Coarse-graining and inverse design in soft matter via local density-dependent potentials and machine learning methods

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Abstract

The fields of material sciences and soft matter have been and continue to be of great importance for both modern research as well as our everyday life. Especially the advent of computers and consecutively the establishment of computer simulations caused these research areas to gain even more momentum and led to great improvements and achievements. However, even with modern computing resources and algorithms, there remain significant challenges when considering systems where microscopic details are important for the macroscopic behavior. While methods like ab-initio-simulations are fairly capable of treating small systems with quantum-mechanical detail, other techniques like finite-element-methods are able to capture macroscopic behavior in the continuous limit. Besides exhibiting interesting phenomena on their own, the intermediate scales are dedicated to bridging these regimes via the methodology of coarse-graining. In recent years, by virtue of machine learning becoming broadly available and a thoroughly studied field, there has been another ad- vancement, that has opened up new, data-driven approaches to statistical physics and computer simulations. This young field has soon led to impressive results, hence establishing itself rapidly as a new pillar of sciences and engi- neering. This work aims at making a contribution to both the field of coarse-graining as well as machine learning and is split in two main parts: In the first contribution we apply neural networks for forward and inverse design, specifically to the tasks of approximating mappings from pair potentials to the resulting equation of state as well as from the radial distribution function to the effective pair potential leading to it. These tasks are very interesting as the first mapping allows for rapid prototyping when searching for materials with a desired equation of state, while the second can be used to improve established, iterative coarse-graining techniques. In both tasks, we focused mainly on the impact of the representation of the respective inputs and outputs, in order to yield good generalization capabilities despite the small number of available training examples. The second contribution is a bottom-up coarse-graining scheme for inhomogeneous systems where whole polymer chains are mapped to single beads. In our parametrization scheme, the coarse-grained beads interact via a pair potential as well as either a three-body Stillinger-Weber potential or a local density-dependent potential. We find that the combination of pair potential and three-body potential fails to reproduce the film-forming properties of our reference system. The systems interacting via local density-dependent potentials on the other hand are able to do so and even show quantitative agreement with regards to the width of the films. On further investigation, we find that there seems to be no unique correspondence between the distribution of the local density, which was optimized in our work, and the density profiles. This non-correspondence becomes stronger for increasing degrees of polymerization and hence increasing interpenetration of the polymer chains, which is why our approach is for now only applicable to smaller molecules. In the corresponding chapters we also elaborate on possible mitigation strategies for this shortcoming.

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