Related papers: Learning Neural Free-Energy Functionals with Pair-…

Finding accurate exchange-correlation (XC) functionals remains the defining challenge in density functional theory (DFT). Despite 40 years of active development, the desired chemical accuracy is still elusive with existing functionals. We…

In this paper, we investigate whether Variational Principles can be associated with the Helmholtz equation subject to impedance (absorbing) boundary conditions. This model has been extensively studied in the literature from both…

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…

Accurate free-energy calculations are essential for predicting thermodynamic properties and phase stability, but existing methods are limited: phonon-based approaches neglect anharmonicity and liquids, while molecular dynamics (MD) is…

Free energy functionals of Ginzburg-Landau type lie at the heart of a broad class of continuum dynamical models, such as the Cahn-Hilliard and Swift-Hohenberg equations. Despite the wide use of such models, the assumptions embodied in the…

Model Hamiltonians with long-range interaction yield energies that are corrected taking into account the universal behavior of the electron-electron interaction at short range. Although the intention of the paper is to explore the…

We present a density functional theory (DFT) for lattice models with local electron-electron (e-e) and electron-phonon (e-ph) interactions. Exchange-correlation potentials are derived via dynamical mean field theory for the…

We present a method for constructing a special type of shallow neural network that learns univariate meromorphic functions with pole-type singularities. Our method is based on using a finite set of Laurent coefficients as input information,…

The unprecedented predictive success of deep generative models in complex many-body systems, such as AlphaFold3, raises an epistemological question: do these networks merely memorize data distributions via high-dimensional interpolation, or…

We study Density Functional Theory models for systems which are translationally invariant in some directions, such as a homogeneous 2-d slab in the 3-d space. We show how the different terms of the energy are modified and we derive reduced…

Energy functionals serve as the basis for different models and methods in quantum and classical many-particle physics. Arguably, one of the most successful and widely used approaches in material science at both ambient and extreme…

Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional…

Employing a local formula for the electron-electron interaction energy, we derive a self-consistent approximation for the total energy of a general $N$-electron system. Our scheme works as a local variant of the Thomas-Fermi approximation…

Density functional theory (DFT) is a cornerstone of computational chemistry and materials science, but its computational cost limits its use in large-scale and high-throughput applications. While machine learning has accelerated energy…

The free energy of a system is central to many material models. Although free energy data is not generally found directly, its derivatives can be observed or calculated. In this work, we present an Integrable Deep Neural Network (IDNN) that…

We introduce a new approach to learning in hierarchical latent-variable generative models called the "distributed distributional code Helmholtz machine", which emphasises flexibility and accuracy in the inferential process. In common with…

Density functional theory (DFT) is the de facto approach for predicting self-consistent-field electronic structures of ground-state configurations of complex atoms, molecules, and solids and providing their property data for materials…

Accurate description of deformed atomic nuclei by the orbital-free density functional theory has been a longstanding textbook challenge, due to the difficulty in accounting for the intricate quantum shell effects that are present in such…

In this paper, we aim at establishing an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN). In contrast to the classical regression methods, the input variables of distribution…

We propose and evaluate a system which learns a neuralnetwork heuristic function for forward search-based, satisficing classical planning. Our system learns distance-to-goal estimators from scratch, given a single PDDL training instance.…