Accelerating real-time hybrid-functional calculations with learned ACE and symmetry-based FFT reuse

Overview & Synopsis

Real-time hybrid-functional calculations require repeated reconstruction of nonlocal exchange, whose cost grows rapidly with Brillouin-zone sampling. We develop two methods to improve the efficiency of time evolution and spatial processing. The first learns the time evolution of adaptively compressed exchange (ACE) factors and predicts their updates, reducing the frequency of explicit reconstruction. The second uses crystal symmetry to reuse exchange fast Fourier transforms (FFTs) among equivalent real-space points. This symmetry-based FFT reuse (SBFR) reduces the number of FFTs while retaining the full $\bm k$-point sum. The methods can be used with a variety of hybrid functionals, and we use HSE06 in this work. Relative to an ACE reference using full-row mesh FFTs, learned prediction provides more than fivefold acceleration, SBFR more than fourteenfold, and their combination more than sixty-threefold. The combined method shows efficient parallel scaling. After learning, propagation takes less than 0.5 s per step. The reduced computational cost allows us to study nonlinear and nonequilibrium electron dynamics with hybrid functionals and to examine the role of excitonic effects in semiconductors and insulators.