The First Star-by-star $N$-body/Hydrodynamics Simulation of Our Galaxy Coupling with a Surrogate Model

TL;DR

This work overcomes the billion-particle barrier in galaxy simulations by coupling a traditional N-body/SPH code with a surrogate neural network that predicts SN shell evolution, enabling a fixed global timestep and extreme parallelism. The approach leverages FDPS for scalable particle management and a PIKG kernel generator for optimized interaction calculations, achieving 300 billion particles on 148,900 Fugaku nodes (about 7.15 million CPU cores). The surrogate model is trained on $1\,M_\odot$ SN simulations, maps SPH to 60 pc voxel grids via SPH kernels, and uses Gibbs sampling to recover particle data, with CPU-only DL inference to minimize data transfer bottlenecks. Results demonstrate scalable performance across architectures (ARM, x86, GPUs) and validate the first star-by-star MW-like galaxy simulation, with potential applicability to other multiscale, short- vs long-time phenomena in physics and beyond.

Abstract

A major goal of computational astrophysics is to simulate the Milky Way Galaxy with sufficient resolution down to individual stars. However, the scaling fails due to some small-scale, short-timescale phenomena, such as supernova explosions. We have developed a novel integration scheme of $N$-body/hydrodynamics simulations working with machine learning. This approach bypasses the short timesteps caused by supernova explosions using a surrogate model, thereby improving scalability. With this method, we reached 300 billion particles using 148,900 nodes, equivalent to 7,147,200 CPU cores, breaking through the billion-particle barrier currently faced by state-of-the-art simulations. This resolution allows us to perform the first star-by-star galaxy simulation, which resolves individual stars in the Milky Way Galaxy. The performance scales over $10^4$ CPU cores, an upper limit in the current state-of-the-art simulations using both A64FX and X86-64 processors and NVIDIA CUDA GPUs.

Figures (7)

• Figure 1: Material circulation in a galaxy: Diffuse warm gas loses energy through radiation and conduction and form a disk like structure (galactic disk). Stars form in clouds with low-temperature ($\sim 10$ K) molecular hydrogen in the disk. When massive stars--roughly 10 times the mass of the Sun--reach the end of their lifetimes, they explode as supernovae, generating extremely hot gas ($\sim10^7$ K). These explosions inject both energy and heavy elements, such as carbon (C), oxygen (O), magnesium (Mg), and iron (Fe) into the surrounding interstellar gas and induce turbulence. A part of these materials is ejected as outflow and eventually fall back to the galactic disk, where forms the next generation stars. These enriched materials finally forms planets like the Earth and lives like us. (credit: NASA/JPL-Caltech, ESA, CSA, STScI).
• Figure 2:
• Figure 3: Schematic illustration of our simulation method. The main nodes integrate the entire region of a galaxy using a shared timestep ($\Delta t_{\rm global}$) with a large number of computational nodes (i.e., $1~{\rm k} \sim 150~{\rm k}$ nodes). Upon detecting SN events, it sends the affected regions to an available pool node. This pool node then uses a pre-trained neural network to predict the 3D evolution of these SN regions. The prediction process is carried out independently from the simulation performed by the main nodes. Every 50 global timesteps, the predicted particle data is sent back to the main nodes. To handle the continuous processing of SN events, the system maintains a set of 50 pool nodes, corresponding to the 50-step interval between updates. © 2010 Takaaki Takeda, Junichi Baba, Takayuki Saitoh, 4D2U Project, NAOJ.
• Figure 4: An example of the domain decomposition sliced at $y=0$.
• Figure 5: Snapshots of gas distribution of the galactic disks integrated with our new scheme with DL surrogate model. The right and left panels show surface density for the face-on ($x-y$ plane) and edge-on ($x-z$ plane), respectively.