Adaptive mixed-precision Monte Carlo integration on GPUs

Abstract Monte Carlo integration (MCI) is widely used for evaluating high-dimensional or non-analytic functions, but its large number of function evaluations can make it computationally demanding. As modern scientific applications increasingly rely on GPU acceleration, balancing numerical accuracy and performance has become a key challenge. To address this, we present a GPU-accelerated mixed-precision MCI framework that adaptively selects precision based on local numerical behavior using heuristics derived from gradient, variance, and average value analysis. Two precision allocation strategies are explored: term-wise and region-wise, both implemented with CUDA batch processing to maximize GPU efficiency. Experimental results on representative test functions of varying dimensionality demonstrate speedups of up to 4.9 $$\times $$ compared to full double precision, while maintaining controlled relative error. The proposed framework achieves a practical balance between computational efficiency and numerical reliability. It allows integration tasks on GPUs to run accurately and to adapt their precision automatically for higher performance.