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目的:针对高精度数值计算对资源需求越来越高的问题，提出一种基于机器学习的高效率数值计算优化方法。方法:采用龙格-库塔(R-K)法框架，使用高阶R-K法获得粒子运动轨迹数据；再以高阶数据为训练目标，通过神经网络算法提取影响计算精度的权重系数；最后将权重系数应用到低阶R-K法。结果:数值实验结果表明，经过机器学习优化的低阶R-K法，在与四阶R-K法相同计算精度情况下，求解速度比高阶方法提高三个数量级。结论:机器学习与传统数值方法的结合展现出强大的协同效应，能够在保持高精度的同时，显著提升计算效率。
Abstract：Aims: Aiming at the problem of increasingly high resource requirements for high-precision numerical calculations, an efficient numerical calculation optimization method based on machine learning is proposed. Methods: The framework adopted the Runge-Kutta(R-K) method. The high-order R-K method was first used to obtain particle trajectory data. Then, by taking the high-order data as the training target, a neural network algorithm was employed to extract weight coefficients that influenced calculation accuracy. Finally, the weight coefficients were applied to the low-order R-K method. Results: Numerical experiment results showed that the low-order R-K method optimized by machine learning achieved the same calculation accuracy as the fourth-order R-K method, while the solution speed was improved by three orders of magnitude compared with the high-order method. Conclusions: The combination of machine learning and traditional numerical methods demonstrates a strong synergistic effect, which can significantly improve computational efficiency while maintaining high accuracy.
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基本信息:
DOI：
中图分类号:TP181
引用信息:
[1]杨轲钧,于明州.基于机器学习的高精度低阶数值格式研究[J].中国计量大学学报,2025,36(02):290-297.
基金信息:
国家自然科学基金项目(No.11872353)