MINT32: A Minimum-Image INT32 Coordinate Representation for Fast and Accurate Molecular Dynamics on GPUs

Molecular dynamics (MD) simulations on GPUs have historically required a trade-off between performance and numerical precision. Mixed-precision approaches, such as AMBER SPFP and OpenMM, accumulate forces with high precision while representing coordinates with single precision (FP32). This design introduces a fundamental "noise floor": quantization error in FP32 coordinates injects artificial heat into the system, degrading the long-term stability and distorting the kinetic properties. We introduce MINT32, a coordinate representation that maps the simulation box onto a 32-bit integer grid. MINT32 achieves a uniform spatial resolution of approximately 0.01 fm, roughly 2 orders of magnitude finer than the worst-case FP32 spacing. This precision comes without the memory bandwidth penalties associated with 64-bit integer arithmetic. In addition, MINT32 offers algorithmic elegance through self-wrapping, whereby periodic boundary conditions are enforced via exact integer overflow, eliminating branch divergence entirely. Benchmark results on three systems spanning 12K to 91K atoms demonstrate that MINT32 reduces energy drift in microcanonical (NVE) simulations by 5-10×, delivering double-precision-level stability for challenging PME water systems and large protein benchmarks alike. When paired with single-precision force evaluations, MINT32 outperforms conventional mixed-precision models, an observation reproduced across two independent protein systems, indicating that coordinate precision is the dominant factor governing simulation stability. The fixed-point grid further supports tightened SHAKE tolerances of 10^-7 Å in production-length runs, with no observed convergence failures in the benchmarks reported here. Tile-matched benchmarks confirm that MINT32 integer arithmetic incurs negligible overhead (0-5%) relative to standard FP32 coordinates on consumer-grade GPUs; the 11-16% speed difference observed in the unoptimized prototype is attributable to the use of older 32 × 32 atom tiles rather than the production 16 × 16 layout. These findings serve as a conceptual foundation for future molecular dynamics (MD) engines. The primary objective of this study is to identify an optimal coordinate representation for the next-generation MD software. To this end, we present a prototype framework designed to isolate and evaluate the numerical behavior of coordinate representations in molecular dynamics, with a modified version of the AMBER simulation package serving solely as a testbed.