Emulation of SPHEREx Galaxy Power Spectra I: Neural Network Details and Optimization

We present neural networks to generate redshift-space galaxy power spectrum multipoles for multiple tracer and redshift bins simultaneously given a set of input cosmology and galaxy bias parameters. This emulator utilizes a combination of fully-connected layers and transformer architecture to accurately predict galaxy power spectrum multipoles $900$ times faster than the SPHEREx pipeline. We quantify network performance using both $\Delta \chi^2$, and likelihood contours for simulated SPHEREx analyses, using two correlated tracer bins and two independent redshift bins. After optimizing network architecture, the loss function, and training set sampling strategy, we achieve $\operatorname{Med}\left( \Delta \chi^2\right) = 0.069$ when comparing to our testing set. At the contour-level our emulator agrees with EFT predictions over a realistic parameter range, with an average 1D best-fit shift of $0.078\sigma$ and $0.82 \%$ change in 1D error bars. These results demonstrate the feasibility of using neural-network emulators to accelerate SPHEREx redshift-space power-spectrum analyses.