Multiscale autonomous forecasting of plasma systems’ dynamics using neural networks

Abstract Plasma systems exhibit complex multiscale dynamics, resolving which poses significant challenges for conventional numerical simulations. Machine learning (ML) offers an alternative by learning data-driven representations of these dynamics. Yet existing ML time-stepping models suffer from error accumulation, instability, and limited long-term forecasting horizons. This paper demonstrates the application of a hierarchical multiscale neural network architecture for autonomous plasma forecasting. The framework integrates multiple neural networks trained across different temporal scales to capture both fine-scale and large-scale behaviors while mitigating compounding error in recursive evaluation. By structuring the model as a hierarchy of sub-networks, each trained at a distinct time resolution, the approach effectively balances short-term resolution with long-term stability. Fine-scale networks accurately resolve fast-evolving features, while coarse-scale networks provide broader temporal context, reducing the frequency of recursive updates and limiting the accumulation of small prediction errors over time. We first evaluate the method using canonical nonlinear dynamical systems and compare its performance against classical single-scale neural networks. The results demonstrate that single-scale neural networks experience rapid divergence due to recursive error accumulation, whereas the multiscale approach improves stability and extends prediction horizons. Next, our ML model is applied to two plasma configurations of high scientific and applied significance, demonstrating its ability to preserve spatial structures and capture multiscale plasma dynamics. By leveraging multiple time-stepping resolutions, the applied framework is shown to outperform conventional single-scale networks for the studied plasma test cases. Additionally, another great advantage of our approach is its parallelizability by design, which enables the development of computationally efficient forecasters. The results of this work position the hierarchical multiscale neural network as a promising tool for efficient plasma forecasting and digital twin applications.