Field-level Emulation of Cosmic Structure Formation with Cosmology and Redshift Dependence (2408.07699v1)

Abstract: We present a field-level emulator for large-scale structure, capturing the cosmology dependence and the time evolution of cosmic structure formation. The emulator maps linear displacement fields to their corresponding nonlinear displacements from N-body simulations at specific redshifts. Designed as a neural network, the emulator incorporates style parameters that encode dependencies on $\Omega_{\rm m}$ and the linear growth factor $D(z)$ at redshift $z$. We train our model on the six-dimensional N-body phase space, predicting particle velocities as the time derivative of the model's displacement outputs. This innovation results in significant improvements in training efficiency and model accuracy. Tested on diverse cosmologies and redshifts not seen during training, the emulator achieves percent-level accuracy on scales of $k\sim~1~{\rm Mpc}^{-1}~h$ at $z=0$, with improved performance at higher redshifts. We compare predicted structure formation histories with N-body simulations via merger trees, finding consistent merger event sequences and statistical properties.

• The paper presents a neural network emulator that maps linear displacement fields to nonlinear outcomes with percent-level accuracy across various redshifts.
• The methodology employs a U-Net/V-Net design with style parameters based on cosmological metrics, enabling adaptable predictions across different cosmic environments.
• The work accelerates simulations significantly, offering a practical tool for upcoming galaxy surveys and enhancing constraints on key cosmological parameters.

Overview of Field-Level Emulation of Cosmic Structure Formation

The paper "Field-level Emulation of Cosmic Structure Formation with Cosmology and Redshift Dependence" presents a cutting-edge approach to modeling large-scale cosmic structures. The authors introduce a field-level emulator that utilizes neural networks to predict the nonlinear dynamical evolution of structure formation in the universe. This model is specifically designed to capture dependencies on cosmological parameters such as $\Omega_{\rm m}$, the matter density parameter, and the redshift-dependent linear growth factor $D(z)$.

Model and Methodology

The emulator serves as a neural network that maps linear displacement fields to nonlinear displacements derived from N-body simulations at different redshifts. It incorporates style parameters that encode cosmology dependence, allowing the emulator to generalize across a diverse range of potential cosmic environments. The training process leverages simulation data to predict particle velocities, which are extracted as the time derivatives of the emulator's displacement outputs. This integrated approach improves the emulator's accuracy and efficiency, particularly on small scales.

The architecture of the neural network is based on a U-Net/V-Net design, suitable for three-dimensional convolutional operations. Style parameters based on $\Omega_{\rm m}$ and $D(z)$ are used to modulate the model weights, effectively creating a family of models that can seamlessly interpolate between different cosmological conditions.

Results and Performance

The emulator was tested across a variety of cosmologies and redshifts not included in the training data, demonstrating remarkable performance with percent-level accuracy in predicting the displacement and velocity fields on scales of $k \sim 1 \, \mathrm{Mpc}^{-1} \, h$ at $z=0$, with enhanced accuracy at higher redshifts. Moreover, the method allows for efficient emulation of the non-linear evolution of large-scale structures rapidly, on the order of milliseconds per model evaluation on a single GPU, with implementation scalability on multi-GPU systems.

Significant improvements over previous models are noted, particularly in its ability to reproduce structure formation histories as illustrated by consistent agreement with N-body simulations in the analysis of merger trees. Such consistency asserts the emulator's potential to replace or augment traditional N-body simulations in scenarios where computational resources are constrained.

Implications

The advancements presented in this research have substantial implications for cosmological data analysis and the larger field of computational astrophysics. By offering a rapid yet accurate tool for modeling nonlinear cosmic structures, this emulator paves a new way forward for conducting field-level analyses, which are crucial for interpreting the data from next-generation galaxy surveys like DESI, Euclid, and LSST. These analyses are instrumental in improving our constraints on cosmological parameters and better understanding the underlying physics governing cosmic structure formation.

The research also presents an exciting frontier for future developments, particularly in refining AI-driven models to accommodate even richer datasets and more complex physical processes, including those related to baryonic physics. As the demand for precision in cosmological inference grows, the methodology explored here highlights the growing intersection between machine learning and theoretical astrophysics.

Conclusion

The work on field-level emulation represents an advancement in how we model and understand cosmic structures. It significantly accelerates simulation processes while maintaining high standards of accuracy, suggesting that emulators of this kind are set to become indispensable in the interpretation of cosmological survey data. Looking ahead, further refinement of these models and the potential incorporation of AI-driven generative techniques signify a promising direction for both theoretical and practical developments in the field.