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

Molecular dynamics 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 in high precision while representing coordinates in single precision (FP32). This design introduces a fundamental “noise floor”: quantization error in FP32 coordinates injects artificial heat into the system, degrading long-term stability and distorting kinetic properties. We introduce MINT32, a coordinate representation that maps the simulation box onto a 32-bit integer grid. MINT32 achieves a spatial resolution of approximately 0.01 fm, roughly 300 times finer than FP32, 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 demonstrate that MINT32 reduces energy drift in microcanonical (NVE) simulations by nearly an order of magnitude (7--10x), delivering double-precision-level stability for challenging PME water systems. When paired with single-precision force evaluations, MINT32 outperforms conventional mixed-precision models, indicating that coordinate precision is the dominant factor governing simulation stability in the systems examined. The fixed-point grid further enables constraint solvers (SHAKE) to converge to tolerances of 10A, effectively eliminating constraint instabilities. Our implementation achieves approximately 85\% of production throughput on consumer-grade GPUs, serving as a conceptual foundation for future molecular dynamics (MD) engines. The primary objective of this study is to identify an optimal coordinate representation for 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.