# Multiscale autonomous forecasting of plasma systems' dynamics using neural networks

arXiv: https://arxiv.org/abs/2502.11203 · HTML: https://mlsanity.com/paper/2502.11203/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 56 references that are in the map.
- First posted on arXiv 16 Feb 2025.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
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- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [Physics-informed neural networks for solving Reynolds-averaged Navierunicodex2013Stokes equations](https://mlsanity.com/paper/2107.10711/) (2021)
- [Hierarchical Deep Learning of Multiscale Differential Equation Time-Steppers](https://mlsanity.com/paper/2008.09768/) (2020)
- [Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification](https://mlsanity.com/paper/2107.10878/) (2021)
- [Preformer: Predictive Transformer with Multi-Scale Segment-wise Correlations for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2202.11356/) (2022)
- [DSTP-RNN: a dual-stage two-phase attention-based recurrent neural networks for long-term and multivariate time series prediction](https://mlsanity.com/paper/1904.07464/) (2019)
- [RecFNO: a resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operator](https://mlsanity.com/paper/2302.09808/) (2023)
- [Gated recurrent units viewed through the lens of continuous time dynamical systems](https://mlsanity.com/paper/1906.01005/) (2019)
- [Dynamic Mode Decomposition for data-driven analysis and reduced-order modelling of ExB plasmas: I. Extraction of spatiotemporally coherent patterns](https://mlsanity.com/paper/2308.13726/) (2023)
- [Dynamic Mode Decomposition for data-driven analysis and reduced-order modelling of ExB plasmas: II. dynamics forecasting](https://mlsanity.com/paper/2308.13727/) (2023)
- [Data-driven local operator finding for reduced-order modelling of plasma systems: I. Concept and verifications](https://mlsanity.com/paper/2403.01523/) (2024)
- [Comparison between DeepESNs and gated RNNs on multivariate time-series prediction](https://mlsanity.com/paper/1812.11527/) (2018)
- [Machine Learning Applications to Computational Plasma Physics and Reduced-Order Plasma Modeling: A Perspective](https://mlsanity.com/paper/2409.02349/) (2024)
- [TSONN: Time-stepping-oriented neural network for solving partial differential equations](https://mlsanity.com/paper/2310.16491/) (2023)
- [Efficient time stepping for numerical integration using reinforcement learning](https://mlsanity.com/paper/2104.03562/) (2021)

## Abstract (arXiv)

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. 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. The results of this work position the hierarchical multiscale neural network as a promising tool for efficient plasma forecasting and digital twin applications.