In this paper, we implement Neural Ordinary Differential Equations in a Variational Autoencoder setting for generative time series modeling. An object-oriented approach to the code was taken to allow for easier development and research and all code used in the paper can be found here: https://github.com/simonmoesorensen/neural-ode-project The results were initially recreated and the reconstructions compared to a baseline Long-Short Term Memory AutoEncoder. The model was then extended with a LSTM encoder and challenged by more complex data consisting of time series in the form of spring oscillations. The model showed promise, and was able to reconstruct true trajectories for all complexities of data with a smaller RMSE than the baseline model. However, it was able to capture the dynamic behavior of the time series for known data in the decoder but was not able to produce extrapolations following the true trajectory very well for any of the complexities of spring data. A final experiment was carried out where the model was also presented with 68 days of solar power production data, and was able to reconstruct just as well as the baseline, even when very little data is available. Finally, the models training time was compared to the baseline. It was found that for small amounts of data the NODE method was significantly slower at training than the baseline, while for larger amounts of data the NODE method would be equal or faster at training. The paper is ended with a future work section which describes the many natural extensions to the work presented in this paper, with examples being investigating further the importance of input data, including extrapolation in the baseline model or testing more specific model setups.

本文提出了基于神经常微分方程和变分自编码器的生成时序模型，加入LSTM编码器并使用多种复杂数据进行了验证；结果表明模型能够有效重构出给定输入并对太阳能生产数据表现良好。但对于复杂数据，其在预测真实轨迹中的表现有限，并建议在未来的研究中探索更多可扩展性。

使用神经常微分方程在变分自编码器中生成时间序列模型