Related papers: Kohn-Sham equations as regularizer: building prior…

The Kohn-Sham scheme of density functional theory is one of the most widely used methods to solve electronic structure problems for a vast variety of atomistic systems across different scientific fields. While the method is fast relative to…

Kohn-Sham regularizer (KSR) is a differentiable machine learning approach to finding the exchange-correlation functional in Kohn-Sham density functional theory (DFT) that works for strongly correlated systems. Here we test KSR for weak…

Modern deep neural networks require a tremendous amount of data to train, often needing hundreds or thousands of labeled examples to learn an effective representation. For these networks to work with less data, more structure must be built…

Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields, ranging from materials science to biochemistry to…

We incorporate in the Kohn-Sham self consistent equation a trained neural-network projection from the charge density distribution to the Hartree-exchange-correlation potential $n \rightarrow V_{\rm Hxc}$ for possible numerical approach to…

In various scientific and engineering applications, there is typically an approximate model of the underlying complex system, even though it contains both aleatoric and epistemic uncertainties. In this paper, we present a principled method…

We demonstrate a convolutional neural network trained to reproduce the Kohn-Sham kinetic energy of hydrocarbons from electron density. The output of the network is used as a non-local correction to the conventional local and semi-local…

Machine learning is employed to build an energy density functional for self-bound nuclear systems for the first time. By learning the kinetic energy as a functional of the nucleon density alone, a robust and accurate orbital-free density…

Kohn-Sham density functional theory is the base of modern computational approaches to electronic structures. Their accuracy vitally relies on the exchange-correlation energy functional, which encapsulates electron-electron interaction…

The Kohn-Sham equations underlie many important applications such as the discovery of new catalysts. Recent machine learning work on catalyst modeling has focused on prediction of the energy, but has so far not yet demonstrated significant…

Although neural machine translation has made significant progress recently, how to integrate multiple overlapping, arbitrary prior knowledge sources remains a challenge. In this work, we propose to use posterior regularization to provide a…

As a proof of principle, self-consistent Kohn--Sham calculations are performed with the exact exchange-correlation functional. Finding the exact functional for even one trial density requires solving the interacting Schr\"odinger equation…

Two of the most widely used electronic structure theory methods, namely Hartree-Fock and Kohn-Sham density functional theory, both requires the iterative solution of a set of Schr\"odinger-like equations. The speed of convergence of such…

We train a neural network as the universal exchange-correlation functional of density-functional theory that simultaneously reproduces both the exact exchange-correlation energy and potential. This functional is extremely non-local, but…

A Kohn-Sham scheme based multi-task neural network is elaborated for the supervised learning of nuclear shell evolution. The training set is composed of the single-particle wave functions and occupation probabilities of 320 nuclei,…

In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on prediction of a physical system, for which in…

A detailed account of the Kohn-Sham algorithm from quantum chemistry, formulated rigorously in the very general setting of convex analysis on Banach spaces, is given here. Starting from a Levy-Lieb-type functional, its convex and lower…

In this thesis, we draw inspiration from both classical system identification and modern machine learning in order to solve estimation problems for real-world, physical systems. The main approach to estimation and learning adopted is…

Improving the predictive capability of molecular properties in ab initio simulations is essential for advanced material discovery. Despite recent progress making use of machine learning, utilizing deep neural networks to improve quantum…

Distilling data into compact and interpretable analytic equations is one of the goals of science. Instead, contemporary supervised machine learning methods mostly produce unstructured and dense maps from input to output. Particularly in…