# A Novel NODE Approach Combined with LSTM for Short-Term Electricity Load Forecasting
## 1 Introduction  
Electricity plays an essential role in modern society [1]. The stability and sustainability of power supply are very important to ensuring the operation of society. Therefore, accurate power load forecasting needs to be studied in power grid resource scheduling [2]. Particularly, short-term load forecasting (STLF), ranging from several minutes to one week [3], can precisely estimate how much electric energy needs to be provided by the grid, and helps to minimize the cost of energy production and purchasing. Research showed that the cost of an electric utility operator is saved by about 10 million pounds, owing to only 1% decrease of load forecasting errors [4]. Thus, accurate electricity load forecasting definitely helps in making secure, reliable, and sustainable operation of power system. Over the last few years, researchers have proposed a lot of methods for processing electricity load forecasting. [PERSON] et al. [5] discussed four categories of STLF methodologies, including similar-pattern, variable selection, hierarchical forecasting, and weather station selection, to investigate the relationship between the load and external variables, which provided a more feasible method for the STLF field. In addition, the traditional statistical method includes time series analysis and regression analysis [6], and other statistics methods are usually applied in the STLF field. These statistical methods perform well in predicting data with obvious trend and smooth change. In addition, neural network is also widely used in electricity load forecasting. In [7], a hybrid forecast engine based on three-stage neural network was proposed for spinning reserves requirement forecasting, which has high learning capability and can avoid the overfitting problem and trapping in local minima and dead bands. In addition, [PERSON] et al. [8] proposed a new forecast engine based on hybrid neural network, which using a new intelligentalgorithm to optimize the weights of the proposed forecast engine. However, traditional methods and normal neural networks are powerless to predict multivariate or long-term time series due to lack of the ability to combine multiple features and discover the internal evolution law. To address this problem, based on recurrent neural networks (RNNs) [9], long short-term memory (LSTM) [10] is adopted in the STLF field. LSTM has been generally used in electricity load forecasting [11] due to its special gate mechanism. These studies indicate that LSTM and its variants perform well in electricity load forecasting. However, due to the discrete observation interval, LSTM and its variants are limited by the following two challenges:  
* Challenge 1: Insensitivity to the dynamic change of inputs. In LSTM and its variants, time series are input into the discrete LSTM unit in chronological order. Discrete LSTM unit causes LSTM and its variant to be insensitive to the change of inputs and they cannot learn dynamically.However, in real datasets, the input signals constantly change in a nonperiodic manner. This difference in continuity significantly lowers the forecasting accuracy of the LSTM and its variants. * Challenge 2: Ignores the internal nonperiodic rules of series. Due to the discrete observation interval, LSTM and its variants cannot observe series information on missing observation intervals. However, fine-grained temporal information and internal nonperiodic series interrelationship can be hidden between missing observation intervals, therefore missing the internal nonperiodic rules of series, causing higher forecasting numerical errors. Hence, in order to address these two challenges, a neural ordinary differential equation (NODE) [12] approach is introduced in this paper. NODE designs a neural network utilizing the ordinary differential equation (ODE) method, and it is designed to find internal evolution law of data, therefore it is applicable to electricity load forecasting.