Real-time prediction of plasma instabilities with sparse-grid-accelerated optimized dynamic mode decomposition

2025-07-03

AI Summary

To address the “curse of dimensionality” in real-time prediction of plasma microinstabilities within high-dimensional parameter spaces, this work proposes a parametric reduced-order modeling (ROM) framework integrating sparse grids with optimized dynamic mode decomposition (optDMD). We innovatively construct nested sparse grids using (L)-Leja points, drastically reducing sampling complexity in high dimensions. By coupling sparse grid interpolation with optDMD, the method synergistically embeds data-driven dynamics and parametric dependence. Using only 28 high-fidelity simulations, we construct a highly accurate parametric ROM over a six-dimensional input parameter space—enabling efficient multi-query analysis and real-time prediction for fusion simulations. This approach establishes a new paradigm for high-dimensional parametric modeling: sample-efficient, computationally lightweight, and high-fidelity.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Learning with Manifolds
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

Parametric data-driven reduced-order models (ROMs) that embed dependencies in a large number of input parameters are crucial for enabling many-query tasks in large-scale problems. These tasks, including design optimization, control, and uncertainty quantification, are essential for developing digital twins in real-world applications. However, standard training data generation methods are computationally prohibitive due to the curse of dimensionality, as their cost scales exponentially with the number of inputs.This paper investigates efficient training of parametric data-driven ROMs using sparse grid interpolation with (L)-Leja points, specifically targeting scenarios with higher-dimensional input parameter spaces. (L)-Leja points are nested and exhibit slow growth, resulting in sparse grids with low cardinality in low-to-medium dimensional settings, making them ideal for large-scale, computationally expensive problems. Focusing on gyrokinetic simulations of plasma micro-instabilities in fusion experiments as a representative real-world application, we construct parametric ROMs for the full 5D gyrokinetic distribution function via optimized dynamic mode decomposition (optDMD) and sparse grids based on (L)-Leja points. We perform detailed experiments in two scenarios: First, the Cyclone Base Case benchmark assesses optDMD ROM prediction capabilities beyond training time horizons and across variations in the binormal wave number. Second, for a real-world electron temperature gradient driven micro-instability simulation featuring six input parameters, we demonstrate that an accurate parametric optDMD ROM can be constructed at a cost of only $28$ high-fidelity gyrokinetic simulations thanks to sparse grids. In the broader context of fusion research, these results demonstrate the potential of sparse grid-based parametric ROMs to enable otherwise intractable many-query tasks.

Problem

• Efficient training of parametric ROMs in high-dimensional spaces
• Real-time prediction of plasma instabilities using sparse grids
• Reducing computational cost for many-query tasks in fusion research

Innovation

• Sparse grid interpolation with L-Leja points
• Optimized dynamic mode decomposition (optDMD)
• Low-cost parametric ROMs for plasma instabilities