Deep Learning Analysis of Ions Accelerated at Shocks

TL;DR

This work examines ion injection and acceleration at non-relativistic collisionless shocks using deep learning on hybrid-pic simulations. A convolutional neural network predicts whether ions are injected into the acceleration process using only initial time-series of local magnetic fields, achieving high accuracy across perpendicular SDA and parallel DSA regimes. Complementary approaches include an MLP with manual features and autoencoder architectures to compress and reconstruct time-series, revealing both the predictive power and current limitations of ML for kinetic plasma insights. The results support a data-driven path toward sub-grid kinetic models in fluid simulations and provide physical validation for the role of early gyrations in determining particle fate at shocks.

Abstract

We study the application of deep learning techniques to the analysis and classification of ions accelerated at collisionless shocks in hybrid (kinetic ions--fluid electrons) simulations. Ions were classified as thermal, suprathermal, or nonthermal, depending on the energy they achieved and the acceleration regime they fell under. These classifications were used to train deep learning models to predict which particles are injected into the acceleration process with high accuracy (>90%), using only time series of the local magnetic field they experienced during their initial interaction with the shock. An autoencoder architecture was also tested, for which time series of various parameters were reconstructed from encoded representations. This study shows the potential of applying machine learning techniques to extract physical insights from kinetic plasma simulations and sets the groundwork for future applications, including the construction of sub-grid models in fluid approaches.

Figures (8)

• Figure 1: Evolution of the postshock energy spectrum for the 2D parallel $M=10$ shock. The distribution begins as a Maxwellian, but over time it develops a distinct nonthermal power-law tail.
• Figure 2: Visualization of the CNN architecture used for classification tasks. Blue blocks represent 1D arrays in convolutional layers, with longer blocks representing arrays of larger lengths. Green circles represent nodes in fully connected layers and the red circle represents the final output of the neural network. Within labels, c is the number of output channels from a convolutional layer, k is kernel size, p is the probability of dropping for a dropout layer, s is the stride, o is the output size for the adaptive pooling layer, and n is the number of nodes in a linear layer. All convolutional layers have a stride of $1$.
• Figure 3: Left: History of training and validation loss for the CNN trained on magnetic field time series from the perpendicular shock (§\ref{['oblique']}). Validation loss eventually starts performing worse than training loss, which indicates overfitting. Actual model used in final tests is taken at the best epoch (39). Center: History of training and validation accuracy. Right: ROC curve for the CNN trained on magnetic field time series from the perpendicular shock.
• Figure 4: For the perpendicular dataset, with magnetic field input data, this shows multiple CNNs trained with varying number of time steps. Time is given in gyro periods, defined as $2\pi\omega_c^{-1}$. One gyro period is about the time it takes to complete a cycle of SDA. Performance begins to deteriorate at less than $0.75$ gyro periods.
• Figure 5: Left: History of training and validation accuracy for the CNN trained on magnetic field time series from the parallel dataset. Actual model used in final tests is taken at the best epoch (21). Center: History of training and validation loss. Right: ROC curve, with AUC shown in legend.