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Petix CL, Fakhraei M, Kieslich CA, Howard MP. Surrogate Modeling of the Relative Entropy for Inverse Design Using Smolyak Sparse Grids. J Chem Theory Comput 2024; 20:1538-1546. [PMID: 37703086 DOI: 10.1021/acs.jctc.3c00651] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/14/2023]
Abstract
Relative entropy minimization, a statistical-mechanics approach for finding potential energy functions that produce target structural ensembles, has proven to be a powerful strategy for the inverse design of nanoparticle self-assembly. For a given target structure, the gradient of the relative entropy with respect to the adjustable parameters of the potential energy function is computed by performing a simulation, and then these parameters are updated using iterative gradient-based optimization. Small parameter updates per iteration and many iterations can be required for numerical stability, but this incurs considerable computational expense because a new simulation must be performed to reevaluate the gradient at each iteration. Here, we investigate the use of surrogate modeling to decouple the process of minimizing the relative entropy from the computationally demanding process of determining its gradient. We approximate the relative-entropy gradient using Chebyshev polynomial interpolation on Smolyak sparse grids. Our approach potentially increases the robustness and computational efficiency of using the relative entropy for inverse design, primarily for physically informed potential energy functions that have a small number of adjustable parameters.
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Affiliation(s)
- C Levi Petix
- Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849, United States
| | - Mohammadreza Fakhraei
- Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849, United States
| | - Chris A Kieslich
- Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849, United States
| | - Michael P Howard
- Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849, United States
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2
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Sherck N, Shen K, Nguyen M, Yoo B, Köhler S, Speros JC, Delaney KT, Shell MS, Fredrickson GH. Molecularly Informed Field Theories from Bottom-up Coarse-Graining. ACS Macro Lett 2021; 10:576-583. [PMID: 35570772 DOI: 10.1021/acsmacrolett.1c00013] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Polymer formulations possessing mesostructures or phase coexistence are challenging to simulate using atomistic particle-explicit approaches due to the disparate time and length scales, while the predictive capability of field-based simulations is hampered by the need to specify interactions at a coarser scale (e.g., χ-parameters). To overcome the weaknesses of both, we introduce a bottom-up coarse-graining methodology that leverages all-atom molecular dynamics to molecularly inform coarser field-theoretic models. Specifically, we use relative-entropy coarse-graining to parametrize particle models that are directly and analytically transformable into statistical field theories. We demonstrate the predictive capability of this approach by reproducing experimental aqueous poly(ethylene oxide) (PEO) cloud-point curves with no parameters fit to experimental data. This synergistic approach to multiscale polymer simulations opens the door to de novo exploration of phase behavior across a wide variety of polymer solutions and melt formulations.
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Affiliation(s)
- Nicholas Sherck
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Kevin Shen
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
| | - My Nguyen
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Brian Yoo
- BASF Corporation, Tarrytown, New York 10591, United States
| | | | - Joshua C. Speros
- California Research Alliance (CARA) by BASF, Berkeley, California 94720, United States
| | - Kris T. Delaney
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
| | - M. Scott Shell
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Glenn H. Fredrickson
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
- Department of Materials, University of California, Santa Barbara, California 93106, United States
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3
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Lindquist BA. Inverse design of equilibrium cluster fluids applied to a physically informed model. J Chem Phys 2021; 154:174907. [PMID: 34241069 DOI: 10.1063/5.0048812] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Inverse design strategies have proven highly useful for the discovery of interaction potentials that prompt self-assembly of a variety of interesting structures. However, often the optimized particle interactions do not have a direct relationship to experimental systems. In this work, we show that Relative Entropy minimization is able to discover physically meaningful parameter sets for a model interaction built from depletion attraction and electrostatic repulsion that yield self-assembly of size-specific clusters. We then explore the sensitivity of the optimized interaction potentials with respect to deviations in the underlying physical quantities, showing that clustering behavior is largely preserved even as the optimized parameters are perturbed.
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Affiliation(s)
- Beth A Lindquist
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Berressem F, Nikoubashman A. BoltzmaNN: Predicting effective pair potentials and equations of state using neural networks. J Chem Phys 2021; 154:124123. [PMID: 33810691 DOI: 10.1063/5.0045441] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Neural networks (NNs) are employed to predict equations of state from a given isotropic pair potential using the virial expansion of the pressure. The NNs are trained with data from molecular dynamics simulations of monoatomic gases and liquids, sampled in the NVT ensemble at various densities. We find that the NNs provide much more accurate results compared to the analytic low-density limit estimate of the second virial coefficient and the Carnahan-Starling equation of state for hard sphere liquids. Furthermore, we design and train NNs for computing (effective) pair potentials from radial pair distribution functions, g(r), a task that is often performed for inverse design and coarse-graining. Providing the NNs with additional information on the forces greatly improves the accuracy of the predictions since more correlations are taken into account; the predicted potentials become smoother, are significantly closer to the target potentials, and are more transferable as a result.
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Affiliation(s)
- Fabian Berressem
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Arash Nikoubashman
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
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Sherman ZM, Howard MP, Lindquist BA, Jadrich RB, Truskett TM. Inverse methods for design of soft materials. J Chem Phys 2020; 152:140902. [DOI: 10.1063/1.5145177] [Citation(s) in RCA: 42] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Affiliation(s)
- Zachary M. Sherman
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA
| | - Michael P. Howard
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA
| | - Beth A. Lindquist
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Ryan B. Jadrich
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Thomas M. Truskett
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA
- Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
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Huang S, Quevillon MJ, Kyhl S, Whitmer JK. Surveying the free energy landscape of clusters of attractive colloidal spheres. J Chem Phys 2020; 152:134901. [PMID: 32268752 DOI: 10.1063/1.5144984] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Controlling the assembly of colloidal particles into specific structures has been a long-term goal of the soft materials community. Much can be learned about the process of self-assembly by examining the early stage assembly into clusters. For the simple case of hard spheres with short-range attractions, the rigid clusters of N particles (where N is small) have been enumerated theoretically and tested experimentally. Less is known, however, about how the free energy landscapes are altered when the inter-particle potential is long-ranged. In this work, we demonstrate how adaptive biasing in molecular simulations may be used to pinpoint shifts in the stability of colloidal clusters as the inter-particle potential is varied. We also discuss the generality of our techniques and strategies for application to related molecular systems.
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Affiliation(s)
- Shanghui Huang
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - Michael J Quevillon
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - Soren Kyhl
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - Jonathan K Whitmer
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA
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Mahynski NA, Mao R, Pretti E, Shen VK, Mittal J. Grand canonical inverse design of multicomponent colloidal crystals. SOFT MATTER 2020; 16:3187-3194. [PMID: 32134420 DOI: 10.1039/c9sm02426c] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Inverse design methods are powerful computational approaches for creating colloidal systems which self-assemble into a target morphology by reverse engineering the Hamiltonian of the system. Despite this, these optimization procedures tend to yield Hamiltonians which are too complex to be experimentally realized. An alternative route to complex structures involves the use of several different components, however, conventional inverse design methods do not explicitly account for the possibility of phase separation into compositionally distinct structures. Here, we present an inverse design scheme for multicomponent colloidal systems by combining active learning with a method to directly compute their ground state phase diagrams. This explicitly accounts for phase separation and can locate stable regions of Hamiltonian parameter space which grid-based surveys are prone to miss. Using this we design low-density, binary structures with Lennard-Jones-like pairwise interactions that are simpler than in the single component case and potentially realizable in an experimental setting. This reinforces the concept that ground states of simple, multicomponent systems might be rich with previously unappreciated diversity, enabling the assembly of non-trivial structures with only few simple components instead of a single complex one.
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Affiliation(s)
- Nathan A Mahynski
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, USA.
| | - Runfang Mao
- Department of Chemical and Biomolecular Engineering, Lehigh University, 111 Research Dr., Bethlehem, Pennsylvania 18015-4791, USA
| | - Evan Pretti
- Department of Chemical and Biomolecular Engineering, Lehigh University, 111 Research Dr., Bethlehem, Pennsylvania 18015-4791, USA
| | - Vincent K Shen
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, USA.
| | - Jeetain Mittal
- Department of Chemical and Biomolecular Engineering, Lehigh University, 111 Research Dr., Bethlehem, Pennsylvania 18015-4791, USA
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