A Machine and Deep Learning methodology is developed and applied to give a high fidelity, fast surrogate for 2D resistive MHD simulations of MagLIF implosions. The resistive MHD code GORGON is used to generate an ensemble of implosions with different liner aspect ratios, initial gas preheat temperatures (that is, different adiabats), and different liner perturbations. The liner density and magnetic field as functions of $x$, $y$, and $t$ were generated. The Mallat Scattering Transformation (MST) is taken of the logarithm of both fields and a Principal Components Analysis is done on the logarithm of the MST of both fields. The fields are projected onto the PCA vectors and a small number of these PCA vector components are kept. Singular Value Decompositions of the cross correlation of the input parameters to the output logarithm of the MST of the fields, and of the cross correlation of the SVD vector components to the PCA vector components are done. This allows the identification of the PCA vectors vis-a-vis the input parameters. Finally, a Multi Layer Perceptron neural network with ReLU activation and a simple three layer encoder/decoder architecture is trained on this dataset to predict the PCA vector components of the fields as a function of time. Details of the implosion, stagnation, and the disassembly are well captured. Examination of the PCA vectors and a permutation importance analysis of the MLP show definitive evidence of an inverse turbulent cascade into a dipole emergent behavior. The orientation of the dipole is set by the initial liner perturbation. The analysis is repeated with a version of the MST which includes phase, called Wavelet Phase Harmonics (WPH). While WPH do not give the physical insight of the MST, they can and are inverted to give field configurations as a function of time, including field-to-field correlations.

翻译：本文开发并应用了一种机器与深度学习方法，为MagLIF内爆的二维电阻磁流体力学模拟提供高保真度的快速代理模型。采用电阻磁流体力学代码GORGON生成具有不同衬套纵横比、初始气体预热温度（即不同绝热线）及不同衬套扰动的内爆系综，并计算了衬套密度和磁场作为$x$、$y$、$t$的函数。对两者场的对数进行Mallat散射变换（MST），并对两场MST的对数执行主成分分析。将场投影至PCA向量，保留少量PCA向量分量。对输入参数与输出场MST对数的互相关，以及SVD向量分量与PCA向量分量的互相关进行奇异值分解，从而识别PCA向量与输入参数的关联。最终，采用含ReLU激活函数的多层感知器神经网络及简单三层编码器/解码器架构，基于该数据集训练模型以预测场PCA向量分量随时间的变化。内爆、停滞及解体过程的细节得到良好捕捉。对PCA向量的分析及MLP的排列重要性分析表明，存在明确的逆湍流级联现象并涌现出偶极子行为。偶极子取向由初始衬套扰动决定。使用包含相位的MST变体——即小波相位谐波（WPH）重复分析。WPH虽无法提供MST的物理洞察，但可进行反演以获取场构型随时间的变化，包括场间相关性。