微-宏观张量神经代理用于碰撞等离子体中的不确定性量化
Micro-Macro Tensor Neural Surrogates for Uncertainty Quantification in Collisional Plasma
- University of Ferrara（费拉拉大学）
- Italian Ministry of University and Research（意大利大学与研究部）
- Royal Society（皇家学会）
- Italian National Institute of High Mathematics（意大利高等数学研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出基于张量神经网络的微-宏观代理方法，用于高效处理碰撞等离子体中的不确定性量化问题。
AI中文摘要：
等离子体动力学方程对模型参数和数据中的微小扰动表现出显著的敏感性，这使得在预测模拟中可靠且高效的不确定性量化（UQ）至关重要。然而，不确定性采样成本、高维相空间以及多尺度刚性对传统数值方法的计算效率和误差控制构成了严峻挑战。在存在碰撞的情况下，高维非局部碰撞积分和守恒性质进一步施加了严格限制。为此，我们提出了一种方差减少的蒙特卡洛框架，用于Vlasov-Poisson-Landau（VPL）系统的UQ，其中神经网络代理替代了多次昂贵的Landau碰撞项评估。该方法耦合了高保真度、渐近保持的VPL求解器，与基于Vlasov-Poisson-Fokker-Planck（VPFP）和Euler-Poisson（EP）方程的低成本、强相关代理模型。对于代理模型，我们引入了分离物理指导神经网络（SPINN）的广义形式，开发了一类基于各向异性微-宏观分解的张量神经网络，以减少速度矩成本、模型复杂性和维度灾难。为进一步提高与VPL的相关性，我们校准了VPFP模型并设计了渐近保持的SPINN，其小尺度和大尺度Knudsen极限分别恢复了EP和VP系统。数值实验显示，与标准蒙特卡洛相比，该方法显著减少了方差，使用远 fewer 的高保真度样本即可获得准确的统计结果，并且具有更低的实时时钟时间，同时保持对随机维度的鲁棒性。
英文摘要：
Plasma kinetic equations exhibit pronounced sensitivity to microscopic perturbations in model parameters and data, making reliable and efficient uncertainty quantification (UQ) essential for predictive simulations. However, the cost of uncertainty sampling, the high-dimensional phase space, and multiscale stiffness pose severe challenges to both computational efficiency and error control in traditional numerical methods. These aspects are further emphasized in presence of collisions where the high-dimensional nonlocal collision integrations and conservation properties pose severe constraints. To overcome this, we present a variance-reduced Monte Carlo framework for UQ in the Vlasov--Poisson--Landau (VPL) system, in which neural network surrogates replace the multiple costly evaluations of the Landau collision term. The method couples a high-fidelity, asymptotic-preserving VPL solver with inexpensive, strongly correlated surrogates based on the Vlasov--Poisson--Fokker--Planck (VPFP) and Euler--Poisson (EP) equations. For the surrogate models, we introduce a generalization of the separable physics-informed neural network (SPINN), developing a class of tensor neural networks based on an anisotropic micro-macro decomposition, to reduce velocity-moment costs, model complexity, and the curse of dimensionality. To further increase correlation with VPL, we calibrate the VPFP model and design an asymptotic-preserving SPINN whose small- and large-Knudsen limits recover the EP and VP systems, respectively. Numerical experiments show substantial variance reduction over standard Monte Carlo, accurate statistics with far fewer high-fidelity samples, and lower wall-clock time, while maintaining robustness to stochastic dimension.
