概化理论
过度拟合
适应性
人工神经网络
计算机科学
稳健性(进化)
人工智能
常微分方程
均方误差
水准点(测量)
结构方程建模
非线性系统
机器学习
算法
数据挖掘
微分方程
数学
统计
数学分析
生态学
生物化学
化学
物理
大地测量学
量子力学
基因
地理
生物
作者
Quan Zhang,Xinping Xiao,Mingyun Gao
标识
DOI:10.1016/j.neucom.2024.127343
摘要
The neural ordinary differential equation (NODE) has attracted much attention for its applicability in dynamic system modeling and continuous time series analysis. When the sample size is limited, models often exhibit weak generalizability and robustness and are susceptible to overfitting. To address this, a novel multivariate grey neural differential equation model is proposed based on the grey model and NODE. The new model leverages the small-sample modeling capabilities of grey systems to enhance the overall generalizability. When the neural network structure changes, the proposed model can degenerate into other grey models, enhancing inclusiveness and adaptability. Two energy forecasting cases show that the new model achieves average MAPE values of 0.82% and 1.13% on the test sets. These values are significantly better than those of the other 10 benchmark models. Furthermore, the proposed model exhibits superior performance in terms of the MAE, RMSE, STD, and APE metrics compared to those of all contrastive models. This study demonstrates that the new model effectively enhances its predictive capabilities on limited nonlinear data, showcasing higher prediction accuracy, stronger adaptability, and better stability.
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