Related papers: Exploring order parameters and dynamic processes i…
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
The dynamic of complex ordering systems with active rotational degrees of freedom exemplified by protein self-assembly is explored using a machine learning workflow that combines deep learning-based semantic segmentation and rotationally…
Electron and scanning probe microscopy produce vast amounts of data in the form of images or hyperspectral data, such as EELS or 4D STEM, that contain information on a wide range of structural, physical, and chemical properties of…
Finding collective variables to describe some important coarse-grained information on physical systems, in particular metastable states, remains a key issue in molecular dynamics. Recently, machine learning techniques have been intensively…
Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state…
This work develops problem statements related to encoders and autoencoders with the goal of elucidating variational formulations and establishing clear connections to information-theoretic concepts. Specifically, four problems with varying…
Electron, optical, and scanning probe microscopy methods are generating ever increasing volume of image data containing information on atomic and mesoscale structures and functionalities. This necessitates the development of the machine…
We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural…
Using ultrashort laser pulses, it has become possible to probe the dynamics of long-range order in solids on microscopic timescales. In the conventional description of symmetry-broken phases within time-dependent Ginzburg-Landau theory, the…
Recent advances in scanning tunneling and transmission electron microscopies (STM and STEM) have allowed routine generation of large volumes of imaging data containing information on the structure and functionality of materials. The…
Atomic-scale engineering typically involves bottom-up approaches, leveraging parameters such as temperature, partial pressures, and chemical affinity to promote spontaneous arrangement of atoms. These parameters are applied globally,…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…
Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…
A general, variational approach to derive low-order reduced systems for nonlinear systems subject to an autonomous forcing, is introduced. The approach is based on the concept of optimal parameterizing manifold (PM) that substitutes the…
Recent advances in scanning transmission electron and scanning probe microscopies have opened exciting opportunities in probing the materials structural parameters and various functional properties in real space with angstrom-level…
We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space…