Quantum Perturbation Theory Using Tensor Cores and a Deep Neural Network

Abstract

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.

A Perspective on Sustainable Computational Chemistry Software Development and Integration

“…In addition to a need for the development of novel programming models, compiler technologies, and optimized libraries to target these platforms, the move to accelerators often requires the re-evaluation of algorithmic design due to fundamental differences in execution strategies being appropriate only for particular classes of workloads (e.g., vectorized, low precision, and high arithmetic-intensity). AI-hardware’s low mixed-precision floating-point operations, in particular, add new challenges to the numerical accuracy, algorithm stability, and convergence estimates for quantum chemical methodologies. − …”

“…While there has been an enormous effort afforded to the incorporation of modern HPC platforms into the scientific computing and computational chemistry ecosystems, − these efforts have been fraught with challenges and cannot yet be considered as mature as their legacy counterparts targeting CPU architectures. Outstanding challenges and opportunities in these areas include how best to leverage low-precision arithmetic for computational chemistry applications and how to develop new or map existing algorithms onto particular compute patterns (such as tensor contractions, convolutions, etc.)…”

DGEMM on integer matrix multiplication unit

“…For instance, Haidar et al used the FP16 Tensor Core to solve FP64 linear equations with an iterative refinement method (Haidar et al, 2018). Finkelstein et al have employed FP16 Tensor Cores to perform time-independent quantum response calculations with sufficient accuracy (Finkelstein et al, 2022). Our previous study has utilized FP16 Tensor Cores to improve the throughput of quantum circuit simulation by emulating single-precision matrix multiplication using an error correction method and avoiding rounding inside Tensor Cores without loss of accuracy (Ootomo et al, 2023; Ootomo and Yokota, 2022).…”

Dynamic Precision Approach for Accelerating Large-Scale Eigenvalue Solvers in Electronic Structure Calculations on Graphics Processing Units

“…A mixed precision (MP) method has been extensively studied to accelerate various scientific computations, including electronic structure calculations. ,,,,− In this method, some part of DP operations is replaced by SP to achieve acceleration. The MP approach has been studied a lot, especially in linear algebra algorithms, − ,, which have also been applied to electronic structure calculations. ,, A detailed explanation can be found in recent review papers. − Many methods using MP have also been proposed to accelerate two-electron integrals in the Hartree–Fock theory and perturbation theory. ,,, …”