Lukas Berg | Searcharxiv

arXiv2026

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

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.

physics.comp-ph↗

arXiv2025

CubeletWorld: A New Abstraction for Scalable 3D Modeling

Modern cities produce vast streams of heterogeneous data, from infrastructure maps to mobility logs and satellite imagery. However, integrating these sources into coherent spatial models for planning and prediction remains a major challenge. Existing agent-centric methods often rely on direct environmental sensing, limiting scalability and raising privacy concerns. This paper introduces CubeletWorld, a novel framework for representing and analyzing urban environments through a discretized 3D grid of spatial units called cubelets. This abstraction enables privacy-preserving modeling by embedding diverse data signals, such as infrastructure, movement, or environmental indicators, into localized cubelet states. CubeletWorld supports downstream tasks such as planning, navigation, and occupancy prediction without requiring agent-driven sensing. To evaluate this paradigm, we propose the CubeletWorld State Prediction task, which involves predicting the cubelet state using a realistic dataset containing various urban elements like streets and buildings through this discretized representation. We explore a range of modified core models suitable for our setting and analyze challenges posed by increasing spatial granularity, specifically the issue of sparsity in representation and scalability of baselines. In contrast to existing 3D occupancy prediction models, our cubelet-centric approach focuses on inferring state at the spatial unit level, enabling greater generalizability across regions and improved privacy compliance. Our results demonstrate that CubeletWorld offers a flexible and extensible framework for learning from complex urban data, and it opens up new possibilities for scalable simulation and decision support in domains such as socio-demographic modeling, environmental monitoring, and emergency response. The code and datasets can be downloaded from here.

cs.LG↗