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Photovoltaic (PV) power has attracted widespread attention from many countries around the world due to its clean and renewable characteristics. To ensure the stable operation of the power system, accurate PV power forecasting has become a mandatory and challenging task. Currently, deep learning methods have become a vital approach in the field of PV power forecasting. In this work, a multistage attention neural network based on neural ordinary differential equation (MANODE) is proposed to address the main limitations of previous deep learning methods applied to PV power forecasting. Based on the neural ordinary differential equation (NODE), MANODE optimizes the long short-term memory network (LSTM) and temporal convolutional neural network (TCN), and combines the attention mechanism to achieve fine-grained spatio-temporal information extraction of PV series. In addition, the proposed MANODE model is applied to three different PV series collected from the Alice Springs meteorological station. Compared to previous state-of-the-art methods, the proposed method reduces the PV power forecasting error by at least 12.05%, 13.15%, and 9.71% on three different PV datasets, in terms of mean absolute error metric. The average errors of the MANODE method in four-hour-ahead PV power forecasting on the three datasets are 0.321, 0.350, and 0.567. • A novel neural network method called MANODE is applied in PV power forecasting. • MANODE addresses drawbacks of previous PV forecasting methods using LSTMs or CNNs. • Three multivariate datasets located in Australia are adopted in this work. • MANODE outperforms previous state-of-the-art neural network method in PV forecasting. [ABSTRACT FROM AUTHOR]