Using physics-informed neural networks to reconstruct 3D electromagnetic fields from sparse measurements of potential and magnetic flux in high-repetition-rate laser experiments

Reconstructing 3D electromagnetic fields is crucial for understanding plasma dynamics. High-repetition-rate laser experiments are enabling unprecedented amounts of 3D data to be collected [1], however, these fields are often difficult to measure or probe with sufficient spatial or temporal resolution. New machine learning techniques that derive data-driven solutions for partial differential equations are emerging that can extract quantities not directly measured [2]. We present a method for reconstructing 3D electromagnetic fields from sparse potential and magnetic flux measurements using physics-informed neural networks (PINNs) [3]. The measurements are from experiments on magnetic reconnection in laser-driven mini-magnetospheres using the Phoenix Laser Laboratory and Large Plasma Device (LAPD) at UCLA [4]. The PINNs combine sparse spatiotemporal measurements of magnetic flux and electric potential from experiments with constraints in the form of Maxwell's equations to reconstruct physically consistent field quantities. We discuss the results from numerical simulations of laser-driven mini-magnetospheres and use them to test the PINN reconstruction method. Finally, we discuss how this method could be applied to large 3D experimental datasets.