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This paper shows how data-driven machine learning approaches can improve growth control, reproducibility, and physical insight in the pulsed laser deposition (PLD) growth of correlated oxides. Despite well-known relationships between growth…

A comparison of the {\it ab initio} calculations using the i-DMFT Method by Di Liu et al. (2025) with benchmark potential curves for three HX(F,Cl,Br) halides shows their inaccuracy in the domain around equilibrium - they do not reproduce…

As a core technology for green chemical synthesis and electrochemical energy storage, electrocatalysis is central to decarbonization strategies aimed at combating climate change. In this context, computational and machine learning driven…

We introduce machine-learned potentials for Ag-Pd to describe the energy of alloy configurations over a wide range of compositions. We compare two different approaches. Moment tensor potentials (MTP) are polynomial-like functions of…

The kinetic energy (KE) kernel, which is defined as the second order functional derivative of the KE functional with respect to density, is the key ingredient to the construction of KE models for orbital free density functional theory…

Kolmogorov $n$-widths and low-rank approximations are studied for families of elliptic diffusion PDEs parametrized by the diffusion coefficients. The decay of the $n$-widths can be controlled by that of the error achieved by best $n$-term…

In the density functional (DF) theory of Kohn and Sham, the kinetic energy of the ground state of a system of noninteracting electrons in a general external field is calculated using a set of orbitals. Orbital free methods attempt to…

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) - built, e.g., through proper orthogonal decomposition (POD) - when applied to…

Atomistic simulations are a powerful tool for studying the dynamics of molecules, proteins, and materials on wide time and length scales. Their reliability and predictiveness, however, depend directly on the accuracy of the underlying…

We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternatives of traditional methods such as Singular Value…

We study property prediction for crystal materials. A crystal structure consists of a minimal unit cell that is repeated infinitely in 3D space. How to accurately represent such repetitive structures in machine learning models remains…

Artificial neural networks are used to fit a potential energy surface. We demonstrate the benefits of using not only energies, but also their first and second derivatives as training data for the neural network. This ensures smooth and…

The evaluation of long-range potentials in periodic, many-body systems arises as a necessary step in the numerical modeling of a multitude of interesting physical problems. Direct evaluation of these potentials requires O(N^2) operations…

Electronic structure descriptors are computationally efficient quantities used to construct qualitative correlations for a variety of properties. In particular, the oxygen p-band center has been used to guide material discovery and…

Accurate structural analysis is essential to gain physical knowledge and understanding of atomic-scale processes in materials from atomistic simulations. However, traditional analysis methods often reach their limits when applied to…

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is…

Large-scale atomistic simulations rely on interatomic potentials providing an efficient representation of atomic energies and forces. Modern machine-learning (ML) potentials provide the most precise representation compared to electronic…

Most model reduction methods reduce the state dimension and then temporally evolve a set of coefficients that encode the state in the reduced representation. In this paper, we instead employ an efficient representation of the entire…

Interatomic potentials are essential to go beyond ab initio size limitations, but simulation results depend sensitively on potential parameters. Forward propagation of parameter variation is key for uncertainty quantification, whilst…

The representations of a compound, called "descriptors" or "features", play an essential role in constructing a machine-learning model of its physical properties. In this study, we adopt a procedure for generating a systematic set of…