Related papers: Solving the Schr\"odinger Equation in the Configur…
Machine-learning generative methods for material design are constructed by representing a given chemical structure, either a solid or a molecule, over appropriate atomic features, generally called structural descriptors. These must be fully…
The design of fusion devices is typically based on computationally expensive simulations. This can be alleviated using high aspect ratio models that employ a reduced number of free parameters, especially in the case of stellarator…
Solving the Schr\"odinger equation is key to many quantum mechanical properties. However, an analytical solution is only tractable for single-electron systems. Recently, neural networks succeeded at modeling wave functions of many-electron…
The non-relativistic Schrodinger equation with the linear and Coulomb potentials is solved numerically in configuration space using the relaxation method. The numerical method presented in this paper is a plain explicit Schrodinger solver…
The fundamental problem faced in quantum chemistry is the calculation of molecular properties, which are of practical importance in fields ranging from materials science to biochemistry. Within chemical precision, the total energy of a…
We propose an approximate solution of the time-dependent Schr\"odinger equation using the method of stationary states combined with a variational matrix method for finding the energies and eigenstates. We illustrate the effectiveness of the…
Understanding structure-property relationships in materials is fundamental in condensed matter physics and materials science. Over the past few years, machine learning (ML) has emerged as a powerful tool for advancing this understanding and…
The discovery of inorganic crystal structures with targeted properties is a significant challenge in materials science. Generative models, especially state-of-the-art diffusion models, offer the promise of modeling complex data…
The size of chemical compound space is too large to be probed exhaustively. This leads high-throughput protocols to drastically subsample and results in sparse and non-uniform datasets. Rather than arbitrarily selecting compounds, we…
We propose a numerical method for evaluating eigenvalues and eigenfunctions of Schr\"odinger operators with general confining potentials. The method is selective in the sense that only the eigenvalue closest to a chosen input energy is…
Although optimization is the longstanding algorithmic backbone of machine learning, new models still require the time-consuming implementation of new solvers. As a result, there are thousands of implementations of optimization algorithms…
We develop several configuration interaction approaches for characterizing the electronic structure of an adsorbate on a metal surface (at least in model form). When one can separate adsorbate from substrate, these methods can achieve a…
Machine learning has recently emerged as a powerful tool for generating new molecular and material structures. The success of state-of-the-art models stems from their ability to incorporate physical symmetries, such as translation,…
Due to the intrinsic complexity and nonlinearity of chemical reactions, direct applications of traditional machine learning algorithms may face with many difficulties. In this study, through two concrete examples with biological background,…
The high-resolution visualization of atomic structures is significant for understanding the relationship between the microscopic configurations and macroscopic properties of materials. However, a rapid, accurate, and robust approach to…
Sampling from known probability distributions is a ubiquitous task in computational science, underlying calculations in domains from linguistics to biology and physics. Generative machine-learning (ML) models have emerged as a promising…
Column generation (CG) is a well-established method for solving large-scale linear programs. It involves iteratively optimizing a subproblem containing a subset of columns and using its dual solution to generate new columns with negative…
We present a generalization of the often-used Crank-Nicolson (CN) method of obtaining numerical solutions of the time-dependent Schr\"odinger equation. The generalization yields numerical solutions accurate to order $(\Delta x)^{2r-1}$ in…
We obtain a complete series solution of stationary Schr\"odinger's equation in the general quantum systems. It is exact in the sense that any approximation means is not used, or that the whole corrections or contributions from all order…
Machine learning (ML) offers considerable promise for the design of new molecules and materials. In real-world applications, the design problem is often domain-specific, and suffers from insufficient data, particularly labeled data, for ML…