Big bang nucleosynthesis (BBN) predictions of primordial light-element abundances offer a powerful probe of early-Universe physics. However, high-accuracy numerical BBN calculations have become a major computational bottleneck for large-scale cosmological inferences due to the complex nuclear network. Here we present bbnet, a fast and accurate deep learning emulator for primordial abundances. The training data are generated by full numerical calculations using two public BBN codes, parthenope and alterbbn, modified to accommodate extended cosmologies that include dark radiation and a stiff equation of state. The network employs a residual multihead architecture to capture convoluted physical relationships. bbnet produces primordial helium-4 and deuterium abundances with negligible errors in milliseconds per sample, achieving a speed-up of up to ${10}^4$ times relative to first-principles solvers while remaining unbiased over wide parameter ranges. Therefore, our emulator can supersede traditional simplified numerical prescriptions that compromise accuracy for speed. Based on extensive assessments of its performance, we conclude that bbnet is an optimal solution to the theoretical prediction of primordial element abundances. It will serve as a reliable tool for precision cosmology and new physics searches.

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• Big bang nucleosynthesis
• Cosmological parameters
• Evolution of the Universe
• Deep learning