Extensive deep neural networks for transferring small scale learning to large scale systems

TL;DR

This paper introduces an physically-motivated deep neural network topology called EDNN, capable of efficiently inferring extensive parameters of large systems with linear scaling, demonstrated on physical models and large-scale materials.

Contribution

The paper presents EDNN, a novel neural network architecture that leverages domain decomposition and physical interaction scales for scalable large-system inference.

Findings

EDNN achieves DFT-level accuracy for energy predictions of large systems.

EDNN can handle systems with over 35 million atoms in under 25 minutes.

The approach enables efficient, parallelizable inference for large-scale physical systems.

Abstract

We present a physically-motivated topology of a deep neural network that can efficiently infer extensive parameters (such as energy, entropy, or number of particles) of arbitrarily large systems, doing so with O(N) scaling. We use a form of domain decomposition for training and inference, where each sub-domain (tile) is comprised of a non-overlapping focus region surrounded by an overlapping context region. The size of these regions is motivated by the physical interaction length scales of the problem. We demonstrate the application of EDNNs to three physical systems: the Ising model and two hexagonal/graphene-like datasets. In the latter, an EDNN was able to make total energy predictions of a 60 atoms system, with comparable accuracy to density functional theory (DFT), in 57 milliseconds. Additionally EDNNs are well suited for massively parallel evaluation, as no communication is necessary during neural network evaluation. We demonstrate that EDNNs can be used to make an energy prediction of a two-dimensional 35.2 million atom system, over 1 square micrometer of material, at an accuracy comparable to DFT, in under 25 minutes. Such a system exists on a length scale visible with optical microscopy and larger than some living organisms.