Resolving Turbulent Magnetohydrodynamics: A Hybrid Operator-Diffusion Framework

• URL: http://arxiv.org/abs/2507.02106v1
• Date: Wed, 02 Jul 2025 19:33:57 GMT
• Title: Resolving Turbulent Magnetohydrodynamics: A Hybrid Operator-Diffusion Framework
• Authors: Semih Kacmaz, E. A. Huerta, Roland Haas,
• Abstract summary: Hybrid machine learning framework is trained on a comprehensive ensemble of high-fidelity simulations with $mathrmRe in 100, 250, 500, 750, 1000, 3000, 10000$.<n>At extreme turbulence levels, it remains the first surrogate capable of recovering the high-wavenumber evolution of the magnetic field.
• Score: 0.2999888908665658
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a hybrid machine learning framework that combines Physics-Informed Neural Operators (PINOs) with score-based generative diffusion models to simulate the full spatio-temporal evolution of two-dimensional, incompressible, resistive magnetohydrodynamic (MHD) turbulence across a broad range of Reynolds numbers ($\mathrm{Re}$). The framework leverages the equation-constrained generalization capabilities of PINOs to predict coherent, low-frequency dynamics, while a conditional diffusion model stochastically corrects high-frequency residuals, enabling accurate modeling of fully developed turbulence. Trained on a comprehensive ensemble of high-fidelity simulations with $\mathrm{Re} \in \{100, 250, 500, 750, 1000, 3000, 10000\}$, the approach achieves state-of-the-art accuracy in regimes previously inaccessible to deterministic surrogates. At $\mathrm{Re}=1000$ and $3000$, the model faithfully reconstructs the full spectral energy distributions of both velocity and magnetic fields late into the simulation, capturing non-Gaussian statistics, intermittent structures, and cross-field correlations with high fidelity. At extreme turbulence levels ($\mathrm{Re}=10000$), it remains the first surrogate capable of recovering the high-wavenumber evolution of the magnetic field, preserving large-scale morphology and enabling statistically meaningful predictions.

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