Related papers: Proper Orthogonal Descriptors for Efficient and Ac…

A central concern of molecular dynamics simulations are the potential energy surfaces that govern atomic interactions. These hypersurfaces define the potential energy of the system, and have generally been calculated using either predefined…

We present a method to make highly accurate pseudopotentials for use with orbital-free density functional theory (OF-DFT) with given exchange-correlation and kinetic energy functionals, which avoids the compounding of errors of Kohn-Sham…

We demonstrate how to determine numerically nearly exact orthonormal orbitals that are optimal for evaluation of the energy of arbitrary (correlated) states of atoms and molecules by minimization of the energy Lagrangian. Orbitals are…

We probe the accuracy of linear ridge regression employing a three-body local density representation derived from the atomic cluster expansion. We benchmark the accuracy of this framework in the prediction of formation energies and atomic…

Computational screening for new and improved catalyst materials relies on accurate and low-cost predictions of key parameters such as adsorption energies. Here, we use recently developed compressed sensing methods to identify descriptors…

The Karhunen-Lo\`eve transform (KLT) stands as a well-established discrete transform, demonstrating optimal characteristics in data decorrelation and dimensionality reduction. Its ability to condense energy compression into a select few…

Machine learned interatomic potentials (MLIPs) are becoming a standard method for DFT-level accurate molecular dynamics simulation and large-scale studies of crystal energetics. Increasingly popular are universal pre-trained potentials,…

Machine learning techniques allow a direct mapping of atomic positions and nuclear charges to the potential energy surface with almost ab-initio accuracy and the computational efficiency of empirical potentials. In this work we propose a…

Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low order models of complex phenomena. In this work, we analyze the…

The dominant approach for learning local patch descriptors relies on small image regions whose scale must be properly estimated a priori by a keypoint detector. In other words, if two patches are not in correspondence, their descriptors…

The correlation and extraction of coherent structures from a turbulent flow is a principle objective of data-driven modal decomposition techniques. The Conditional space-time Proper Orthogonal Decomposition (CPOD) offers insight into…

We propose an efficient computational methodology for predicting the synthesizability of high entropy oxides (HEOs) in a large space of possible candidate compounds. HEOs are a growing field with an enormous potential chemical composition…

Interatomic potentials provide a means to simulate extended length and time scales that are outside the reach of ab initio calculations. The development of an interatomic potential for a particular material requires the optimization of the…

The Hohenberg-Kohn (HK) theorem -- the bedrock of density functional theory (DFT) -- establishes a universal map from the external potential to the energy. It also relates the electron density and atomic forces to the variation of the…

A theoretical scheme for the analysis of experimental data on IR spectroscopy for a quantum particle in a double well potential (DWP) is suggested. The analysis is based on the trigonometric DWP for which the exact analytic solution of the…

Fluid antenna systems (FAS) achieve spatial diversity by dynamically switching among $N$ densely packed ports, but the resulting spatially correlated Rayleigh channels render exact outage analysis intractable. Existing block-correlation…

In this paper, we introduce Proper Orthogonal Decomposition Neural Operators (PODNO) for solving partial differential equations (PDEs) dominated by high-frequency components. Building on the structure of Fourier Neural Operators (FNO),…

In a recent work [B. Koc et al., arXiv:2010.03750, SIAM J. Numer. Anal., to appear], the authors showed that including difference quotients (DQs) is necessary in order to prove optimal pointwise in time error bounds for proper orthogonal…

In this paper, we introduce the proper latent decomposition (PLD) as a generalization of the proper orthogonal decomposition (POD) on manifolds. PLD is a nonlinear reduced-order modeling technique for compressing high-dimensional data into…

This interdisciplinary study, which combines machine learning, statistical methodologies, high-fidelity simulations, and flow physics, demonstrates a new process for building an efficient surrogate model for predicting spatiotemporally…