Neural-Network Chemical Emulator for First-Star Formation: Robust Iterative Predictions over a Wide Density Range

TL;DR

This paper introduces a neural-network emulator that accurately and rapidly predicts the thermochemical evolution during Population III star formation across a vast density range, significantly speeding up simulations.

Contribution

It develops a novel, efficient neural emulator with a timescale-based update method for robust, iterative predictions in star formation modeling.

Findings

Achieves <10% error in over 90% of cases for temperature and chemical abundances.

Emulator is ~10 times faster on CPU and >1000 times faster on GPU than traditional methods.

Validates the approach with one-zone collapse calculations showing good agreement with numerical integration.

Abstract

We present a neural-network emulator for the thermal and chemical evolution in Population III star formation. The emulator accurately reproduces the thermochemical evolution over a wide density range spanning 21 orders of magnitude (10$^{-3}$-10$^{18}$ cm$^{-3}$), tracking six primordial species: H, H$_2$, e$^{-}$, H$^{+}$, H$^{-}$, and H$_2^{+}$. To handle the broad dynamic range, we partition the density range into five subregions and train separate deep operator networks (DeepONets) in each region. When applied to randomly sampled thermochemical states, the emulator achieves relative errors below 10% in over 90% of cases for both temperature and chemical abundances (except for the rare species H$_2^{+}$). The emulator is roughly ten times faster on a CPU and more than 1000 times faster for batched predictions on a GPU, compared with conventional numerical integration. Furthermore, to ensure robust predictions under many iterations, we introduce a novel timescale-based update method, where a short-timestep update of each variable is computed by rescaling the predicted change over a longer timestep equal to its characteristic variation timescale. In one-zone collapse calculations, the results from the timescale-based method agree well with traditional numerical integration even with many iterations at a timestep as short as 10$^{-4}$ of the free-fall time. This proof-of-concept study suggests the potential for neural network-based chemical emulators to accelerate hydrodynamic simulations of star formation.