Design and optimization of neural networks for multifidelity cosmological emulation

Abstract: Accurate and efficient simulation-based emulators are essential for interpreting cosmological survey data down to nonlinear scales. Multifidelity emulation techniques reduce simulation costs by combining high- and low-fidelity data, but traditional regression methods such as Gaussian processes struggle with scalability in sample size and dimensionality. In this work, we present T2N-MusE, a neural network framework characterized by (i) a novel 2-step multifidelity architecture, (ii) a 2-stage Bayesian hyperparameter optimization, (iii) a 2-phase $k$-fold training strategy, and (iv) a per-$z$ principal component analysis strategy. We apply T2N-MusE to selected data from the Goku simulation suite, covering a 10-dimensional cosmological parameter space, and build emulators for the matter power spectrum over a range of redshifts with different configurations. We find the emulators outperform our earlier Gaussian process models significantly and demonstrate that each of these techniques is efficient in training neural networks or/and effective in improving generalization accuracy. We observe a reduction in validation error by more than a factor of five compared to previous work. This framework has been used to build the most powerful emulator for the matter power spectrum, GokuNEmu, and will also be used to construct emulators for other statistics in future.