# A Novel NODE Approach Combined with LSTM for Short-Term Electricity Load Forecasting
## 5 Experimental Results and Analysis
### Forecasting Results Comparison  
In this section, we compare the prediction results of different models. Because the trend between different steps and different years is similar, we show prediction results and their local characteristic over three, five, and seven steps in 2019. Figures 12-14 shows the prediction results and part local observation over three, five, and seven steps forecasting in 2019. As we can see from Figure 12B, there is an unpredictable peak between time step 45-50. Obviously, our model more or less predicts the peak ahead of time, while models without NODE even show a downward trend when the actual data are approaching peak. However, the prediction peak produced by NODE models uniformly closely approaches the actual peak, especially for OBBLL, compared with the prediction peak produced by models without NODE. Figure 12C also shows the same condition, but it is more intuitive and comparative because the prediction  
which adds uncertainty to NODE and makes it more robust and flexible. This robustness can be observed in Figures 9-11. Compared with models without NODE, numerical errors of NODE-based models increase slowly. This means that the NODE-based model is more robust. Finally, ordinary LSTM and BiLSTM require discrete observation and transmission intervals, while NODE can learn differential equation relations of sequences to continuously describe the relation of features, i.e., NODE can learn the law of internal evolution equation of time series. The continuity allows the NODE-based model to learn potential dynamics to adapt acute changing of time series and capture continuous internal rules of series, which more suitably fits the trend of real-life dataset. In our model groups, stacked LSTM and its variants can capture long-term temporal dependency but they ignore nonperiodic trends hidden in discrete time intervals. In this paper, NODE is used to address this problem. As we discussed above, NODE can continuously extrapolate input series to match expected target series in latent space. In this way, nonperiodic trends hidden in discrete time intervals can be dynamically inferred by NODE. Hence, a NODE-based model has more potential to predict complex and dynamic future trends. As shown in Figures 12-14, sometimes models without NODE mistakenly judge the time of peak power consumption, but NODE-based models always correctly predict the time of peak power consumption because nonperiodic trend and rich temporal dynamics are captured. In a word, with powerful continuity and dynamism, NODE captures deep nonperiodic trends and adaptively fits real-life datasets according to the input, to lower the numerical error of forecasting. Therefore, compared with directly throwing input series into a sequence learner, i.e., stacked LSTM and its variants, adding an NODE block ahead can provide continuous hidden temporal information for the sequence learner and enhance the flexibility of the model. In addition, as mentioned above, the prediction results of models with NODE for one-step seem unsatisfactory. According to [27], focusing on recent local time series can help improve prediction accuracy. Therefore, an important reason is that when processing one-step forecasting, models tend to observe recent local time series to capture latest trends, but rich nonperiodic temporal information cannot be precisely captured because shorter local time series store less continuous information about the whole series. Therefore, the continuity of NODE is not outstanding when future step is small. In addition, adding NODE will increase the complexity and overfitting of the model when processing easy one-step forecasting. These two reasons explain why NODE-based models seem to perform similar to models without NODE when future step is one. Figure 12: The prediction results and local observation for 3-step forecasting in 2019. (**A**) represents the whole prediction result. (**B–D**) describe the prediction result of different local observation interval.