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

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 grid-based data generation methods are computationally prohibitive due to the curse of dimensionality. 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 with six input parameters, we demonstrate that a predictive parametric optDMD ROM that is up to three orders of magnitude cheaper to evaluate can be constructed using only 28 high-fidelity gyrokinetic simulations, enabled by the use of 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.

31 pages, 15 figures, 10 tables

References in corpus (18)

• On Dynamic Mode Decomposition: Theory and Applications
• ORB5: a global electromagnetic gyrokinetic code using the PIC approach in toroidal geometry
• Fast modeling of turbulent transport in fusion plasmas using neural networks
• Adaptive Leja sparse grid constructions for stochastic collocation and high-dimensional approximation
• Characterizing Magnetized Plasmas with Dynamic Mode Decomposition
• Dynamic Mode Decomposition for Plasma Diagnostics and Validation
• Parametric Dynamic Mode Decomposition for Reduced Order Modeling
• VPIC 2.0: Next Generation Particle-in-Cell Simulations
• Non-intrusive reduced-order models for parametric partial differential equations via data-driven operator inference
• Plasma Surrogate Modelling using Fourier Neural Operators
• A Dynamic Mode Decomposition Extension for the Forecasting of Parametric Dynamical Systems
• Reduced models for ETG transport in the pedestal
• Koopman-Based Approach to Non-intrusive Projection-Based Reduced-Order Modeling with Black-Box High-Fidelity Models. Part II: Application
• On Error Estimation for Reduced-order Modeling of Linear Non-parametric and Parametric Systems
• Data-driven low-fidelity models for multi-fidelity Monte Carlo sampling in plasma micro-turbulence analysis
• Distributed computing for physics-based data-driven reduced modeling at scale: Application to a rotating detonation rocket engine
• Turbulence suppression by energetic particles: A sensitivity-driven dimension-adaptive sparse grid framework for discharge optimization
• Advanced surrogate model for electron-scale turbulence in tokamak pedestals