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

• Published in: Journal of chemical theory and computation Vol. 17; no. 4; pp. 2256 - 2265
• Main Authors: Finkelstein, Joshua, Smith, Justin S, Mniszewski, Susan M, Barros, Kipton, Negre, Christian F. A, Rubensson, Emanuel H, Niklasson, Anders M. N
• Format: Journal Article
• Language: English
• Published: United States American Chemical Society 13-04-2021
• Subjects: algorithms, chemical calculations; Artificial neural networks; deep neural networks; Electron states; Electronic structure; fermi operator expansion; Floating point arithmetic; Hamiltonians; INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; layers; Machine learning; Mathematical analysis; mathematics; mixed precision; Optimization; Quantum Electronic Structure; Quantum mechanics; tensor cores; Tensors; Thermal expansion
• DOI: 10.1021/acs.jctc.1c00057
• EISSN: 1549-9626
• ISSN: 1549-9618; 1549-9626

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 the fractional occupation numbers of the electronic states at finite temperatures.