Mixed Precision Fermi-Operator Expansion on Tensor Cores From a Machine Learning Perspective

TL;DR

This paper introduces a novel mixed-precision recursive Fermi-operator expansion scheme implemented on tensor cores, leveraging machine learning techniques to improve electronic structure calculations with high computational efficiency.

Contribution

It formulates the Fermi-operator expansion as a differentiable neural network and optimizes its parameters to enhance convergence and accuracy in quantum mechanical electronic structure problems.

Findings

Achieved over 100 teraFLOPs performance on Nvidia A100 tensor cores.

Reduced number of layers for convergence through weight and bias optimization.

Accurately represented fractional occupation numbers at finite temperatures.

Abstract

We present a second-order recursive Fermi-operator expansion scheme using mixed precision floating point operations to perform electronic structure calculations using tensor core units. A performance of over 100 teraFLOPs is achieved for half-precision floating point operations on Nvidia's A100 tensor core units. The second-order recursive Fermi-operator scheme is formulated in terms of a generalized, differentiable deep neural network structure, which solves the quantum mechanical electronic structure problem. We demonstrate how this network can be accelerated by optimizing the weight and bias values to substantially reduce the number of layers required for convergence. We also show how this machine learning approach can be used to optimize the coefficients of the recursive Fermi-operator expansion to accurately represent fractional occupation numbers of the electronic states at finite temperatures.