# Kinetic Energy Density Functionals by Axiomatic Approach

## TL;DR

This paper introduces an axiomatic method to derive physically valid kinetic energy density functionals, demonstrating significant accuracy improvements over standard models through statistical training on 1D systems, advancing orbital-free DFT.

## Contribution

It presents a new axiomatic framework for formulating kinetic energy density functionals and shows how to optimize their accuracy using statistical training on model problems.

## Key findings

- Achieved mean relative accuracy better than 10^{-4} for systems with four occupied states.
- The approach captures most known forms of one-point KEDFs.
- Fitting coefficients to known KEDFs approaches exact analytic values.

## Abstract

An axiomatic approach is herein used to determine the physically acceptable forms for general $D$-dimensional kinetic energy density functionals (KEDF). The resulted expansion captures most of the known forms of one-point KEDFs. By statistically training the KEDF forms on a model problem of non-interacting kinetic energy in 1D (6 terms only), the mean relative accuracy for 1000 randomly generated potentials is found to be better than the standard KEDF by several orders of magnitudes. The accuracy improves with the number of occupied states and was found to be better than $10^{-4}$ for a system with four occupied states. Furthermore, we show that free fitting of the coefficients associated with known KEDFs approaches the exactly analytic values. The presented approach can open a new route to search for physically acceptable kinetic energy density functionals and provide an essential step towards more accurate large-scale orbital free density functional theory calculations.