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.