Goodrich, Carl PeterIST Austria ; King, Ella M.; Schoenholz, Samuel S.; Cubuk, Ekin D.; Brenner, Michael P.
The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing emergent kinetics, but this has received considerably less attention. Using recent advances in automatic differentiation, we show how kinetic pathways can be precisely designed by directly differentiating through statistical physics models, namely free energy calculations and molecular dynamics simulations. We consider two systems that are crucial to our understanding of structural self-assembly: bulk crystallization and small nanoclusters. In each case, we are able to assemble precise dynamical features. Using gradient information, we manipulate interactions among constituent particles to tune the rate at which these systems yield specific structures of interest. Moreover, we use this approach to learn nontrivial features about the high-dimensional design space, allowing us to accurately predict when multiple kinetic features can be simultaneously and independently controlled. These results provide a concrete and generalizable foundation for studying nonstructural self-assembly, including kinetic properties as well as other complex emergent properties, in a vast array of systems.
We thank Agnese Curatolo, Megan Engel, Ofer Kimchi, Seong Ho Pahng, and Roy Frostig for helpful discussions. This material is based on work supported by NSF Graduate Research Fellowship Grant DGE1745303. This research was funded by NSF Grant DMS-1715477, Materials Research Science and Engineering Centers Grant DMR-1420570, and Office of Naval Research Grant N00014-17-1-3029. M.P.B. is an investigator of the Simons Foundation.
Goodrich CP, King EM, Schoenholz SS, Cubuk ED, Brenner MP. Designing self-assembling kinetics with differentiable statistical physics models. PNAS. 2021;118(10). doi:10.1073/pnas.2024083118
Goodrich, C. P., King, E. M., Schoenholz, S. S., Cubuk, E. D., & Brenner, M. P. (2021). Designing self-assembling kinetics with differentiable statistical physics models. PNAS. Proceedings of the National Academy of Sciences. https://doi.org/10.1073/pnas.2024083118
Goodrich, Carl Peter, Ella M. King, Samuel S. Schoenholz, Ekin D. Cubuk, and Michael P. Brenner. “Designing Self-Assembling Kinetics with Differentiable Statistical Physics Models.” PNAS. Proceedings of the National Academy of Sciences, 2021. https://doi.org/10.1073/pnas.2024083118.
C. P. Goodrich, E. M. King, S. S. Schoenholz, E. D. Cubuk, and M. P. Brenner, “Designing self-assembling kinetics with differentiable statistical physics models,” PNAS, vol. 118, no. 10. Proceedings of the National Academy of Sciences, 2021.
Goodrich CP, King EM, Schoenholz SS, Cubuk ED, Brenner MP. 2021. Designing self-assembling kinetics with differentiable statistical physics models. PNAS. 118(10), e2024083118.
Goodrich, Carl Peter, et al. “Designing Self-Assembling Kinetics with Differentiable Statistical Physics Models.” PNAS, vol. 118, no. 10, e2024083118, Proceedings of the National Academy of Sciences, 2021, doi:10.1073/pnas.2024083118.
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