This paper introduces a polynomial feedforward neural network based on Chebyshev polynomials able to effectively model non-linear and highly complex environmental data. The data sets were cautiously selected from the fields of biology, ecology, climate, and environmental management, and economics as to represent a scientifically meaningful and consistent corpus of disparate domains of intensive focus and interest in current ecological/environmental research, covering issues related to body growth/age, biomass production, energy efficiency/consumption, and ecology/geographic extension. The proposed network uses a number of layers to estimate the output in terms of a weighted sum of truncated Chebyshev series expansions applied to linear combinations of the input variables, and it is trained by the differential evolution algorithm. Its performance was compared to three neural networks. First, a polynomial feedforward network that uses Hermite polynomials as activation function in the hidden nodes; second, a radial basis function neural network; third, a Takagi-Sugeno-Kang neuro-fuzzy network. All the above networks were trained by evolutionary optimization algorithms. The comparison was carried out by standard criteria such as the root mean square error and the mean absolute error. Moreover, a non-parametric Kruskal-Wallis statistical test used to compare the median values of the root mean square errors between methods. The main experimental outcomes are: (a) the network's efficiency improves for higher polynomial orders, (b) the statistical analysis suggests that the proposed network appears to be very competitive to the other three networks.

本文介绍了一种基于Chebyshev多项式的多项式前馈神经网络，能够有效地对非线性和高度复杂的环境数据进行建模。这些数据集是从生物学，生态学，气候和环境管理以及经济学领域中谨慎选择的，代表了对当前生态/环境研究集中关注和关注的不同领域的科学意义和一致的语料库，涵盖了与人体生长/年龄，生物量生产，能源效率/消耗量以及生态/地理范围。所提出的网络使用多个层来根据应用于输入变量的线性组合的截断的Chebyshev级数展开的加权和来估计输出，并且通过差分演化算法对其进行训练。将其性能与三个神经网络进行了比较。首先，在隐蔽节点中使用Hermite多项式作为激活函数的多项式前馈网络；第二，径向基函数神经网络；第三，高木-宿野-康神经模糊网络。以上所有网络均经过进化优化算法训练。比较是通过标准标准进行的，例如均方根误差和平均绝对误差。此外，非参数Kruskal-Wallis统计检验用于比较方法之间的均方根误差的中值。主要的实验结果是：（a）对于较高的多项式阶数，网络的效率有所提高；（b）统计分析表明，拟议的网络似乎对其他三个网络具有非常强的竞争力。