# Fast Neural Network Approach for Direct Covariant Forces Prediction in Complex Multi-Element Extended Systems

## TL;DR

This paper introduces a novel neural network architecture that directly predicts atomic force vectors in complex multi-element systems, significantly reducing computational costs and enabling advanced molecular dynamics simulations.

## Contribution

The paper presents a staggered NNFF architecture that separately exploits rotation-invariant and covariant features to directly predict atomic forces, reducing computational expense by up to 480 times.

## Key findings

- Achieved ~180-480x speedup in structural feature calculation.
- Successfully predicted atomic forces in complex ternary and quaternary systems.
- Applicable to domains beyond material science for vector output prediction.

## Abstract

Neural network force field (NNFF) is a method for performing regression on atomic structure-force relationships, bypassing expensive quantum mechanics calculation which prevents the execution of long ab-initio quality molecular dynamics simulations. However, most NNFF methods for complex multi-element atomic systems indirectly predict atomic force vectors by exploiting just atomic structure rotation-invariant features and the network-feature spatial derivatives which are computationally expensive. We develop a staggered NNFF architecture exploiting both rotation-invariant and covariant features separately to directly predict atomic force vectors without using spatial derivatives, thereby reducing expensive structural feature calculation by ~180-480x. This acceleration enables us to develop NNFF which directly predicts atomic forces in complex ternary and quaternary-element extended systems comprised of long polymer chains, amorphous oxide, and surface chemical reactions. The staggered rotation-invariant-covariant architecture described here can also directly predict complex covariant vector outputs from local physical structures in domains beyond computational material science.

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Source: https://tomesphere.com/paper/1905.02791