The Vlasov-Poisson system is employed in its reduced form version (1D1V) as a
test bed for the applicability of Physics Informed Neural Network (PINN) to the
wave-particle resonance. Two examples are explored: the Landau damping and the
bump-on-tail instability. PINN is first tested as a compression method for the
solution of the Vlasov-Poisson system and compared to the standard neural
networks. Second, the application of PINN to solving the Vlasov-Poisson system
is also presented with the special emphasis on the integral part, which
motivates the implementation of a PINN variant, called Integrable PINN
(I-PINN), based on the automatic-differentiation to solve the partial
differential equation and on the automatic-integration to solve the integral
equation.

使用简化形式的 Vlasov-Poisson 系统（1D1V）作为物理启发神经网络（PINN）应用于波粒共振的测试样本。首先将 PINN 作为 Vlasov-Poisson 系统解法的压缩方法进行测试，并与标准神经网络进行比较。其次，还介绍了将 PINN 应用于 Vlasov-Poisson 系统求解，重点放在积分部分，这促使了基于自动微分求解偏微分方程和自动积分求解积分方程的 PINN 变体，称为可积性 PINN（I-PINN）的实现。

应用基于物理的神经网络描述融合等离子体动力学模拟中的波粒共振

Physics informed Neural Networks applied to the description of  wave-particle resonance in kinetic simulations of fusion plasmas

How turbulent energy is dissipated in weakly collisional space and
astrophysical plasmas is a major open question. Here, we present the
application of a field-particle correlation technique to directly measure the
transfer of energy between the turbulent electromagnetic field and electrons in
the Earth's magnetosheath, the region of solar wind downstream of the Earth's
bow shock. The measurement of the secular energy transfer from the parallel
electric field as a function of electron velocity shows a signature consistent
with Landau damping. This signature is coherent over time, close to the
predicted resonant velocity, similar to that seen in kinetic Alfv\'en
turbulence simulations, and disappears under phase randomisation. This suggests
that electron Landau damping could play a significant role in turbulent plasma
heating, and that the technique is a valuable tool for determining the particle
energisation processes operating in space and astrophysical plasmas.

本研究应用场粒子相关技术，直接测量了地球磁层下的太阳风区域内的电磁场与电子之间的能量转移，结果表明电子朗道阻尼作用可能在研究空间和天体物理等领域的等离子体加热过程中发挥重要作用。