基于泰勒公式和遗传算法的函数拟合研究

Study on Function Fitting Based on Taylor Formula and Genetic Algorithm

摘要: 基于函数表达式绘制函数图像容易实现，但是将数据表述为函数表达式较为困难。在统计学和机器学习中，该问题通常表现为回归建模、插值和参数优化等形式，虽然计算高效，但在非线性复杂数据环境下表现受限。近年来，深度神经网络、进化计算等智能优化方法的引入，为函数拟合提供了更强大的建模能力和优化策略。该研究基于泰勒公式和遗传算法，实现了较好的函数拟合效果。具体来说，泰勒公式可以用函数多项式的形式近似表达函数值，很大程度上简化了函数拟合的难度。遗传算法可以迭代探索函数拟合的最优结果，实现了在较短的时间内获得较优的函数拟合表达式。该研究的方法在线性函数、非线性函数的实验中均取得了有竞争性的优化增益结果。

Abstract: Drawing function image based on function expression is easy to realize, but it is difficult to express data as function expression. In statistics and machine learning, this problem is usually expressed in the form of regression modeling, interpolation and parameter optimization, which are computationally efficient but limited in nonlinear and complex data environments. In recent years, the introduction of intelligent optimization methods such as deep neural networks and evolutionary computation has provided more powerful modeling capabilities and optimization strategies for function fitting. The study achieves a good function fitting effect based on Taylor formula and genetic algorithm. Specifically, Taylor formula can be used to approximately express function values in the form of function polynomials, which greatly simplifies the difficulty of function fitting. Genetic algorithm can iteratively explore the optimal result of function fitting, and achieve a better function fitting expression in a shorter time. The method of this study achieves competitive optimization gains in both linear and nonlinear functions.