Quantum Perturbation Theory Using Tensor Cores and a Deep Neural Network

Time-independent quantum response calculations are performed using Tensor cores. This is achieved by mapping density matrix perturbation theory onto the computational structure of a deep neural network. The main computational cost of each deep layer is dominated by tensor contractions, i.e., dense matrix-matrix multiplications, in mixed-precision arithmetics, which achieves close to peak performance. Quantum response calculations are demonstrated and analyzed using self-consistent charge density-functional tight-binding theory as well as coupled-perturbed Hartree-Fock theory. For linear response calculations, a novel parameter-free convergence criterion is presented that is well-suited for numerically noisy low-precision floating point operations and we demonstrate a peak performance of almost 200 Tflops using the Tensor cores of two Nvidia A100 GPUs.

Automated summary

In this paper, density matrix perturbation theory is mapped onto the computational structure of a deep neural network, and time-independent quantum response calculations are performed using Tensor cores. The main computational cost of each deep layer is dominated by tensor contractions in mixed-precision arithmetics, achieving close to peak performance. Quantum response calculations are demonstrated and analyzed with self-consistent charge density-functional tight-binding theory and coupled-perturbed Hartree-Fock theory. A novel parameter-free convergence criterion is presented for linear response calculations, suitable for numerically noisy low-precision floating point operations, and a peak performance of almost 200 Tflops is demonstrated using the Tensor cores of two Nvidia A100 GPUs.