Simple lessons from complex learning: what a neural network model learns about cosmic structure formation

06/09/2022
∙
by   Drew Jamieson, et al.
∙
0
∙

We train a neural network model to predict the full phase space evolution of cosmological N-body simulations. Its success implies that the neural network model is accurately approximating the Green's function expansion that relates the initial conditions of the simulations to its outcome at later times in the deeply nonlinear regime. We test the accuracy of this approximation by assessing its performance on well understood simple cases that have either known exact solutions or well understood expansions. These scenarios include spherical configurations, isolated plane waves, and two interacting plane waves: initial conditions that are very different from the Gaussian random fields used for training. We find our model generalizes well to these well understood scenarios, demonstrating that the networks have inferred general physical principles and learned the nonlinear mode couplings from the complex, random Gaussian training data. These tests also provide a useful diagnostic for finding the model's strengths and weaknesses, and identifying strategies for model improvement. We also test the model on initial conditions that contain only transverse modes, a family of modes that differ not only in their phases but also in their evolution from the longitudinal growing modes used in the training set. When the network encounters these initial conditions that are orthogonal to the training set, the model fails completely. In addition to these simple configurations, we evaluate the model's predictions for the density, displacement, and momentum power spectra with standard initial conditions for N-body simulations. We compare these summary statistics against N-body results and an approximate, fast simulation method called COLA. Our model achieves percent level accuracy at nonlinear scales of kâˆĵ 1Mpc^-1 h, representing a significant improvement over COLA.

READ FULL TEXT
research
∙ 06/09/2022

Field Level Neural Network Emulator for Cosmological N-body Simulations

We build a field level emulator for cosmic structure formation that is a...
research
∙ 03/23/2023

Predicting the Initial Conditions of the Universe using Deep Learning

Finding the initial conditions that led to the current state of the univ...
research
∙ 12/20/2013

Exact solutions to the nonlinear dynamics of learning in deep linear neural networks

Despite the widespread practical success of deep learning methods, our t...
research
∙ 09/06/2022

Stochastic Data-Driven Variational Multiscale Reduced Order Models

Trajectory-wise data-driven reduced order models (ROMs) tend to be sensi...
research
∙ 11/20/2020

Deep learning insights into cosmological structure formation

While the evolution of linear initial conditions present in the early un...
research
∙ 06/24/2022

Predicting the Stability of Hierarchical Triple Systems with Convolutional Neural Networks

Understanding the long-term evolution of hierarchical triple systems is ...
research
∙ 03/19/2012

The Initial Conditions of the Universe from Constrained Simulations

I present a new approach to recover the primordial density fluctuations ...

Please sign up or login with your details

Forgot password? Click here to reset