An imperative aspect of agricultural planning is accurate yield prediction. Artificial Intelligence (AI) techniques, such as Deep Learning (DL), have been recognized as effective means for achieving practical solutions to this problem. However, these approaches most often provide deterministic estimates and do not account for the uncertainties involved in model predictions. This study presents a framework that employs the Bayesian Model Averaging (BMA) and a set of Copula functions to integrate the outputs of multiple deep neural networks, including the 3DCNN (3D Convolutional Neural Network) and ConvLSTM (Convolutional Long Short-Term Memory), and provides a probabilistic estimate of soybean crop yield over a hundred counties across three states in the United States. The results of this study show that the proposed approach produces more accurate and reliable soybean crop yield predictions than the 3DCNN and ConvLSTM networks alone while accounting for the models’ uncertainties.

农业规划的一个重要方面是准确的产量预测。人工智能 (AI) 技术，例如深度学习 (DL)，已被公认为实现该问题的实际解决方案的有效手段。然而，这些方法通常提供确定性估计，并且不考虑模型预测中涉及的不确定性。本研究提出了一个框架，该框架采用贝叶斯模型平均 (BMA) 和一组 Copula 函数来集成多个深度神经网络的输出，包括 3DCNN（3D 卷积神经网络）和 ConvLSTM（卷积长短期记忆），并提供了美国三个州一百多个县的大豆作物产量的概率估计。