  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.
