Ionosphere Tomographic Model Based on Neural Network with Balance Cost and Dynamic Correction Using Multi-Constraints

Abstract

A Neural network (NN) is a promising tool for the tomographic inversion of the ionosphere. However, existing research has adopted an unbalanced cost function for training purposes and a preset image for constraint purposes, resulting in the output image being dominated by measurements. To address these problems, we proposed an NN-based tomographic model with a balance cost function and a dynamic correction process (BCDC) for ionosphere inversion. The cost function is composed of two balance terms corresponding to the measurements and the selected constraints, respectively. The produced image in the forward process of the NN is corrected dynamically by fitting each vertical profile with orthogonal basis functions (EOFs) and the Chapman function and then by smoothing the voxels of each layer with a moving window approach horizontally. The corrected image is then used to calculate the slant total electron content (STEC) parameter, which is further translated into the term of the cost for the vertical and horizontal constraints. Experiments were carried out to validate the BCDC method and compared with a recently developed tomographic method and the international reference ionosphere (IRI) model. Results show that the parameters derived from the BCDC model demonstrate good consistency with the observations. Comparing with the reference methods, the BCDC method performs better in the validations of vertical profiles, F2 layer peak density (NmF2), STEC parameter and vertical total electron content map. Further analysis also shows that a balance cost function is of benefit to achieve an image of better quality.

A Novel Ionospheric Inversion Model: PINN‐SAMI3 (Physics Informed Neural Network Based on SAMI3)

“…The ionosphere, being a dynamic and large‐scale plasma cloud and its immense scale, high dimensionality, and the complex transport process within the plasma pose substantial obstacles when applying PINN to ionospheric problems. While scholars have ventured into the exploration of large‐scale ionospheric modeling using purely data‐driven methods (Hirooka et al., 2011; Ma et al., 2005; Zhu et al., 2022), it is possible that these data‐driven ionospheric modeling methods may struggle to adhere to fundamental physical laws. This limitation can lead to results from inversion and prediction that are unreliable, inexplicable, and even erroneous.…”

Tomographic Inversion of the Ionosphere by Rejecting Abnormal Corrections and Rays

“…Such constraints [24,25] can be the assumptions of smoothing or similarity, functions to describe the horizontal and vertical ionosphere and the prior knowledge derived or directly taken from a third method. For example, Kondo et al [26], Sui et al [27] and Zhu et al [28] treated the distribution of plasma in the ionosphere to be smooth. Yu et al [24] took the Chapman function as the vertical distribution and assumed the four parameters of the Chapman function in horizontal space to be smooth.…”

“…Razin and Voosoghi [30] and Farzaneh and Forootan [31] treated the distribution of the horizontal ionosphere as the combination of a few basic functions. Minkwitz et al [32], Tang and Gao [33], Sui et al [27] and Zhu et al [28] used the derived information, e.g., gradients, covariance, empirical orthogonal functions (EOFs) or principal component, from a reference model to restrain their models.…”