Junior research group leader Miriam Klopotek, who joined SimTech in April 2022, was awarded the Förster Prize by the Eberhard Karls University of Tübingen for her dissertation on "Hard Rods on Lattices between Two and Three Dimensions: Nonequilibrium, Equilibrium, and Machine Learning" (2021) .
The prize, established by Dr. Friedrich Förster in 1983, was awarded during the Kepler Lecture in the colloquium of the Department of Physics and honours young scientists from the fields of physics and physical chemistry who have distinguished themselves through particularly outstanding, creative and application-oriented work with an interdisciplinary approach.
In her thesis, written under the supervision of Prof. Martin Oettel from the Department of Physics (chair for Computational Soft Matter and Nano-Science), Miriam took up the study of the physics of simple statistical model systems of interacting hard rods, using mainly particle-based simulations as a tool. The original motivation was to better understand the self-assembly of collections of elongated particles, like organic molecules, at surface substrates.
“Her studies uncovered surprising, nonequilibrium phenomena that occur during the growth of films of rods, including the formation of transient gel states, as well as the playing out of an extremely rich variety of phase transition dynamics - despite apparent simplicity of the model. Notably, however, she took her thesis in a completely new direction. By using the same model systems of hard rods, she explored a generic class of unsupervised and generative machine learning algorithms. In trying to open up the "black box" of these algorithms - by training them on possible configurations - she uncovered that the algorithms inherently coarse-grain and automatically find collective variables in the many-body system - a remarkable insight into the nature of machine learning, and one that could also be of great practical use”, explains Prof. Oettel.
He further states that “the prize honours creative results in the fields of physics and physical chemistry and emphasizes what a central element of PhD research still should be: the own, creative work of the young researcher towards a new piece of discovery or understanding in nature. This worked especially well with Miriam's own ideas and the connection to the new machine learning environment in Tübingen.”
Abstract: This thesis explores the statistical mechanics of idealized model systems of hard-core rods and “sticky” hard rods, as well as the behavior of a machine learning algorithm. Rods are constrained to square and cubic-type lattices: in monolayer confinement ((2+1)D), in the three-dimensional bulk (3D), and in full confinement to two dimensions (2D). We study rods in (2+1)D in a basic model system for early stages of thin film growth with anisotropic particles. We write, develop, and execute a very large array of kinetic Monte Carlo (KMC) simulations of the nonequilibrium dynamics. The physics of monolayer growth with sticky hard rods is extremely rich. The bounty of phenomena on metastable phases and complex phase transition kinetics we find has not been addressed before by comparable simulation or analytical models. We identify at least five different phase transition scenarios; the different dynamical regimes are traceable in the 2D plane (“map”) spanned by the reduced temperature (or attraction strength) and deposition-flux–to–diffusion ratio. The rod-length as well as simple substrate potentials further shift these regimes and alter the topology of the “map”, i.e. the set of phase transition scenarios. The specific model choice for microscopic rotational dynamics of rods is another, surprisingly important factor altering the kinetics and, therewith, the morphological evolution. For the limiting case of purely hard-core rods, we find excellent agreement between KMC simulations and a corresponding lattice dynamical density functional theory formulated for monolayer growth. The latter is based on a lattice fundamental measure theory formulated for our hard-core rods on lattices. Deviations to KMC simulations are most visible near jamming transitions. In the same, purely hard-core limit, we compare the lattice rods to a continuum model of hard spherocylinders – first in equilibrium, then under growth conditions. These show strong qualitative similarities, despite entailing different “equation-of-states” (virial coefficients). We simulate 3D and 2D systems of hard and sticky hard rods in the grand canonical ensemble to characterize their phase behavior, focusing on the isotropic–nematic orientational transitions. The nature of 3D nematic ordering is very different when compared to e.g. liquid crystal models in the continuum. We find this transition is only weakly first-order in the purely hard-core limit. Moreover, for rod-lengths 5 and 6, ordering is realized when one orientation is suppressed rather than dominant – a unique feature of the fully discretized degrees of freedom. We present the 3D bulk phase diagrams for sticky hard rods at multiple rod-lengths, and another for full 2D confinement. In the latter, a heightened competition between isotropic–nematic and vapor–liquid ordering transitions leads to presumably tricritical behavior. We train beta-variational autoencoders (β-VAEs) – an unsupervised and generative machine learning algorithm – on configurations of the 2D sticky-hard-rod model in order to better understand their learning capabilities and limits. The algorithms appear to “coarse grain” the configurations of the hard rods. The upper limit on the resolution, i.e. how detailed the reconstructed or generated configurations appear, is set by the chosen latent-space dimension. The specific level-of-resolution is also sensitive to the hyperparameter β, where mode collapse occurs past a threshold value. We interpret the latent variables as fluctuating collective variables in the rod system. Intriguingly, at the threshold state of β, these form a broad, “disentangled” coarse-graining hierarchy. The first two latent variables are identifiable with the 2D thermodynamic order parameter of the rod system. The paired encoding on latent space – the means and variances for the multivariate Gaussian model posterior – renders highly sensitive information to thermodynamic (Boltzmann-Gibbs) states of the rod system. The full generative model appears to (approximately) represent a critical state that could be expected for a finite-sized system. However, the interpretability of the model remains limited as it does not represent a true thermodynamic state.