  At the core of some of the most important problems in plasma physics -- from
controlled nuclear fusion to the acceleration of cosmic rays -- is the
challenge to describe nonlinear, multi-scale plasma dynamics. The development
of reduced plasma models that balance between accuracy and complexity is
critical to advancing theoretical comprehension and enabling holistic
computational descriptions of these problems. Here, we report the data-driven
discovery of accurate reduced plasma models, in the form of partial
differential equations, directly from first-principles particle-in-cell
simulations. We achieve this by using an integral formulation of sparsity-based
model-discovery techniques and show that this is crucial to robustly identify
the governing equations in the presence of discrete particle noise. We
demonstrate the potential of this approach by recovering the fundamental
hierarchy of plasma physics models -- from the Vlasov equation to
magnetohydrodynamics. Our findings show that this data-driven methodology
offers a promising new route to accelerate the development of reduced
theoretical models of complex nonlinear plasma phenomena and to design
computationally efficient algorithms for multi-scale plasma simulations.
