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<p>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<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\times \)</EquationSource> </InlineEquation> 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.</p>

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Adaptive mixed-precision Monte Carlo integration on GPUs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月6日

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  • Ferhat Onur Özgan,
  • Berke Kabasakal,
  • Fahreddin Şükrü Torun

摘要

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.