Numerical field optimization for enhanced efficiency in time-reversible gradient computation of open-source GPU-accelerated FDTD simulations

Abstract

Finite-difference time-domain (FDTD) simulations often involve physical quantities spanning multiple orders of magnitude, such as the speed of light or electromagnetic field amplitudes. The standard practice for maintaining numerical accuracy in many FDTD implementations is to use 32-bit or 64-bit floating-point values to represent the electric and magnetic fields. However, this approach is not always optimal when recording field values, particularly during time-reversible gradient computation where electric and magnetic field values need to be saved at the boundary of the simulation domain. Since this memory bottleneck is often the limiting factor in time-reversible inverse design for nanophotonics, we present two field optimizations for enhancing memory efficiency in FDTD simulations. Using a smaller bit-width representation of field values as well as interpolation, we achieve similar accuracy at lower memory cost. This approach is particularly beneficial for GPU-accelerated computing, where reduced-precision data types are increasingly preferred due to their computational efficiency and prevalence in machine learning frameworks. We integrate our approach into FDTDX, an open-source, differentiable FDTD solver that natively supports time-reversible gradient computation. Our approach is especially important for future developments towards large-scale open-source simulations, which are critical for advancing computational nanophotonic applications.