Multi-Scale Attention Recurrent Network with Multi-order Taylor Differential Knowledge for Deep Spatiotemporal Sequence Prediction
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摘要: 融合先验物理知识的深度时空序列预测方法通常使用偏微分方程(PDE)进行建模，这种做法通常存在两大问题：(1)偏微分方程的近似精度低；(2)无法在循环网络中有效捕捉多种空间尺度的时空特征和时空序列的边缘相关空间信息。为此，该文提出了融合泰勒微分的卷积循环神经网络(TDI-CRNN)。首先，为了提高高阶偏微分方程的近似精度并缓解偏微分方程应用的局限性，设计了一种多阶泰勒近似物理模块。该模块首先使用泰勒展开式对输入序列作微分逼近，再将不同阶数之间的微分卷积层使用微分系数耦合，最后动态调整泰勒展开结果的截断阶数与微分项数。其次，为了捕获循环网络隐藏状态的多种空间尺度特征并更好地捕捉时空序列的边缘相关空间信息，设计了一种多尺度注意力循环模块(MSARM)，在该模块的多尺度卷积空间注意力UNet(即MCSA-UNet)的卷积层中使用了多尺度卷积和空间注意力机制，目的是关注时空序列的局部空间区域。在Moving MNIST, KTH以及CIKM数据集上开展了大量实验，Moving MNIST数据集的均方误差(MSE)指标下降到42.7，结构相似性指数(SSIM)提高到0.912；KTH数据集的SSIM和峰值信噪比(PSNR)分别提高到0.882和29.03；CIKM数据集上的临界成功指数(CSI)提高到0.515。最终的可视化和定量预测结果均验证了TDI-CRNN模型的合理性和有效性。Abstract: Deep spatiotemporal sequence prediction methods that incorporate a priori physical knowledge are commonly characterized by the utilization of Partial Differential Equations (PDE) for modeling. However, two main issues are concerned: (1) the limited precision in approximations with PDEs; and (2) the inability to efficiently capture spatiotemporal features at multiple spatial scales as well as the edge spatial information of the spatiotemporal sequences in the recurrent network. To address these challenges, one Taylor Differential Incorporated Convolutional Recurrent Neural Network (TDI-CRNN) is proposed in this paper. Firstly, in order to enhance the approximation accuracy of higher-order partial differential equations and to alleviate the limitations of PDE applications, one physical module with multi-order Taylor approximation is designed. The module is firstly used for the differential approximation of the input sequence by means of the Taylor expansion, and then couples the differential convolution layers with different orders via differential coefficients, and dynamically adjusts the truncation order and the number of differential terms of the Taylor expansions. Secondly, to capture the multiple spatial scale features of the hidden states in the recurrent network and to better capture the edge spatial information of the spatiotemporal sequences, one Multi-Scale Attention Recurrent Module (MSARM) is devised. Multi-scale convolution and spatial attention mechanisms are utilized in the convolution layer of the Multi-scale Convolution Spatial Attention UNet (MCSA-UNet), aiming to focus on local spatial regions within spatiotemporal sequences. Extensive experiments are conducted on the Moving MNIST, KTH, and CIKM datasets. The Mean Squared Error (MSE) on the Moving MNIST dataset dropped to 42.7, while the Structural Similarity Index Measure (SSIM) increased to 0.912. The SSIM and Peak Signal-to-Noise Ratio (PSNR) on the KTH dataset increased to 0.882 and 29.03, respectively. The Correct Skill Index (CSI) on the real weather radar echo CIKM dataset increased to 0.515. The final visualization and quantitative prediction results verify the rationality and effectiveness of the TDI-CRNN model.
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表 1 数据驱动的预测模型
类别 模型内涵 模型名称 模型思想 基于门控机制或堆叠方式的改进模型 ConvLSTM[5] 提出使用卷积运算代替LSTM中的普通乘法运算 Conv-TT-LSTM[8] 提出了高阶卷积LSTM PredRNN[9] 使用共享输出门实现无缝的记忆融合 MIM[12] 提出的网络能够同时捕捉平稳信息和非平稳信息 E3D-LSTM[26] 将三维卷积集成到循环网络中 ZNet[27] 提出新的堆叠方式，隐藏状态沿Z曲线更新 IM-LSTM[28] 设计了SIM模块，用于更新隐藏状态 DFN[29] 生成动态卷积学习，以实现自适应特征提取 使用编码器-解码器架构的模型 MCNet[30] 在编码器-解码器以及ConvLSTM上进行预测 STMFANet[31] 提出空间小波分析模块，统一处理时空信息 FRNN[32] 堆叠多个循环单元层，得到自动编码器 引入注意力机制的模型 SA-ConvLSTM[7] 加入自注意机制，捕获长程空间依赖关系 CSAConvLSTM[33] 加入自注意力机制，捕获全局时空特征 
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表 3 Moving MNIST数据集上的实验结果(10个时间步上的平均预测结果)
模型 SSIM↑ $ \varDelta $ MSE↓ $ \varDelta $ ConvLSTM[5]* 0.707 – 103.3 – IM-LSTM[28]* 0.876 +0.169 67.4 –35.9 PredRNN[9]* 0.867 +0.160 56.8 –46.5 Conv-TT-LSTM[8]* 0.905 +0.198 53.0 –50.3 MIM[12]* 0.901 +0.194 44.2 –59.1 SA-ConvLSTM[7]* 0.903 +0.196 43.9 –59.4 LMC-memory[34]* 0.904 +0.197 42.9 –60.4 PDE-Net[16]· 0.621 –0.086 160.2 +56.9 CDNA[19]· 0.721 +0.014 97.4 –5.9 VPN[22]· 0.870 +0.163 70.2 –33.1 DDPAE[18]· 0.905 +0.198 43.5 –59.8 MSARM(4层)× 0.873 +0.166 43.9 –59.4 Taylor+ST-LSTM(4层)× 0.893 +0.186 44.2 –59.1 TDI-CRNN 0.912 +0.205 42.7 –60.6
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表 4 不同泰勒截断阶数和微分项数对模型性能的影响
微分项数 截断阶数 2 3 4 3阶 MSE=45.80
SSIM=0.886MSE=44.31
SSIM=0.892MSE=45.26
SSIM=0.8844阶 MSE=43.77
SSIM=0.902MSE=42.71
SSIM=0.910MSE=43.54
SSIM=0.8975阶 MSE=46.27
SSIM=0.886MSE=43.54
SSIM=0.898MSE=46.514
SSIM=0.880
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表 5 KTH数据集的实验结果(20个时间步上的平均预测结果)
模型 SSIM↑ $ \varDelta $ PSNR (dB)↑ $ \varDelta $ ConvLSTM[5]* 0.712 — 23.58 — FRNN[32]* 0.771 +0.059 26.12 +2.54 DFN[29]* 0.794 +0.082 27.26 +3.68 ZNet[27]* 0.817 +0.105 27.58 +4.00 MCNet[30]* 0.804 +0.092 25.95 +2.37 PredRNN[9]* 0.839 +0.127 27.55 +3.97 CSAConvLSTM[33]* 0.840 +0.128 27.91 +4.33 STMFANet[31]* 0.851 +0.139 27.24 +3.66 E3D-LSTM[26]* 0.879 +0.167 29.31 +5.73 PDE-Net[16]· 0.662 –0.05 22.45 –1.13 DDPAE[18]· 0.845 +0.133 28.42 +4.84 TDI-CRNN 0.882 +0.170 29.03 +5.45
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表 6 CIKM雷达回波数据集在十个时间步上的平均预测结果
模型 HSS↑ CSI↑ MSE↓ $\tau \ge 5$ $\tau \ge 15$ $\tau \ge 30$ 平均值 $ \varDelta $ $\tau \ge 5$ $\tau \ge 15$ $\tau \ge 30$ 平均值 $ \varDelta $ $ \varDelta $ ConvLSTM[5]* 0.662 0.569 0.272 0.501 — 0.743 0.557 0.185 0.495 — 94.7 — PredRNN[9]* 0.678 0.571 0.281 0.508 +0.007 0.755 0.569 0.199 0.508 +0.013 104.1 +9.3 RC-LSTM[34]* 0.682 0.580 0.288 0.513 +0.012 0.761 0.571 0.225 0.509 +0.014 88.2 –9.2 PDE-Net[16]· 0.664 0.574 0.275 0.503 +0.002 0.749 0.558 0.192 0.501 +0.006 78.6 –16.1 Advection-diffusion[21]· 0.679 0.579 0.288 0.509 +0.008 0.759 0.571 0.209 0.510 +0.015 55.4 –39.3 DDPAE[18]· 0.682 0.581 0.291 0.514 +0.013 0.764 0.572 0.227 0.512 +0.017 43.2 –51.5 TDI-CRNN 0.685 0.582 0.293 0.516 +0.015 0.767 0.578 0.260 0.515 +0.02 36.8 –57.9
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