标题： 基于物理信息神经网络的表面通量传输建模 显示英文标题

标题： Surface Flux Transport Modeling using Physics Informed Neural Networks

摘要： 研究太阳表面的磁场特性对于理解太阳和日球层活动至关重要，这反过来又影响太阳系中的空间天气。 表面通量传输（SFT）建模帮助我们模拟和分析太阳表面上磁通量的传输和演化，为太阳活动的机制提供了有价值的见解。 在这项工作中，我们展示了机器学习技术在解决磁通量传输中的应用，使其更加精确。 我们开发了一种基于物理信息神经网络（PINN）的新模型，使用一维轴对称平均和二维的SFT来研究双极磁区（BMRs）的演化。 我们通过将基于PINN的模型的性能和准确性与使用龙格-库塔隐式显式（RK-IMEX）方案实现的数值模型进行比较，证明了我们的PINN模型的效率和计算可行性。 该与网格无关的PINN方法可以用于更准确地再现观测到的极区磁场。 这一进展对于准确再现观测到的极区磁场非常重要，从而提供对未来太阳周期强度的见解。 这项工作为更高效和精确的太阳磁通量传输模拟铺平了道路，并展示了PINN在解决特定关注天体物理学的对流-扩散方程中的适用性。 显示英文摘要

摘要： Studying the magnetic field properties on the solar surface is crucial for understanding the solar and heliospheric activities, which in turn shape space weather in the solar system. Surface Flux Transport (SFT) modeling helps us to simulate and analyse the transport and evolution of magnetic flux on the solar surface, providing valuable insights into the mechanisms responsible for solar activity. In this work, we demonstrate the use of machine learning techniques in solving magnetic flux transport, making it accurate. We have developed a novel Physics-Informed Neural Networks (PINN)-based model to study the evolution of Bipolar Magnetic Regions (BMRs) using SFT in one-dimensional azimuthally averaged and also in two-dimensions. We demonstrate the efficiency and computational feasibility of our PINN-based model by comparing its performance and accuracy with that of a numerical model implemented using the Runge-Kutta Implicit-Explicit (RK-IMEX) scheme. The mesh-independent PINN method can be used to reproduce the observed polar magnetic field with better flux conservation. This advancement is important for accurately reproducing observed polar magnetic fields, thereby providing insights into the strength of future solar cycles. This work paves the way for more efficient and accurate simulations of solar magnetic flux transport and showcases the applicability of PINN in solving advection-diffusion equations with a particular focus on heliophysics.