Establishing an accurate and efficient prediction model is of great significance for governments and other social organizations to formulate prevention and control policies and curb the explosive spread of the pandemic. To improve prediction accuracy of cumulative COVID-19 confirmed data, a new hybrid prediction model based on gradient-based optimizer variational mode decomposition (GVMD), extreme learning machine (ELM), and autoregressive integrated moving average (ARIMA), named GVMD-ELM-ARIMA, is proposed. To solve the problem of selecting the $k$ value and the penalty factor $\alpha$ in variational mode decomposition (VMD), this paper proposes gradient-based optimizer variational mode decomposition (GVMD), which realizes the self-adaptive determination of $k$ value and $\alpha$ value. Firstly, GVMD decomposes the cumulative COVID-19 confirmed data into some intrinsic mode functions (IMFs) and a residual component (IMFr). Secondly, IMFs are predicted by ELM. Then, IMFr is predicted by ARIMA. Finally, the final prediction results are obtained by reconstructing the prediction result of IMFs and IMFr. The cumulative COVID-19 confirmed data of the United States, India and Russia is used to verify its effectiveness. Taking the United States as an example, compared with the average MAPE, RMSE and MAE of the single model, the average MAPE of the hybrid model is reduced by 47.27%, the average RMSE is reduced by 44.50%, and the average MAE is reduced by 55.34%. Compared with GVMD-ELM-ELM, GVMD-ELM-ARIMA proposed in this paper reduces the MAPE by 60%, the RMSE by 56.85%, and the MAE by 61.61%. The experimental results show that GVMD-ELM-ARIMA has best prediction accuracy, and it provides a new method for predicting the cumulative COVID-19 confirmed data.

建立准确高效的预测模型，对于政府等社会组织制定防控政策、遏制疫情爆发式蔓延具有重要意义。为了提高累积 COVID-19 确认数据的预测精度，一种基于梯度优化器变分模式分解 (GVMD)、极限学习机 (ELM) 和自回归积分移动平均 (ARIMA) 的新型混合预测模型，命名为 GVMD-ELM -ARIMA，建议。为了解决选择问题$克$ 值和惩罚因子 $\alpha$ 在变分模式分解（VMD）中，本文提出了基于梯度的优化器变分模式分解（GVMD），实现了自适应确定 $克$ 价值和 $\alpha$价值。首先，GVMD 将累积的 COVID-19 确认数据分解为一些固有模式函数（IMF）和残差分量（IMFr）。其次，IMF 是由 ELM 预测的。然后，IMFr 由 ARIMA 预测。最后通过重构IMFs和IMFr的预测结果得到最终的预测结果。美国、印度和俄罗斯的累积 COVID-19 确认数据用于验证其有效性。以美国为例，与单一车型平均MAPE、RMSE和MAE相比，混合车型平均MAPE降低47.27%，平均RMSE降低44.50%，平均MAE降低55.34%。与 GVMD-ELM-ELM 相比，本文提出的 GVMD-ELM-ARIMA 降低了 MAPE 60%，RMSE 降低了 56.85%，MAE 降低了 61.61%。