Core surface flow inversion using physics-informed neural networks

Core surface flow inversion using physics-informed neural networks

Jinfeng Li (1) and Yufeng Lin (1)

(1) Department of Earth and Space Sciences, Southern University of Science and Technology, Shenzhen 518055, China.

Physics-informed neural networks (PINNs) have recently been widely used to solve PDEs or ODEs. An attractive feature of this method is that it can calculate the derivatives without truncation errors by the automatic differentiation method (Lu et al., 2021). Another advantage is that it can solve the inverse problem with slightly modified code for solving the forward problem (Raissi et al., 2020). In this study, we use the PINN to inverse the core surface flow from the geomagnetic observations. We start from the radial component of the induction equation under the frozen-flux approximation (Robert and Scott, 1965) and tangentially geostrophic flows assumption (Hills, 1979). Instead of using the large-scale approximation, which assumes the flows that generate the observed secular variation (SV) are large-scale, we model the flow field in the physic space and construct the unobserved magnetic field based on the power spectrum of numerical dynamo simulations. We examine the nonuniqueness of the inversion results by pre-setting the different initial parameters of the neural network. Our tests show that the uncertainty of large-scale flow field is small and the inversion scheme is robust.

We retrieve the core surface flow field between 2000 and 2020 using the core magnetic field model CHAOS-7 (Finlay et al., 2020). We then perform the dynamic mode decomposition method (DMD) (Schmid, 2010) of the retrieved core flow. This method decomposes the flow field and SV into several eigenmodes with time evolution. The consistency time evolution between the flow and the SV modes indicates the inversion algorithm is stable. Moreover, we calculate the secular acceleration (SA) of the magnetic field for each dynamic modes and find the mode with 8 years period can match the jerk events occurred in the equatorial region.

Reference

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• Lu, X. Meng, Z. Mao and G. E. Karniadakis, 2021, DeepXDE: A Deep Learning Library for Solving Differential Equations, SIAM Review, 63, pp. 208-228.
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• H. Robert and S. Scott, 1965, On analysis of the secular variation. 1: A hydromagnetic constraint: Theory, Journal of Geomagnetism and Geoelectricity, 17, pp. 137-151.
• J. Schmid, 2010, Dynamic mode decomposition of numerical and experimental data, J. Fluid Mech, 65, pp. 5-28.