  Despite the advancements in high-performance computing and modern numerical
algorithms, the cost remains prohibitive for multi-query kinetic plasma
simulations. In this work, we develop data-driven reduced-order models (ROM)
for collisionless electrostatic plasma dynamics, based on the kinetic
Vlasov-Poisson equation. Our ROM approach projects the equation onto a linear
subspace defined by principal proper orthogonal decomposition (POD) modes. We
introduce an efficient tensorial method to update the nonlinear term using a
precomputed third-order tensor. We capture multiscale behavior with a minimal
number of POD modes by decomposing the solution into multiple time windows
using a physical-time indicator and creating a temporally-local ROM. Applied to
1D-1V simulations, specifically the benchmark two-stream instability case, our
time-windowed reduced-order model (TW-ROM) with the tensorial approach solves
the equation approximately 280 times faster than Eulerian simulations while
maintaining a maximum relative error of 4% for the training data and 13% for
the testing data.
