Related papers: Analytical classical density functionals from an e…

We introduce a novel deep learning algorithm for computing convex conjugates of differentiable convex functions, a fundamental operation in convex analysis with various applications in different fields such as optimization, control theory,…

Adversarial Robustness Distillation (ARD) has emerged as an effective method to enhance the robustness of lightweight deep neural networks against adversarial attacks. Current ARD approaches have leveraged a large robust teacher network to…

Classical density functional theory (DFT) provides an exact variational framework for determining the equilibrium properties of inhomogeneous fluids. We report a generalization of DFT to treat the non-equilibrium dynamics of classical…

The implicit solvent approach offers a computationally efficient framework to model solvation effects in molecular simulations. However, its accuracy often falls short compared to explicit solvent models, limiting its use in precise…

In modeling low-dimensional electronic nanostructures, the evaluation of the electron-electron interaction is a challenging task. Here we present an accurate and practical density-functional approach to the two-dimensional many-electron…

We use voxel deep neural networks to predict energy densities and functional derivatives of electron kinetic energies for the Thomas-Fermi model and Kohn-Sham density functional theory calculations. We show that the ground-state electron…

Density functional theory (DFT) offers a desirable balance between quantitative accuracy and computational efficiency in practical many-electron calculations. Its central component, the exchange-correlation energy functional, has been…

Hohenberg and Kohn have proven that the electronic energy and the one-particle electron density can, in principle, be obtained by minimizing an energy functional with respect to the density. While decades of theoretical work have produced…

We report a direct scheme calculation of kinetic energy functional derivative using Machine Learning. Support Vector Regression and Kernel Ridge Regression techniques were independently employed to estimate the kinetic energy functional and…

We introduce a new computationally efficient and accurate classical density-functional theory for water and apply it to hydration of hard spheres and inert gas atoms. We find good agreement with molecular dynamics simulations for the…

A compact analytical form is derived via an integration approach for the interaction between a sphere and a thin rod of both finite and infinite lengths, with each object treated as a continuous medium of materials points interacting by the…

For the nonlinear Richards equation as an unsaturated flow through heterogeneous media, we build a new coarse-scale approximation algorithm utilizing numerical homogenization. This approach follows deep neural networks (DNNs) to quickly and…

Despite prior advances in PINNs, significant challenges remain in localized solid mechanics problems because of the limitations of single network formulations in simultaneous resolution of smooth global responses and near-tip singularities,…

Generative models are a promising tool to address the sampling problem in multi-body and condensed-matter systems in the framework of statistical mechanics. In this work, we show that normalizing flows can be used to learn a transformation…

Traditional energy-based learning models associate a single energy metric to each configuration of variables involved in the underlying optimization process. Such models associate the lowest energy state to the optimal configuration of…

We propose a methodology to generate hybrid machine learning models for the potential energy surface trained simultaneously on data from ab initio electronic structure calculations and on thermodynamic and/or structural observables from…

Deep energy-based models are powerful, but pose challenges for learning and inference (Belanger and McCallum, 2016). Tu and Gimpel (2018) developed an efficient framework for energy-based models by training "inference networks" to…

We introduce a machine-learning density-functional-theory formalism for the spinless Hubbard model in one dimension at both zero and finite temperature. In the zero-temperature case this establishes a one-to-one relation between the site…

This work presents an efficient numerical method to evaluate the free energy density and associated thermodynamic quantities of (quasi) one-dimensional classical systems, by combining the transfer operator approach with a numerical…

Recently Dijkman et al. (arXiv:2403.15007) proposed training classical neural density functionals via bulk pair-correlation matching. We show their method to be an efficient regularizer for neural functionals based on local learning of…