5:15 PM - 6:45 PM
[PEM14-P02] Data smoothing using neural networks for symbolic regression in sunspot decay
Keywords:symbolic regression, sunspot decay, neural network, data smoothing
In recent years, several studies have suggested the method of using machine learning to discover new physical laws or governing equations from the data itself. The discovery of equations that explain the data is called symbolic regression. Udrescu et al. (2020) suggests a new symbolic regression algorithm, AI-Feynman, which enables efficient symbolic regression via finding symmetry and divisibility in the data using high-precision data interpolation or exploration by neural networks, and recursively simplifying the data. Some studies, such as Koksbang (2023) and Kubo (2023), have addressed symbolic regression from data using AI-Feynman, but these only from pseudo data, such as numerical simulation data without measurement noise. In addition, Cava et al. (2021) compared the recent symbolic regression methods and found that the methods, especially AI-Feynman, are vulnerable to noisy data, and so noise in the real observed data is a critical problem.
To this end, we aim at symbolic regression using AI-Feynman from actual observation data containing measurement noise and, as a first step, investigate how to deal with measurement noise by smoothing the data using a neural network. The target is the decaying process of sunspots. Sunspot decay is a relatively mild phenomenon and time series data can be expected to be obtained at sufficient time intervals, so sunspot decay is a reasonable setting for this research topic.
We selected 20 circular-symmetric decaying sunspots from the Space-weather HMI Active Region Patches (SHARPs) observed by the solar observing satellite. We made the one-dimensional data reduce the observational noise and simplify learning by azimuthally averaging at the center of the sunspots. Next, to smooth the data, we constructed a neural network that takes the magnetic fields, Bz(r,t) and Bt(r,t), at each time point as input and predicts the change of the magnetic fields, ΔBz(r,t+Δt) and ΔBt(r,t+Δt), over two hours. We then used the output of a neural network that learned the average temporal evolution of the sunspot magnetic field to produce smoothed one-dimensional sunspot decay data from initial conditions to sunspot extinction.
To assess the validity of the smoothing method, we compared the time from the initial state to the extinction of actual and smoothed sunspot decay for a total of 20 sunspots. The results showed that the RMSE was 35.6 hours, which is smaller than the sunspot decay time and confirms that the sunspot decay data smoothed by the neural network can capture the approximate time evolution of sunspot decay.
The results of this study provide the effectiveness of the smoothing process using neural networks which will be helpful for symbolic regression methods in finding the new physical law or governing equation from the observational data.
To this end, we aim at symbolic regression using AI-Feynman from actual observation data containing measurement noise and, as a first step, investigate how to deal with measurement noise by smoothing the data using a neural network. The target is the decaying process of sunspots. Sunspot decay is a relatively mild phenomenon and time series data can be expected to be obtained at sufficient time intervals, so sunspot decay is a reasonable setting for this research topic.
We selected 20 circular-symmetric decaying sunspots from the Space-weather HMI Active Region Patches (SHARPs) observed by the solar observing satellite. We made the one-dimensional data reduce the observational noise and simplify learning by azimuthally averaging at the center of the sunspots. Next, to smooth the data, we constructed a neural network that takes the magnetic fields, Bz(r,t) and Bt(r,t), at each time point as input and predicts the change of the magnetic fields, ΔBz(r,t+Δt) and ΔBt(r,t+Δt), over two hours. We then used the output of a neural network that learned the average temporal evolution of the sunspot magnetic field to produce smoothed one-dimensional sunspot decay data from initial conditions to sunspot extinction.
To assess the validity of the smoothing method, we compared the time from the initial state to the extinction of actual and smoothed sunspot decay for a total of 20 sunspots. The results showed that the RMSE was 35.6 hours, which is smaller than the sunspot decay time and confirms that the sunspot decay data smoothed by the neural network can capture the approximate time evolution of sunspot decay.
The results of this study provide the effectiveness of the smoothing process using neural networks which will be helpful for symbolic regression methods in finding the new physical law or governing equation from the observational data.