# Learning from the Density to Correct Total Energy and Forces in First Principle Simulations

## TL;DR

This paper introduces a hybrid simulation approach that uses DFT to generate electronic densities and neural networks to correct energies and forces, achieving high accuracy at reduced computational cost.

## Contribution

It presents a novel framework combining DFT and machine learning to improve the accuracy and efficiency of molecular simulations.

## Key findings

- Achieves quantum chemical accuracy for liquid water at standard DFT cost.
- Attains high-level DFT accuracy with lower-cost baseline calculations.
- Demonstrates significant computational savings while maintaining accuracy.

## Abstract

We propose a new molecular simulation framework that combines the transferability, robustness and chemical flexibility of an ab initio method with the accuracy and efficiency of a machine learned force field. The key to achieve this mix is to use a standard density functional theory (DFT) simulation as a pre-processor for the atomic and molecular information, obtaining a good quality electronic density. General, symmetry preserving, atom-centered electronic descriptors are then built from this density to train a neural network to correct the baseline DFT energies and forces. These electronic descriptors encode much more information than local atomic environments, allowing a simple neural network to reach the accuracy required for the problem of study at a negligible cost. The balance between accuracy and efficiency is determined by the baseline simulation. This is shown in results where high level quantum chemical accuracy is obtained for simulations of liquid water at standard DFT cost, or where high level DFT-accuracy is achieved in simulations with a low-level baseline DFT calculation, at a significantly reduced cost.