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Flow-based generative models can be viewed through a physics lens: sampling transports a particle from noise to data by integrating a time-varying velocity field, and each sample corresponds to a trajectory with its own dynamical effort.…
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…
The accuracy and effectiveness of Hermite spectral methods for the numerical discretization of partial differential equations on unbounded domains, are strongly affected by the amplitude of the Gaussian weight function employed to describe…
The average energy curvature as a function of the particle number is a molecule-specific quantity, which measures the deviation of a given functional from the exact conditions of density functional theory (DFT). Related to the lack of…
We explore the feasibility of using machine learning methods to obtain an analytic form of the classical free energy functional for two model fluids, hard rods and Lennard--Jones, in one dimension . The Equation Learning Network proposed in…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
The construction of a better exchange-correlation potential in time-dependent density functional theory (TDDFT) can improve the accuracy of TDDFT calculations and provide more accurate predictions of the properties of many-electron systems.…
The standard way to calculate the Kohn-Sham orbitals utilizes an approximation of the potential. The approximation consists in a projection of the potential into a finite subspace of basis functions. The orbitals, calculated with the…
Differentiable programming has facilitated numerous methodological advances in scientific computing. Physics engines supporting automatic differentiation have simpler code, accelerating the development process and reducing the maintenance…
We present a $\Delta$-machine learning model for obtaining Kohn-Sham accuracy from orbital-free density functional theory (DFT) calculations. In particular, we employ a machine learned force field (MLFF) scheme based on the kernel method to…
Within exact electron density-functional theory, we investigate Kohn-Sham (KS) potentials, orbital energies, and non-interacting kinetic energies of the fractional ions of Li, C and F. We use quantum Monte Carlo densities as input, which…
We study the performance of fourth-order gradient expansions of the kinetic energy density (KED) in semi-local kinetic energy functionals depending on the density-dependent variables. The formal fourth-order expansion is convergent for…
Energy-based models (EBMs) have experienced a resurgence within machine learning in recent years, including as a promising alternative for probabilistic regression. However, energy-based regression requires a proposal distribution to be…
Learning the governing equations from time-series data has gained increasing attention due to its potential to extract useful dynamics from real-world data. Despite significant progress, it becomes challenging in the presence of noise,…
We present a hybrid scheme based on classical density functional theory and machine learning for determining the equilibrium structure and thermodynamics of inhomogeneous fluids. The exact functional map from the density profile to the…
Neural density estimators are flexible families of parametric models which have seen widespread use in unsupervised machine learning in recent years. Maximum-likelihood training typically dictates that these models be constrained to specify…
Effectively leveraging prior knowledge of a system's physics is crucial for applications of machine learning to scientific domains. Previous approaches mostly focused on incorporating physical insights at the architectural level. In this…
In practical implementations of density-functional theory, the only term where an orbital description is needed is the kinetic one. Even this term in principle depends on the density only, but its explicit form is unknown. We provide a…
In orbital-free density functional theory the kinetic potential (KP), the functional derivative of the kinetic energy density functional, appears in the Euler equation for the electron density and may be more amenable to simple…
We try to improve the Thomas-Fermi model for the total energy and electron density of atoms and molecules by directly modifying the Euler equation for the electron density, which we argue is less affected by nonlocal corrections. Here we…