{"ID":2899360,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.02106","arxiv_id":"2507.02106","title":"Resolving Turbulent Magnetohydrodynamics: A Hybrid Operator-Diffusion Framework","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.","short_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 (...","url_abs":"https://arxiv.org/abs/2507.02106","url_pdf":"https://arxiv.org/pdf/2507.02106v2","authors":"[\"Semih Kacmaz\",\"E. A. Huerta\",\"Roland Haas\"]","published":"2025-07-02T19:33:57Z","proceeding":"physics.flu-dyn","tasks":"[\"physics.flu-dyn\",\"cs.AI\",\"cs.LG\",\"gr-qc\",\"physics.comp-ph\"]","methods":"[\"Diffusion Model\"]","has_code":false}