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The use of machine learning methods for accelerating the design of crystalline materials usually requires manually constructed feature vectors or complex transformation of atom coordinates to input the crystal structure, which either…

The modeling of realistic magnetic materials requires the inclusion of defects. Based on the pseudospectral Landau-Lifshitz description of magnetisation dynamics, we propose a statistical model that takes into account defects, specifically…

Microstructure evolution, which plays a critical role in determining materials properties, is commonly simulated by the high-fidelity but computationally expensive phase-field method. To address this, we approximate microstructure evolution…

Machine learning offers attractive solutions to challenging image processing tasks. Tedious development and parametrization of algorithmic solutions can be replaced by training a convolutional neural network or a random forest with a high…

Inorganic crystal materials have broad application potential due to excellent physical and chemical properties, with elastic properties (shear modulus, bulk modulus) crucial for predicting materials' electrical conductivity, thermal…

In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the…

Many types of data from fields including natural language processing, computer vision, and bioinformatics, are well represented by discrete, compositional structures such as trees, sequences, or matchings. Latent structure models are a…

The inner structure of a material is called microstructure. It stores the genesis of a material and determines all its physical and chemical properties. While microstructural characterization is widely spread and well known, the…

The dominant paradigm in computational materials discovery relies on heavily parameterized deep architectures, including message-passing graph networks and equivariant models, that require millions of DFT-labeled training structures and…

Interacting defect systems are ubiquitous in materials under realistic scenarios, yet gaining an atomic-level understanding of these systems from a computational perspective is challenging - it often demands substantial resources due to the…

Feature selection is one of the most prominent learning tasks, especially in high-dimensional datasets in which the goal is to understand the mechanisms that underly the learning dataset. However most of them typically deliver just a flat…

Solving optimization problems with unknown parameters often requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the…

Machine learning models have become firmly established across all scientific fields. Extracting features from data and making inferences based on them with neural network models often yields high accuracy; however, this approach has several…

This work is directed to uncertainty quantification of homogenized effective properties for composite materials with complex, three dimensional microstructure. The uncertainties arise in the material parameters of the single constituents as…

Designing functional materials requires a deep search through multidimensional spaces for system parameters that yield desirable material properties. For cases where conventional parameter sweeps or trial-and-error sampling are impractical,…

Machine learning (ML) is widely used to explore crystal materials and predict their properties. However, the training is time-consuming for deep-learning models, and the regression process is a black box that is hard to interpret. Also, the…

This paper puts forward an integrated microstructure design methodology that replaces the common existing design approaches: 1) reconstruction of microstructures, 2) analyzing and quantifying material properties, and 3) inverse design of…

Rapidly determining structure-property correlations in materials is an important challenge in better understanding fundamental mechanisms and greatly assists in materials design. In microscopy, imaging data provides a direct measurement of…

Machine learning has emerged as a powerful approach in materials discovery. Its major challenge is selecting features that create interpretable representations of materials, useful across multiple prediction tasks. We introduce an…

A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…