SageNet: Fast Neural Network Emulation of the Stiff-amplified Gravitational Waves from Inflation - Fan Zhang; Yifang Luo; Bohua Li; Ruihan Cao; Wenjin Peng; Joel Meyers; Paul R. Shapiro (The Astrophysical Journal Supplement Series)
Accurate modeling of the inflationary gravitational waves (GWs) requires time-consuming, iterative numerical integrations of differential equations to take into account their backreaction on the expansion history. To improve computational efficiency while preserving accuracy, we present the Stiff-amplified Gravitational-wave Emulator Network ( SageNet ), a deep learning framework designed to replace conventional numerical solvers (code available at https://github.com/YifangLuo/SageNet ). SageNet employs a long short-term memory architecture to emulate the present-day energy density spectrum of the inflationary GWs with possible stiff amplification, Ω _GW ( f ). Trained on a data set of 25,689 numerically generated solutions, SageNet allows accurate reconstructions of Ω _GW ( f ) and generalizes well to a wide range of cosmological parameters; 90.9% of the test emulations with randomly distributed parameters exhibit errors of under 4%. In addition, SageNet demonstrates its ability to learn and reproduce the artificial, adaptive sampling patterns in numerical calculations, which implement denser sampling of frequencies around changes in spectral indices in Ω _GW ( f ). The dual capability of learning both physical and artificial features of the numerical GW spectra establishes SageNet as a robust alternative to exact numerical methods. Finally, our benchmark tests show that SageNet reduces the computation time from tens of seconds to milliseconds, achieving a speedup of ∼10 ^4 times over standard CPU-based numerical solvers with the potential for further acceleration on GPU hardware. These capabilities make SageNet a powerful tool for accelerating Bayesian inference procedures for extended cosmological models. In a broad sense, the SageNet framework offers a fast, accurate, and generalizable solution to modeling cosmological observables whose theoretical predictions demand costly differential equation solvers.