Random close packing at extreme size ratios with an Adam-based inflation protocol

We present $\mathtt{\text{rcpgenerator}}$, an openly available code for generating $d$-dimensional dense, disordered, non-overlapping close packings from an arbitrary prescribed list of particle diameters. The method adapts the Clarke–Wiley inflation protocol, but instead uses the Adam optimizer to relax the particle configuration. Typically, particle coordinates are advanced with a single, global step size, which must shrink as the size ratio $S\equiv D_{\max }\mathrm{/}{D}_{\min }$ grows, generally stalling the optimization. Adam instead gives each coordinate its own adaptive step size, stabilizing the optimization time across a broader range of $S$. We demonstrate this in three-dimensional periodic tests that reach $S\sim 5\times {10}^5$ for a continuous lognormal distribution ($N\sim {10}^6$ diameters) and particle numbers up to $N\approx 5.6\times {10}^6$ for power-law distributions, with the densest packings reaching $\phi \simeq 0.87$, each completed in minutes to hours on a multicore machine. Across truncated-lognormal, truncated-power-law, and Weibull distributions, the resulting $\phi$ reproduces trends such as the locations of peaks and knees with distribution shape and $S$ found in prior numerical results and in the parameter-free Farr–Groot prediction, with a remaining offset typically $0.005$–$0.01$. Additionally, results are commensurate with multimodal packing densities measured in vibrated-bed experiments. The code and the complete per-case census behind every figure are released with the paper.