Resolving Turbulent Magnetohydrodynamics: A Hybrid Operator-Diffusion Framework

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.

AI-driven Conservative-to-Primitive Conversion in Hybrid Piecewise Polytropic and Tabulated Equations of State

We present a novel AI-based approach to accelerate conservative-to-primitive inversion in relativistic hydrodynamics simulations, focusing on hybrid piecewise polytropic and tabulated equations of state. Traditional root-finding methods are computationally intensive, particularly in large-scale simulations. To address this, we employ feedforward neural networks (NNC2PS and NNC2PL), trained in PyTorch and optimized for GPU inference using NVIDIA TensorRT, achieving significant speedups with minimal loss in accuracy. The NNC2PS model achieves $L_1$ and $L_\infty$ errors of $4.54 \times 10^{-7}$ and $3.44 \times 10^{-6}$, respectively, with the NNC2PL model yielding even lower error values. TensorRT optimization ensures high accuracy, with FP16 quantization offering 7x faster performance than traditional root-finding methods. Our AI models outperform conventional CPU solvers, demonstrating enhanced inference times, particularly for large datasets. We release the scientific software developed for this work, enabling the validation and extension of our findings. These results highlight the potential of AI, combined with GPU optimization, to significantly improve the efficiency and scalability of numerical relativity simulations.