[论文解读] Shallow Recurrent Decoder for Reduced Order Modeling of Plasma Dynamics

J. Nathan Kutz, Maryam Reza+2 more|arXiv (Cornell University)|May 20, 2024

Plasma Diagnostics and Applications被引用 7

一句话总结

本文提出 SHRED，一种用于 E×B 等离子体动力学的浅层递归解码器神经网络，用于降阶建模，可在有限传感器测量下实现重构和预测。

ABSTRACT

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 ${\bf E} imes {\bf B}$ 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 ${\bf E} imes {\bf B}$ 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.

研究动机与目标

• 阐明需要降阶模型以使多尺度等离子体动力学在计算上具可行性。
• 开发基于 SHallow REcurrent Decoder (SHRED) 架构的数据驱动 ROM，该架构使用来自少量传感器的时间序列来重构完整的时空场。
• 在一个代表 Hall 推进器的二维径向-方位等离子体配置上演示 SHRED，以展示重构和预测能力。
• 实现对压缩表示的训练以及对未直接测量场的重构。
• 突出分离变量在理论上的基础以及对非线性偏微分方程的适用性。

提出的方法

• 使用时间序列编码器（LSTM）对来自有限数量传感器的测量进行建模。
• 使用浅层解码器将 LSTM 潜在状态映射回高维场空间或其压缩的 SVD 空间。
• 训练 SHRED 以从稀疏传感器数据重构十四个耦合的等离子体场。
• 利用随机化SVD获得低秩表示以实现高效训练。
• 将 SHRED 应用于一个类似二维 Hall 推进器的设置，以通过神经网络滚动/展开演示重构和短时预测。

实验结果

研究问题

• RQ1 SHRED 是否能够仅从少量传感器位置的测量中重构完整的时空等离子体场？
• RQ2 SHRED 是否能够利用学习到的时间编码来预测等离子体动力学的未来状态？
• RQ3 在对数据的压缩（低秩）表示进行训练时，SHRED 的表现如何？
• RQ4 SHRED 对多场等离子体动力学中的非线性和耦合是否鲁棒？
• RQ5 传感器放置和轨迹在实现准确重构中的作用是什么？Denise? (Note: keep as stated in paper)

主要发现

• SHRED 能从最少仅三个点传感器重构出完整的时空场。
• SHRED 可以在压缩表示上进行训练，并通过 SVD 的 U 矩阵映射回高维空间。
• SHRED 在测试数据上对十四个耦合的等离子体场给出准确的重构。
• SHRED 在非线性、耦合的准 PDE 动力学中保持保真度，并通过 LSTM 展开实现对未来状态的预测。
• 重构利用单个观测场加上时间历史来恢复所有场，包括未直接测量的场。
• 在随机化 SVD 表示上的训练在不牺牲精度的前提下显著降低了计算成本。