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.

翻译：尽管高性能计算和现代数值算法取得了进步，多查询动力学等离子体模拟的成本仍然高昂。在本工作中，我们基于动力学Vlasov-Poisson方程，针对无碰撞静电等离子体动力学开发了数据驱动的降阶模型（ROM）。我们的ROM方法将方程投影到由主本征正交分解（POD）模态定义的线性子空间上。我们引入了一种高效的张量方法，利用预计算的三阶张量来更新非线性项。通过使用物理时间指标将解分解为多个时间窗口，并创建时间局域ROM，我们以最少数量的POD模态捕捉了多尺度行为。将该方法应用于一维一速度（1D-1V）模拟，特别是基准的双束不稳定性算例，我们提出的带张量时间窗口降阶模型（TW-ROM）求解方程的速度约为欧拉模拟的280倍，同时训练数据的最大相对误差保持在4%，测试数据的最大相对误差保持在13%。