Related papers: Generalized convex hull construction for materials…
High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…
Machine-learning function representations such as neural networks have proven to be excellent constructs for constitutive modeling due to their flexibility to represent highly nonlinear data and their ability to incorporate constitutive…
We discuss the method of bounding suprema of canonical processes based on the inclusion of their index set into a convex hull of a well-controlled set of points. While the upper bound is immediate, the reverse estimate was established to…
The interfacial structures and interactions of two-dimensional (2D) materials on solid substrates are of fundamental importance for the fabrication and application of 2D materials. However, selection of a suitable solid substrate to grow 2D…
There has been a long history of works showing that neural networks have hard time extrapolating beyond the training set. A recent study by Balestriero et al. (2021) challenges this view: defining interpolation as the state of belonging to…
Convex clustering is a well-regarded clustering method, resembling the similar centroid-based approach of Lloyd's $k$-means, without requiring a predefined cluster count. It starts with each data point as its centroid and iteratively merges…
In this study, we present a novel approach along with the needed computational strategies for efficient and scalable feature engineering of the crystal structure in compounds of different chemical compositions. This approach utilizes a…
An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of provable guarantees. In this work, we show how…
Machine Learning (ML) techniques are revolutionizing the way to perform efficient materials modeling. Nevertheless, not all the ML approaches allow for the understanding of microscopic mechanisms at play in different phenomena. To address…
When a hole is introduced into an elastic material, it will usually act to reduce the overall mechanical stiffness. A general ambition is to investigate whether a stiff shell around the hole can act to maintain the overall mechanical…
As data-driven methods rise in popularity in materials science applications, a key question is how these machine learning models can be used to understand microstructure. Given the importance of process-structure-property relations…
Organizations are collecting increasingly large amounts of data for data driven decision making. These data are often dumped into a centralized repository, e.g., a data lake, consisting of thousands of structured and unstructured datasets.…
In this paper, we consider the polyhedral structure of the unit commitment polytope. In particular, we provide the convex hull results for the problem under the following different settings: 1) the convex hulls for the integrated…
Statistical inference of the dependence between objects often relies on covariance matrices. Unless the number of features (e.g. data points) is much larger than the number of objects, covariance matrix cleaning is necessary to reduce…
A main goal of data-driven materials research is to find optimal low-dimensional descriptors, allowing us to predict a physical property, and to interpret them in a human-understandable way. In this work, we advance methods to identify…
Tensegrity structures have been extensively studied over the last years due to their potential applications in modern engineering like metamaterials, deployable structures, planetary lander modules, etc. Many of the form-finding methods…
Many complex tasks can be decomposed into simpler, independent parts. Discovering such underlying compositional structure has the potential to enable compositional generalization. Despite progress, our most powerful systems struggle to…
Oceanic surface flows are dominated by finite-time Lagrangian coherent structures that separate regions of qualitatively different dynamical behavior. Among these, eddy boundaries are of particular interest. Their exact identification is…
A number of results related to statistical classification on convex sets are presented. In particular, the focus is on the case where some of the covariates in the data and observation being classified can be missing. The form of the…
Automating the design of heuristic search methods is an active research field within computer science, artificial intelligence and operational research. In order to make these methods more generally applicable, it is important to eliminate…