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Using an end-to-end differentiable implementation of the Kohn-Sham self-consistent field equations, we obtain an accurate neural network-based exchange and correlation (XC) functional of the electronic density. The functional is optimized…

We propose a general machine learning-based framework for building an accurate and widely-applicable energy functional within the framework of generalized Kohn-Sham density functional theory. To this end, we develop a way of training…

We introduce a data-driven framework for approximating the convex set of $N$-representable two-electron reduced density matrices (2-RDMs). Traditional approaches characterize this set through linear matrix inequalities that define its…

Despite a large number of nonlocal kinetic energy density functionals (KEDFs) available for large-scale calculations, most of those nonlocal KEDFs designed for the extended systems cannot be directly applied to isolated systems. In this…

Machine learning is used to approximate the kinetic energy of one dimensional diatomics as a functional of the electron density. The functional can accurately dissociate a diatomic, and can be systematically improved with training. Highly…

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…

Density functional calculations can fail for want of an accurate exchange-correlation approximation. The energy can instead be extracted from a sequence of density functional calculations of conditional probabilities (CP-DFT). Simple CP…

This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…

Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of…

Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard…

The energy minimization involved in density functional calculations of electronic systems can be carried out using an exponential transformation that preserves the orthonormality of the orbitals. The energy of the system is then represented…

Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep…

A new method is proposed for constructing energy density functionals, which include a nonlocal dependence on the density gradients. This method is used to construct functionals for kinetic energy, which is a nonlocal generalization of the…

Koopmans spectral functionals are a powerful extension of Kohn-Sham density-functional theory (DFT) that enable the prediction of spectral properties with state-of-the-art accuracy. The success of these functionals relies on capturing the…

We present a differentiable formalism for learning free energies that is capable of capturing arbitrarily complex model dependencies on coarse-grained coordinates and finite-temperature response to variation of general system parameters.…

Kernel density estimation (KDE) is integral to a range of generative and discriminative tasks in machine learning. Drawing upon tools from the multidimensional calculus of variations, we derive an optimal weight function that reduces bias…

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…

Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In…

We present a real-space formulation for coarse-graining Kohn-Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss of accuracy. The approximation scheme consists of two steps.…

Density functional theory (DFT) is one of the main methods in Quantum Chemistry that offers an attractive trade off between the cost and accuracy of quantum chemical computations. The electron density plays a key role in DFT. In this work,…