Accelerating kinetic plasma simulations with machine learning generated initial conditions

TL;DR

This work addresses the computational bottleneck of reaching quasi-steady states in kinetic plasma simulations by introducing machine-learning–generated initial conditions (ICGs) that steer PIC simulations toward convergence more quickly. It develops and evaluates three ML approaches—MLP for ion density, PCA+MLP, and CNN for IVDF—trained on 1D-3V CCP simulations across varying frequency and pressure, and defines robust offline and online convergence criteria. The CNN-based IVDF ICG achieves the highest acceleration, with up to 17.1x offline and 4.4x online speedups, while PCA+MLP and MLP offer substantial but smaller gains, all while preserving final converged states. A workflow for iterative data-driven model improvement and digital-twin generation is outlined, highlighting practical implications for rapid design optimization and real-time control in CCP-based microelectronics manufacturing. The results demonstrate a viable path to hybrid ML+HPC acceleration of multi-time-scale plasma simulations and motivate further development toward larger parameter spaces and higher-fidelity, multi-dimensional simulations.

Abstract

Computer aided engineering of multi-time-scale plasma systems which exhibit a quasi-steady state solution are challenging due to the large number of time steps required to reach convergence. Machine learning techniques combined with traditional first-principles simulations and high-performance computing offer many interesting pathways towards resolving this challenge. We consider acceleration of kinetic plasma simulations via machine learning generated initial conditions. The approach is demonstrated through modeling of capacitively coupled plasma discharges relevant to the microelectronics industry. Three models are trained on simulations across a parameter space of device driving frequency and operating pressure. The models incorporate elements of a multi-layer perceptron, principal component analysis, and convolutional neural networks to predict the final time-averaged profiles of ion-density and velocity distribution functions. These data-driven initial condition generators (ICGs) provide a mean speedup of 17.1x in convergence time, when measured using an offline procedure, or a 4.4x speedup with an online procedure, with convolutional neural networks leading to the best performance. The paper also outlines a workflow for continuous data-driven model improvement and simulation speedup, with the aim of generating sufficient data for full device digital twins.

Figures (11)

• Figure 1: Two-dimensional schematic of an argon capacitively coupled plasma discharge with gap width $d$, gas pressure $P$, driving voltage amplitude $\phi_0$ and angular frequency $\omega_{RF}=2 \pi F$. The blue dashed line indicates the 1D spatial domain modeled by 1D-3V PIC simulations in this work.
• Figure 2: (a) Plots of $\Gamma_i$ and $\Lambda$ early in the simulation (at 10 RF periods) and, (b) after convergence has been achieved (at 5,000 RF periods) for 1D-3V PIC simulations of an argon CCP operating at $F=27.12$$MHz$ and $P = 20$$mTorr$. Thicker lines correspond to functions smoothed over space with a Gaussian filter. (c) Evolution of $\epsilon(t)$ with time including the point of convergence measured by the offline procedure. The thicker line corresponds to the same data smoothed with a centered uniform filter. (d) Evolution of $\epsilon(t)$ and $\langle \epsilon_c \rangle(t)$ with time including the point of convergence measured by the online procedure. Temporal smoothing is realized with a backward uniform filter.
• Figure 3: Workflow and model structure for the PCA+MLP training and resulting initial condition generator (ICG). The data is initially split into train and test samples. Dimensionality is reduced via a 27 component PCA decomposition, retaining 91% of explained variance. The eigenvalues of these components for a given CCP frequency and pressure are then learned via an MLP with 4 hidden layers. Initial conditions are generated by first predicting the PCA eigenvalues from the MLP and then reconstructing the profiles.
• Figure 4: Model structure of the CNN trained to produce an initial condition generator (ICG) for the IVDF. The model includes 6 fully connected layers, followed by reshaping and then 4 convolutional layers.
• Figure 5: (a) Converged time-averaged ion density profile (blue line) of an argon CCP discharge operating at 27.12 MHz with 20 mTorr gas pressure and a range of uniform initial conditions (dashed lines). The thicker dashed line corresponds to the density predicted by the global model. (b) Converged time-average ion velocity distribution function (IVDF) for the same discharge parameters.