Reduced order models are becoming increasingly important for rendering complex and multiscale spatio-temporal dynamics computationally tractable. The computational efficiency of such surrogate models is especially important for design, exhaustive exploration and physical understanding. Plasma simulations, in particular those applied to the study of ${\bf E}\times {\bf B}$ plasma discharges and technologies, such as Hall thrusters, require substantial computational resources in order to resolve the multidimentional dynamics that span across wide spatial and temporal scales. Although high-fidelity computational tools are available to simulate such systems over limited conditions and in highly simplified geometries, simulations of full-size systems and/or extensive parametric studies over many geometric configurations and under different physical conditions are computationally intractable with conventional numerical tools. Thus, scientific studies and industrially oriented modeling of plasma systems, including the important ${\bf E}\times {\bf B}$ technologies, stand to significantly benefit from reduced order modeling algorithms. We develop a model reduction scheme based upon a {\em Shallow REcurrent Decoder} (SHRED) architecture. The scheme uses a neural network for encoding limited sensor measurements in time (sequence-to-sequence encoding) to full state-space reconstructions via a decoder network. Based upon the theory of separation of variables, the SHRED architecture is capable of (i) reconstructing full spatio-temporal fields with as little as three point sensors, even the fields that are not measured with sensor feeds but that are in dynamic coupling with the measured field, and (ii) forecasting the future state of the system using neural network roll-outs from the trained time encoding model.

翻译：降阶模型在使复杂多尺度时空动力学计算变得可行方面日益重要。此类替代模型的计算效率对于设计、全面探索及物理理解尤为关键。等离子体模拟，特别是应用于研究${\bf E}\times {\bf B}$等离子体放电与霍尔推进器等技术的模拟，需消耗大量计算资源以解析跨越宽广时空尺度的多维动力学。尽管已有高保真计算工具可在有限条件及高度简化几何构型下模拟此类系统，但全尺寸系统模拟及/或在多种几何构型与不同物理条件下的广泛参数化研究，仍因传统数值工具而面临计算不可行性。因此，等离子体系统（包括重要的${\bf E}\times {\bf B}$技术）的科学研究与工业导向建模，将显著受益于降阶建模算法。我们发展了一种基于浅层递归解码器（Shallow REcurrent Decoder, SHRED）架构的模型降阶方案。该方案采用神经网络对时域有限传感器测量数据进行编码（序列到序列编码），并通过解码器网络重建完整状态空间。基于变量分离理论，SHRED架构能够：（i）仅凭三个点传感器即可重建完整时空场，甚至包括未通过传感器馈送测量但与测量场存在动态耦合的场；（ii）利用训练后的时间编码模型通过神经网络推演预测系统未来状态。