[Paper Review] An efficient plasma-surface interaction surrogate model for sputtering processes based on autoencoder neural networks

Tobias Gergs, Borislav Borislavov+1 more|arXiv (Cornell University)|Sep 3, 2021

Nuclear Materials and Properties32 references24 citations

TL;DR

This paper proposes a physics-informed, autoencoder-based surrogate model for plasma-surface sputtering processes that reduces high-dimensional energy-angular distributions (EADs) to a two-component latent space. By leveraging a conditional β-variational autoencoder and transfer learning, the method achieves competitive prediction accuracy with only 15,111 parameters—0.378% of a standard multilayer perceptron—enabling efficient, generalizable modeling of variable Ti-Al stoichiometry and ion energy distributions.

ABSTRACT

Simulations of thin film sputter deposition require the separation of the plasma and material transport in the gas-phase from the growth/sputtering processes at the bounding surfaces. Interface models based on analytic expressions or look-up tables inherently restrict this complex interaction to a bare minimum. A machine learning model has recently been shown to overcome this remedy for Ar ions bombarding a Ti-Al composite target. However, the chosen network structure (i.e., a multilayer perceptron) provides approximately 4 million degrees of freedom, which bears the risk of overfitting the relevant dynamics and complicating the model to an unreliable extend. This work proposes a conceptually more sophisticated but parameterwise simplified regression artificial neural network for an extended scenario, considering a variable instead of a single fixed Ti-Al stoichiometry. A convolutional $\beta$-variational autoencoder is trained to reduce the high-dimensional energy-angular distribution of sputtered particles to a latent space representation of only two components. In addition to a primary decoder which is trained to reconstruct the input energy-angular distribution, a secondary decoder is employed to reconstruct the mean energy of incident Ar ions as well as the present Ti-Al composition. The mutual latent space is hence conditioned on these quantities. The trained primary decoder of the variational autoencoder network is subsequently transferred to a regression network, for which only the mapping to the particular latent space has to be learned. While obtaining a competitive performance, the number of degrees of freedom is drastically reduced to 15,111 and 486 parameters for the primary decoder and the remaining regression network, respectively. The underlying methodology is general and can easily be extended to more complex physical descriptions with a minimal amount of data required.

Motivation & Objective

• Address the computational inefficiency and overfitting risks of high-parameter machine learning models in plasma-surface interaction simulations.
• Extend prior work on sputtered particle EAD prediction to include variable Ti-Al stoichiometry as a tunable surface parameter.
• Reduce the dimensionality of complex, high-dimensional EAD data while preserving physical relevance through a conditional variational autoencoder.
• Enable efficient regression via transfer learning by transferring the pretrained decoder to a lightweight model with minimal parameters.
• Develop a generalizable, data-efficient framework suitable for complex, computationally expensive physical scenarios like molecular dynamics simulations.

Proposed method

• Train a convolutional β-variational autoencoder (β-VAE) to compress 30×20 energy-angular distribution (EAD) data into a two-dimensional latent space, conditioned on incident Ar ion energy and Ti-Al composition.
• Implement a dual-decoder architecture: a primary decoder reconstructs the full EAD, while a secondary decoder predicts mean incident ion energy and surface stoichiometry from the shared latent space.
• Use transfer learning by freezing the pretrained β-VAE encoder and decoder, then fine-tuning only the regression head to map input ion energy distributions to the latent space.
• Apply a power-of-two padding strategy to ensure compatibility with convolutional layers and improve training stability.
• Train the model on a small, realistic dataset of 1,350 samples (450 per stoichiometry x = 0.3, 0.5, 0.7) generated via TRIDYN sputtering simulations.
• Validate generalization using out-of-distribution data (x = 0.2, 0.4, 0.8) to assess interpolation and extrapolation performance.

Experimental results

Research questions

• RQ1 Can a conditional β-variational autoencoder effectively reduce the dimensionality of complex, multi-species sputtered particle energy-angular distributions while preserving physical fidelity?
• RQ2 Does transferring the pretrained decoder from a variational autoencoder to a regression network significantly reduce model complexity without sacrificing predictive accuracy?
• RQ3 How well does the resulting surrogate model generalize to unseen Ti-Al stoichiometries (interpolation and extrapolation) with limited training data?
• RQ4 To what extent does the method reduce the number of trainable parameters compared to standard multilayer perceptrons while maintaining competitive performance in sputtering process modeling?

Key findings

• The proposed model reduces the number of trainable parameters in the primary decoder to 15,111 (0.378% of a standard multilayer perceptron), drastically lowering the risk of overfitting.
• The remaining regression network requires only 486 parameters (0.012% of the MLP), enabling highly efficient inference and deployment.
• The model achieves competitive prediction accuracy for EADs across varying Ar ion energies and Ti-Al compositions, even with a small dataset of 1,350 samples.
• Generalization to unseen stoichiometries (x = 0.2, 0.4, 0.8) demonstrates robust interpolation and extrapolation capabilities, indicating strong transferability.
• The conditional β-VAE architecture successfully learns a disentangled, two-dimensional latent space that encodes both EAD structure and key physical inputs (ion energy and composition).
• The method is generalizable and can be extended to include dynamic surface properties or more complex material systems with minimal additional data.