Development of a 3D-CNN-based Prediction Model for Migration Barriers in Plasma-Wall Interactions

Abstract: Understanding the long-term transport of hydrogen isotopes in plasma-facing materials, such as tungsten, is critical for the steady-state operation of magnetic confinement fusion reactors. However, dynamically updating the transition parameters for kinetic Monte Carlo (kMC) simulations as the atomic structure evolves under continuous plasma irradiation remains a severe computational bottleneck. Conventionally, calculating these migration barriers requires the iterative and computationally expensive Nudged Elastic Band (NEB) method. To overcome this limitation, this article presents a highly efficient surrogate model for predicting migration barriers using a three-dimensional Convolutional Neural Network (3D-CNN), establishing the final component necessary to realize on-the-fly molecular dynamics (MD) and kMC hybrid simulations. The proposed deep learning model takes a two-channel volumetric input, the local three-dimensional potential energy distribution and the voxelized spatial coordinates of the initial and final trapping sites, to directly output the migration barrier as a scalar value. Trained on a comprehensive dataset of tungsten-hydrogen configurations evaluated using the Embedded Atom Method (EAM) potential, the model demonstrated robust predictive accuracy, achieving a Mean Absolute Error (MAE) of 0.124 eV and a high coefficient of determination of 0.890. Furthermore, utilizing GPU acceleration, the inference time is reduced to approximately 2.7 milliseconds per barrier, achieving a speed-up ratio of over 23,000 compared to conventional NEB calculations. This extraordinary acceleration effectively resolves the computational barrier of transition rate evaluations, paving the way for large-scale, dynamic modeling of plasma-wall interactions.

• The paper presents a 3D-CNN surrogate that accurately predicts migration barriers for hydrogen in tungsten, significantly reducing computational cost.
• The model achieves a mean absolute error of 0.124 eV and a GPU inference time of 2.7 ms, demonstrating high precision and speed.
• This approach enables real-time, atomistic plasma-wall simulations, facilitating advanced studies in fusion material behavior.

3D Convolutional Neural Network Surrogate for Migration Barrier Prediction in Plasma-Wall Interaction Simulations

Introduction

Accurate modeling of plasma-wall interactions in fusion environments is critically dependent on simulating the migration dynamics of hydrogen isotopes within plasma-facing components, especially tungsten. The dynamic evolution of atomic structure under continuous plasma irradiation renders static parameterization insufficient for kinetic Monte Carlo (kMC) models, which rely on energetically accurate migration barriers between trapping sites. Conventionally, the evaluation of migration barriers via the Nudged Elastic Band (NEB) method incurs prohibitive computational overhead, precluding on-the-fly barrier calculation in large-scale, atomistically resolved molecular dynamics (MD)-kMC hybrid workflows. This work introduces a 3D Convolutional Neural Network (3D-CNN) architecture as an efficient surrogate for NEB-based migration barrier prediction, thus eliminating a major performance bottleneck in dynamic plasma-facing material simulations (2604.05521).

Methodology

The surrogate model operates on a two-channel three-dimensional input tensor. The first channel encodes the spatial coordinates of the initial and final hydrogen trapping sites as voxelized one-hot representations, with the starting site at the center of a 63 × 63 × 63 grid. The second channel comprises the 3D local potential energy distribution—computed using the Embedded Atom Method (EAM) potential tailored for tungsten-hydrogen systems—encompassing the possible migration pathway. Data samples are systematically constructed such that the start and end points reside within a 1.58 Å sphere, corresponding to the tungsten lattice constant.

The 3D-CNN architecture comprises a sequence of Conv3D blocks (kernel size: 3×3×3, filters increasing from 16 to 64), interleaved with Layer Normalization and LeakyReLU activation, and regularized by Dropout (0.1). Progressive spatial downsampling is achieved with stride-2 convolutions. A global average pooling layer reduces the spatial dimensions, followed by a dense layer (128 units, ReLU) and a final linear readout layer. The network is trained to regress the migration barrier (ΔU), defined as the energy difference between the highest saddle point on the NEB-calculated minimum energy path and the initial state, with all barriers above 5.0 eV excluded as physically rare events.

Results

The surrogate was trained on a dataset of 82,000 tungsten-hydrogen configurations, with NEB-evaluated migration barriers as ground truth. The model attained a mean absolute error (MAE) of 0.124 eV, a root mean square error (RMSE) of 0.185 eV, and a coefficient of determination ($R^2$) of 0.890 on test data. Notably, the prediction error exhibits moderate inflation in the regime of higher migration barriers, consistent with the distributional sparsity of such events in the training set.

From a computational perspective, the surrogate achieves remarkable acceleration: single-barrier inference on CPU is 0.101 s, and on GPU, 2.7 ms. Relative to the 63.1 seconds required for NEB calculations (single-core CPU), this constitutes a speed-up factor of over 23,000 on GPU, fully enabling real-time updating of transition parameters for kMC simulations under dynamically changing atomic environments.

Implications for Plasma-Wall Modeling

The successful integration of a deep learning surrogate for migration barriers completes a scalable and fully differentiable parameterization pipeline for hybrid MD-kMC plasma-wall simulations. By integrating this 3D-CNN (Model-C) with prior neural models for potential energy field estimation (Model-A: pix2pix variant) and trapping site identification (Model-B: U-Net), on-the-fly adaptation to evolving wall morphologies is made computationally tractable.

This development substantially enhances both the fidelity and scale of simulation campaigns addressing hydrogen retention, trapping, and permeation under reactor-relevant flux and damage conditions. Theoretical implications extend to more mechanistic, data-driven studies of isotope effects, defect-structure evolution, and benchmarking of interatomic potentials. Practically, it will facilitate investigation of wall conditioning, lifetime prediction, and mitigation strategies for tritium inventory in fusion devices.

Future Directions

The modular architecture of the prediction pipeline is conducive to further expansion. Future research should prioritize three axes: (1) expansion to multicomponent plasma-facing materials, incorporating carbon, beryllium, and complex alloys; (2) uncertainty quantification of surrogate predictions, to underpin robust kMC event selection; and (3) recursive integration with active learning loops, refreshing the training set with rare-event NEB calculations for extrapolative regime coverage. Additionally, transfer learning approaches can further reduce data requirements for new alloy systems.

Conclusion

The introduction of a 3D-CNN surrogate for hydrogen migration barriers in tungsten delivers the necessary acceleration to enable atomistic, real-time, and dynamic plasma-wall simulations at scales commensurate with fusion device operation. With robust accuracy and orders-of-magnitude computational speed-up, this architecture addresses a longstanding bottleneck and opens new possibilities for physically resolved, multi-scale modeling of plasma-material interfaces in magnetic confinement fusion scenarios.