ABSTRACT In this article, we present a new method based on extreme learning machine (ELM) algorithm for solving nonlinear curve fitting problems. Curve fitting is a computational problem in which we seek an underlying target function with a set of data points given. We proposed that the unknown target function is realized by an ELM with introducing an additional linear neuron to correct the localized behavior caused by Gaussian type neurons. The number of hidden layer neurons of ELM is a crucial factor to achieve a good performance. An evolutionary computation algorithm–particle swarm optimization (PSO) technique is applied to determine the optimal number of hidden nodes. Several numerical experiments with benchmark datasets, simulated spectral data and measured data from high energy physics experiments have been conducted to test the proposed method. Accurate fitting has been accomplished for various tough curve fitting tasks. Comparing with the results of other methods, the proposed method outperforms the traditional numerical-based technique. This work clearly demonstrates that the classical numerical analysis problem-curve fitting can be satisfactorily resolved via the approach of artificial intelligence.

中文翻译：

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一种基于优化极限学习机的曲线拟合新方法

摘要 在本文中，我们提出了一种基于极限学习机 (ELM) 算法的新方法，用于解决非线性曲线拟合问题。曲线拟合是一个计算问题，我们在其中寻找具有给定数据点集的潜在目标函数。我们提出未知目标函数是通过引入额外的线性神经元来纠正由高斯型神经元引起的局部行为的 ELM 实现的。ELM 的隐藏层神经元数量是实现良好性能的关键因素。应用进化计算算法-粒子群优化 (PSO) 技术来确定隐藏节点的最佳数量。使用基准数据集进行的几个数值实验，已经进行了模拟光谱数据和来自高能物理实验的测量数据来测试所提出的方法。为各种艰巨的曲线拟合任务完成了精确拟合。与其他方法的结果相比，所提出的方法优于传统的基于数值的技术。这项工作清楚地表明，通过人工智能的方法可以令人满意地解决经典的数值分析问题-曲线拟合。