Inferring Lorentz-covariant reduced plasma models from fully-kinetic simulations

Techniques from data science and machine learning are offering new approaches to developing theoretical and computational models of plasma dynamics directly from data. In particular, recent work has demonstrated the possibility of leveraging sparse regression techniques to recover interpretable plasma models [in the form of partial differential equations (PDEs)] from the data of fully-kinetic-particle-in-cell simulations. However, to robustly apply this methodology to uncover new reduced models of poorly understood plasma dynamics, it is important to embed fundamental physical constraints and symmetries in the inference procedure. Here, we show that embedding these known physical symmetries through data-augmentation  is highly effective in improving the accuracy and robustness of the inferred PDEs. We specifically focus on enforcing Lorentz covariance of the inferred PDE models, which we achieve by Lorentz-boosting the data into reference frames moving at random velocities. We demonstrate the benefits of this approach on the inference of the fundamental hierarchy of plasma models, from the kinetic Vlasov equation to the single-fluid plasma equations, from PIC simulation data. We show that using Lorentz-augmented data leads to 1) more accurate identification of model coefficients (up to three orders of magnitude more accurate compared with using original lab-frame data alone), and 2) the elimination of spurious unphysical PDE terms that do not satisfy Lorentz covariance. We further show that this data augmentation approach greatly relaxes the amount of original lab-frame data from expensive kinetic simulations needed for accurate and robust inference of reduced plasma PDE models.