# Multi-Attention Recurrent Neural Network for Multi-Step Prediction of ChlorophyllI Concentration
## 1 Introduction and Problem Definition  
### Introduction  
Red tide is a catastrophic natural phenomenon that result in the ocean's color changing from its normal blue to red or almost brown, thereby causing severe repercussions for marine ecosystems, coastal economies, and humans [1]. ChlorophyllI concentration indicates the biomass of phytoplankton and water eutrophication [2], while its evolution reveals the dynamic changes in the physical and chemical properties of seawater. It denotes a pivotal indicator for red tide prediction (red tide occurs when chlorophyllI concentration exceeds 10 mg\(\cdot\)m\({}^{-3}\)) [3,4]. Therefore, the prediction of chlorophyllI concentration is regarded as one of the red tide warning technologies. Moreover, chlorophyllI concentration is closely related to the spatiotemporal distribution of fish communities and serves as an important reference for building artificial fishing grounds [5].Obviously, the scientific prediction of chlorophyllI concentration not only contributes to the disaster preparedness and mitigation efforts of government departments, but also helps maintain the healthy development of the marine aquaculture industry [1,6]. The traditional method based on physicochemical analysis takes the chemical properties of water as the cornerstone to establish a complex water dynamics model, thereby facilitating the prediction of chlorophyllI concentration [7,8]. However, it is difficult to establish an accurate dynamic model since the diversity of ocean variables, and the incomplete physical parameterization scheme further compromises the prediction accuracy [9]. Multivariate time series (MTS) forecasting plays a critical role in a variety of fields, such as financial stock prediction [10] and influenza virus analysis [11]. For example,Li et al. [12] extracted components of different frequencies from raw wind power data through wavelets, and then employed support vector regression (SVR) to reduce errors caused by data fluctuations. Recently, researchers have applied deep learning to time series forecasting, such as recurrent neural networks (RNNs), LSTM, and gated recurrent unit (GRU) [1; 13; 14]. Since the success of encoder-decoder in the long sequence task, many scholars are committed to developing various multi-step prediction methods based on this framework [15; 16]. The attention mechanism proposed by [PERSON] et al. [17] further inspired the research on multi-step prediction of time series [5]. [PERSON] et al. [18] proposed an RNN with dual-stage two-phase attention, which effectively captures both spatial correlations between variables and temporal dependencies between input sequences. Motivated by MTS forecasting theory, researchers have successively developed various models aimed at predicting chlorophyll concentrations [19; 20; 21]. [PERSON] et al. [22] proposed a nonlinear autoregressive neural network (NARX) to model the dynamic correlation between chlorophyll and influencing factors by detecting temporal dependencies. [PERSON] et al. [1] combined convolutional neural networks (CNN) and long short-term memory networks (LSTM) to predict chlorophyll concentration. [PERSON] et al. [23] used the encoder-decoder framework with attention for multi-step prediction of chlorophyll and achieved good performance in the coastal area of China. [PERSON] et al. [24] integrated LSTM and CNN to forecast short-term chlorophyll concentration and found that the hybrid model outperformed independent deep learning methods. [PERSON] et al. [25] proposed a hybrid model combining deep belief network (DBN) and autoregressive integrated moving average model (ARIMA) for red tide prediction tasks. [PERSON] et al. [26] enhanced the prediction accuracy of algal blooms by incorporating multivariate time series analysis theory into DBN. [PERSON] et al. [27] demonstrated that deep learning models outperform traditional shallow networks in terms of generalization ability and prediction accuracy.