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：我们开发并应用了一种机器与深度学习方法，为二维电阻磁流体动力学（MHD）模拟的MagLIF内爆过程构建高保真度、快速响应的替代模型。采用电阻MHD代码GORGON生成一系列内爆集成数据，涵盖不同的内衬纵横比、初始气体预热温度（即不同绝热指数）以及不同内衬扰动。生成了内衬密度与磁场作为$x$、$y$和$t$的函数。对两者的对数场进行Mallat散射变换（MST），并对两个场的MST对数进行主成分分析（PCA）。将场投影到PCA向量上，并保留少量PCA向量分量。通过输入参数与场MST对数输出之间的互相关奇异值分解（SVD），以及SVD向量分量与PCA向量分量的互相关分解，实现PCA向量相对于输入参数的辨识。最终，基于该数据集训练一个采用ReLU激活函数、三层简单编码器/解码器架构的多层感知器（MLP）神经网络，用于预测场PCA向量分量随时间的变化。该方法能精确捕捉内爆、停滞及解体过程的细节。对PCA向量的分析及MLP的置换重要性分析提供了反向湍流级联形成偶极子涌现行为的明确证据，偶极子取向由初始内衬扰动决定。我们采用包含相位的MST变体——小波相位谐波（WPH）重复上述分析。尽管WPH无法提供MST的物理洞察力，但其可逆性使我们能重构场构型随时间的变化，包括场与场之间的相关性。