Reduced-Precision Stochastic Simulation for Mathematical Biology

TL;DR

This paper explores using reduced-precision floating-point arithmetic, especially mixed-precision with stochastic rounding, to accelerate stochastic simulation algorithms in biology without losing accuracy.

Contribution

It demonstrates that mixed-precision SSA with stochastic rounding maintains statistical fidelity and offers significant speedups, facilitating efficient biological simulations.

Findings

Mixed-precision SSA closely matches 64-bit reference statistics.

Uniform 16-bit precision introduces biases, but stochastic rounding fixes this.

Mixed-precision yields 2-4x data size reduction and up to 1.5x speedup.

Abstract

The stochastic simulation algorithm (SSA) is widely used to perform exact forward simulation of discrete stochastic processes in biology. However, the computational cost, driven by sequential event-by-event sampling across large ensembles, remains a computational barrier. We investigate whether reduced-precision floating-point arithmetic can accelerate SSA without degrading statistical fidelity, drawing on the success of reduced-precision methods in weather and climate modelling. We evaluate two strategies across five canonical models (birth--death, Schl\"{o}gl, Telegraph, dimerisation, repressilator): (i) mixed precision, computing propensities in 16-bit while maintaining accumulators in 32-bit; and (ii) uniform precision, performing all arithmetic in 16-bit. Mixed-precision SSA produces ensemble statistics that closely match the 64-bit reference for all models, as measured by Kolmogorov--Smirnov tests and Wasserstein distances. Under uniform precision, deterministic rounding introduces systematic biases across several models, with catastrophic failures in some cases. Stochastic rounding (SR) and propensity normalisation eliminate these biases, restoring distributional fidelity across all models tested (KS $p > 0.05$). Our results establish mixed-precision SSA with SR as a viable acceleration strategy for mathematical biology: 16-bit formats shrink per-variable data size by $2$--$4\times$ relative to \texttt{fp32}/\texttt{fp64}, yielding comparable reductions in memory footprint and up to $\sim 1.5\times$ wall-clock speedup on CPU hardware that lacks native 16-bit arithmetic. As a hardware-level acceleration, mixed-precision SSA complements algorithmic methods such as tau-leaping and maps naturally onto modern GPU and TPU architectures with native 16-bit arithmetic.