Learned plasma transport surrogates can match short horizon states while failing over long rollouts because charge accounting, density admissibility, and Poisson compatible field reconstruction are not enforced. We study this issue in a controlled nondimensional one dimensional drift diffusion Poisson benchmark with Dirichlet electrostatic potential boundaries and zero species wall fluxes. The benchmark is a conservation and rollout test, not a complete sheath wall model. We compare Conservative FluxNet, a structure preserving flux correction model with a conservative finite volume update and positivity aware limiting, against direct next state regressors, direct variants with Poisson recomputation, charge projection, and rollout training, and a classical conservative core without learned correction. The central result is that the classical finite volume core alone achieves near roundoff rollout error, so the paper is primarily about conservative discrete structure rather than learned closure. On the headline experiment, the conservative model achieves rollout MSE $7.35\times 10^{-9}$ versus $4.23\times 10^{1}$ for the unconstrained baseline, $2.53\times 10^{1}$ with Poisson recomputation, $6.72\times 10^{1}$ with charge projection, and $2.71\times 10^{1}$ with four step rollout training. Across $64$ prespecified configurations, it wins rollout mean squared error in $60/64$ cases despite winning one step mean squared error in only $19/64$. These results show that, for this controlled benchmark and comparison class, local conservative finite volume structure is more important than one step neural regression accuracy for stable autoregressive rollout.

翻译：学习得到的等离子体输运代理模型可在短时域内匹配状态，但由于未强制执行电荷平衡、密度可容许性及泊松兼容场重构，在长程展开中会失败。本研究在受控的无量纲一维漂移扩散泊松基准中探讨该问题，该基准采用狄利克雷静电势边界条件及零物种壁面通量。该基准为守恒性和展开性测试，而非完整的鞘层壁面模型。我们比较了三种方法：Conservative FluxNet（采用保守有限体积更新和正性感知限制的结构保持通量校正模型）、直接下一状态回归器（含泊松重新计算、电荷投影及展开训练的变体），以及无学习校正的经典保守核。核心发现是：经典有限体积核单独即可实现接近舍入误差的展开误差，因此本文主要关注保守离散结构而非学习型闭合。在主要实验中，保守模型的展开均方误差为 $7.35\times 10^{-9}$，而无约束基线为 $4.23\times 10^{1}$，泊松重新计算变体为 $2.53\times 10^{1}$，电荷投影变体为 $6.72\times 10^{1}$，四步展开训练变体为 $2.71\times 10^{1}$。在64个预设配置中，保守模型在60/64个案例中赢得了展开均方误差，尽管仅在一阶均方误差中赢得19/64个案例。这些结果表明，对于该受控基准和比较类别而言，局部保守有限体积结构比一步神经回归精度对稳定自回归展开更为重要。