization.” Sci. Adv. 7 (42): eabf7435. https://doi.org/10.1126/sciadv.abf7435.
Frazier, P. I. 2018. “A tutorial on Bayesian optimization. “Preprint, submitted July 8, 2018. https://arxiv.org/abs/1807.02811.
Gibson, L. J., and M. F. Ashby. 1997. “Cellular solids: Structure and properties.” In Cambridge solid state science series. 2nd ed. Cambridge, UK: Cambridge University Press.
Gongora, A. E., K. L. Snapp, E. Whiting, P. Riley, K. G. Reyes, E. F. Morgan, and K. A. Brown. 2021. “Using simulation to accelerate autonomous experimentation: A case study using mechanics.” iScience 24 (4): 102262. https://doi.org/10.1016/j.isci.2021.102262.
Gongora, A. E., B. Xu, W. Perry, C. Okoye, P. Riley, K. G. Reyes, E. F. Morgan, and K. A. Brown. 2020. “A bayesian experimental autonomous researcher for mechanical design.” Sci. Adv. 6 (15): eaaz1708. https://doi.org/10.1126/sciadv.aaz1708.
Gu, G. X., C.-T. Chen, and M. J. Buehler. 2018. “De novo composite design based on machine learning algorithm.” Extreme Mech. Lett. 18 (10): 19–28. https://doi.org/10.1016/j.eml.2017.10.001.
Habibi, M. K., and Y. Lu. 2014. “Crack propagation in bamboo’s hierarchical cellular structure.” Sci. Rep. 4 (1): 5598.
Hanakata, P. Z., E. D. Cubuk, D. K. Campbell, and H. S. Park. 2018. “Accelerated search and design of stretchable graphene kirigami using machine learning.” Phys. Rev. Lett. 121 (Jan): 255304. https://doi.org/10.1103/PhysRevLett.121.255304.
Jiang, Z., and J. H. Pikul. 2021. “Centimetre-scale crack-free self-assembly for ultra-high tensile strength metallic nanolattices.” Nat. Mater. 20 (11): 1512–1518. https://doi.org/10.1038/s41563-021-01039-7.
Kirschner, J., M. Mutny, N. Hiller, R. Ischebeck, and A. Krause. 2019. “Adaptive and safe bayesian optimization in high dimensions via one-dimensional subspaces.” In Proc., Int. Conf., on Machine Learning, 3429–3438. Ithaca, NY: Cornell Univ. https://arxiv.org/abs/1902.03229.
Li, Z., et al. 2020. “Robot-accelerated perovskite investigation and discovery.” Chem. Mater. 32 (13): 5650–5663. https://doi.org/10.1021/acs.chemmater.0c01153.
Liu, C., J. Lertthanasarn, and M.-S. Pham. 2021. “The origin of the boundary strengthening in polycrystal-inspired architected materials.” Nat. Commun. 12 (1): 4600. https://doi.org/10.1038/s41467-021-24886-z.
Maddox, W. J., M. Balandat, A. G. Wilson, and E. Bakshy. 2021. “Bayesian optimization with high-dimensional outputs.” Adv. Neural Inf. Process. Syst. 34 (Jun): 19274–19287. https://doi.org/10.48550/arXiv.2106.12997.
Mao, Y., Q. He, and X. Zhao. 2020. “Designing complex architectured materials with generative adversarial networks.” Sci. Adv. 6 (17): eaaz4169. https://doi.org/10.1126/sciadv.aaz4169.
Meredig, B., et al. 2018. “Can machine learning identify the next high-temperature superconductor? Examining extrapolation performance for materials discovery.” Mol. Syst. Des. Eng. 3 (39): 819–825. https://doi.org/10.1039/C8ME00012C.
Meza, L. R., S. Das, and J. R. Greer. 2014. “Strong, lightweight, and recoverable three-dimensional ceramic nanolattices.” Science 345 (6202): 1322–1326. https://doi.org/10.1126/science.1255908.
Mirkhalaf, M., A. K. Dastjerdi, and F. Barthelat. 2014. “Overcoming the brittleness of glass through bio-inspiration and micro-architecture.” Nat. Commun. 5 (1): 1–9. https://doi.org/10.1038/ncomms4166.
Montgomery, S. M., H. Hilborn, C. M. Hamel, X. Kuang, K. N. Long, and H. J. Qi. 2021. “The 3d printing and modeling of functionally graded kelvin foams for controlling crushing performance.” Extreme Mech. Lett. 46 (Jan): 101323. https://doi.org/10.1016/j.eml.2021.101323.
Perdikaris, P. 2020. “JAX-BO: A Bayesian optimization library in JAX.” Accessed March 1, 2020. https://github.com/PredictiveIntelligenceLab/JAX-BO.
Pham, M. S., C. Liu, I. Todd, and J. Lertthanasarn. 2019. “Damage-tolerant architected materials inspired by crystal microstructure.” Nature 565 (7739): 305–311. https://doi.org/10.1038/s41586-018-0850-3.
Portela, C. M., B. W. Edwards, D. Veysset, Y. Sun, K. A. Nelson, D. M. Kochmann, and J. R. Greer. 2021. “Supersonic impact resilience of nanoarchitected carbon.” Nat. Mater. 20 (11): 1491–1497. https://doi.org/10.1038/s41563-021-01033-z.
Santer, M., and S. Pellegrino. 2009. “Topological optimization of compliant adaptive wing structure.” AIAA J. 47 (3): 523–534. https://doi.org/10.2514/1.36679.
Santos, A. G., G. O. da Rocha, and J. B. de Andrade. 2019. “Occurrence of the potent mutagens 2-nitrobenzanthrone and 3-nitrobenzanthrone in fine airborne particles.” Sci. Rep. 9 (1): 1. https://doi.org/10.1038/s41598-018-37186-2.
Smith, M. L., N. Napp, and K. H. Petersen. 2021. “Imperfect comb construction reveals the architectural abilities of honeybees.” Proc. Natl. Acad. Sci. U.S.A. 118 (31): e2103605118. https://doi.org/10.1073/pnas.2103605118.
Snoek, J., H. Larochelle, and R. P. Adams. 2012. Practical Bayesian optimization of machine learning algorithms. https://doi.org/10.48550/arXiv.1206.2944.
Solomou, A., G. Zhao, S. Boluki, J. K. Joy, X. Qian, I. Karaman, R. Arròyave, and D. C. Lagoudas. 2018. “Multi-objective bayesian materials discovery: Application on the discovery of precipitation strengthened niti shape memory alloys through micromechanical modeling.” Mater. Des. 160 (14): 810–827. https://doi.org/10.1016/j.matdes.2018.10.014.
Song, J., Y. Wang, W. Zhou, R. Fan, B. Yu, Y. Lu, and L. Li. 2019. “Topology optimization-guided lattice composites and their mechanical characterizations.” Composites, Part B 160 (12): 402–411. https://doi.org/10.1016/j.compositesb.2018.12.027.
Stach, E., et al. 2021. “Autonomous experimentation systems for materials development: A community perspective.” Matter 4 (9): 2702–2726. https://doi.org/10.1016/j.matt.2021.06.036.
Torres, A. M., A. A. Trikanad, C. A. Aubin, F. M. Lambers, M. Luna, C. M. Rimnac, P. Zavattieri, and C. J. Hernandez. 2019. “Bone-inspired microarchitectures achieve enhanced fatigue life.” Proc. Natl. Acad. Sci. U.S.A. 116 (49): 24457–24462. https://doi.org/10.1073/pnas.1905814116.
Vangelatos, Z., H. M. Sheikh, P. S. Marcus, C. P. Grigoropoulos, V. Z. Lopez, G. Flamourakis, and M. Farsari. 2021. “Strength through defects: A novel bayesian approach for the optimization of architected materials.” Sci. Adv. 7 (41): eabk2218. https://doi.org/10.1126/sciadv.abk2218.
Wang, Z., F. Hutter, M. Zoghi, D. Matheson, and N. De Feitas. 2016. “Bayesian optimization in a billion dimensions via random embeddings.” J. Artif. Intell. Res. 55 (Jun): 361–387. https://doi.org/10.1613/jair.4806.
Xue, D., P. V. Balachandran, J. Hogden, J. Theiler, D. Xue, and T. Lookman. 2016. “Accelerated search for materials with targeted properties by adaptive design.” Nat. Commun. 7 (1): 11241. https://doi.org/10.1038/ncomms11241.
Yang, C., Y. Kim, S. Ryu, and G. X. Gu. 2020. “Prediction of composite microstructure stress-strain curves using convolutional neural networks.” Mater. Des. 189 (45): 108509. https://doi.org/10.1016/j.matdes.2020.108509.
Yin, Z., F. Hannard, and F. Barthelat. 2019. “Impact-resistant nacre-like transparent materials.” Science 364 (6447): 1260–1263. https://doi.org/10.1126/science.aaw8988.
Yu, C.-H., Z. Qin, and M. J. Buehler. 2019. “Artificial intelligence design algorithm for nanocomposites optimized for shear crack resistance.” Nano Futures 3 (3): 035001. https://doi.org/10.1088/2399-1984/ab36f0.
Yuan, R., Z. Liu, P. V. Balachandran, D. Xue, Y. Zhou, X. Ding, J. Sun, D. Xue, and T. Lookman. 2018. “Accelerated discovery of large electrostrains in batio3-based piezoelectrics using active learning.” Adv. Mater. 30 (7): 1702884. https://doi.org/10.1002/adma.201702884.
Zheng, X., et al. 2014. “Ultralight, ultrastiff mechanical metamaterials.” Science 344 (6190): 1373–1377. https://doi.org/10.1126/science.1252291.
Zhong, M., et al. 2020. “Accelerated discovery of co2 electrocatalysts using active machine learning.” Nature 581 (7807): 178–183. https://doi.org/10.1038/s41586-020-2242-8.
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© 2023 American Society of Civil Engineers.
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Received: Oct 28, 2022
Accepted: Dec 12, 2022
Published online: Mar 30, 2023
Published in print: Jun 1, 2023
Discussion open until: Aug 30, 2023
ASCE Technical Topics:
- Absorption
- Analysis (by type)
- Bayesian analysis
- Building design
- Chemical processes
- Chemistry
- Compression
- Continuum mechanics
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- Environmental engineering
- Materials engineering
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- Sorption
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- Structural dynamics
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