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.