Machine learning-driven conservative-to-primitive conversion in hybrid piecewise polytropic and tabulated equations of state

TL;DR

This paper introduces a machine learning approach using neural networks and GPU optimization to significantly accelerate conservative-to-primitive inversion in relativistic hydrodynamics, reducing computation time with minimal accuracy loss.

Contribution

The authors develop and optimize neural network models for fast, accurate conservative-to-primitive conversion, leveraging GPU inference and quantization for large-scale simulations.

Findings

Neural network models achieve errors below 10^{-6}.

TensorRT optimization yields 400x speedup over CPU methods.

Sub-linear scaling observed with increasing dataset size.

Abstract

We present a novel machine learning (ML) method to accelerate conservative-to-primitive inversion, focusing on hybrid piecewise polytropic and tabulated equations of state. Traditional root-finding techniques are computationally expensive, particularly for large-scale relativistic hydrodynamics 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 accuracy loss. The NNC2PS model achieves $ L_1 $ and $ L_\infty $ errors of $ 4.54 \times 10^{-7} $ and $ 3.44 \times 10^{-6} $, respectively, while the NNC2PL model exhibits even lower error values. TensorRT optimization with mixed-precision deployment substantially accelerates performance compared to traditional root-finding methods. Specifically, the mixed-precision TensorRT engine for NNC2PS achieves inference speeds approximately 400 times faster than a traditional single-threaded CPU implementation for a dataset size of 1,000,000 points. Ideal parallelization across an entire compute node in the Delta supercomputer (Dual AMD 64 core 2.45 GHz Milan processors; and 8 NVIDIA A100 GPUs with 40 GB HBM2 RAM and NVLink) predicts a 25-fold speedup for TensorRT over an optimally-parallelized numerical method when processing 8 million data points. Moreover, the ML method exhibits sub-linear scaling with increasing dataset sizes. We release the scientific software developed, enabling further validation and extension of our findings. This work underscores the potential of ML, combined with GPU optimization and model quantization, to accelerate conservative-to-primitive inversion in relativistic hydrodynamics simulations.