11:00 AM - 1:00 PM
[SGD02-P07] LSTM deep learning of time-series data with (quasi-)periodic variation
Keywords:Deep learning, LSTM, Machine learning
In geodesy, time-series data frequently include periodic variations originating from tides, earth rotation, groundwater, and so on. It is elementary to evaluate these periodic variations when a sophisticated physical model is constructed such as for tides, or when the period of variation is fixed. However, there are cases where the period of variation fluctuates, or where the period of variation is not clear due to large noises. We introduce a multi-layer neural network (deep learning) and evaluate (quasi-)periodic variations.
Similar to previous studies that attempted machine learning on GNSS time-series data (Yamaga and Mitsui, 2019), we use a recurrent neural network (RNN) suitable for learning time-series data. In RNN, the data in a certain time window is used as input, and the following data is used as output. As the time window is shifted, the parameters of the intermediate layer between the input and output are estimated, and the relation between the input and output is learned. After that, the data in the time range not used for learning is input again, and the output is obtained as the forecasted value. In the intermediate layer, we place four LSTM units (Hochreiter and Schmidhuber, 1997) that can store long-term information to enable deep learning.
First, we tried numerical tests on artificial data with random noise added to periodic variations. For the artificial data of five sine periods, we performed deep learning of LSTM by shifting the time window by two periods. After that, the forecasts for three periods were output and checked for consistency with the artificial data. The results of this deep learning were compared with the results of regression analysis, where the period of the sine function was given in advance, in terms of the value of the absolute sum of residuals. As a result, when the amplitude of the random noise was a few tens of percent of the amplitude of the sine function, the deep learning showed better forecast performance than the regression analysis. On the other hand, when the noise amplitude became even larger, the forecast performance of deep learning decreased significantly. Conversely, even when the noise amplitude was smaller, the forecast performance of deep learning did not exceed that of simple regression analysis. Thus, deep learning can be a powerful tool for noise removal, but it requires certain conditions to be met to achieve high performance. In the presentation, we will also show the results of numerical experiments on actual geodetic data.
Similar to previous studies that attempted machine learning on GNSS time-series data (Yamaga and Mitsui, 2019), we use a recurrent neural network (RNN) suitable for learning time-series data. In RNN, the data in a certain time window is used as input, and the following data is used as output. As the time window is shifted, the parameters of the intermediate layer between the input and output are estimated, and the relation between the input and output is learned. After that, the data in the time range not used for learning is input again, and the output is obtained as the forecasted value. In the intermediate layer, we place four LSTM units (Hochreiter and Schmidhuber, 1997) that can store long-term information to enable deep learning.
First, we tried numerical tests on artificial data with random noise added to periodic variations. For the artificial data of five sine periods, we performed deep learning of LSTM by shifting the time window by two periods. After that, the forecasts for three periods were output and checked for consistency with the artificial data. The results of this deep learning were compared with the results of regression analysis, where the period of the sine function was given in advance, in terms of the value of the absolute sum of residuals. As a result, when the amplitude of the random noise was a few tens of percent of the amplitude of the sine function, the deep learning showed better forecast performance than the regression analysis. On the other hand, when the noise amplitude became even larger, the forecast performance of deep learning decreased significantly. Conversely, even when the noise amplitude was smaller, the forecast performance of deep learning did not exceed that of simple regression analysis. Thus, deep learning can be a powerful tool for noise removal, but it requires certain conditions to be met to achieve high performance. In the presentation, we will also show the results of numerical experiments on actual geodetic data.