Emulation of $f(R)$ modified gravity from $\Lambda$ CDM using conditional GANs

This repository contains code for developing a field-level, neural-network-based emulator that generates density and velocity divergence fields under the f(R) gravity MG model from the corresponding $\Lambda$ CDM simulated fields.

The code here is a modification to the BicycleGAN approach for multimodal image-to-image translation; the official BicycleGAN codebase is here and the paper on BicycleGAN is here. Our modifications to the BicycleGAN code are located here.

Motivation

Testing deviations from the $\Lambda$ CDM cosmological model is a key science target of astronomical surveys. However, the simulations of these alternatives are immensely slow. We use the f(R) gravity model in this study as an example, which is a widely studied modified gravity (MG) theory.

To alleviate the computational bottleneck imposed by f(R) gravity simulations, we use a GAN conditioned on the outputs of $\Lambda$ CDM simulations that emulate f(R) simulation outputs. We focus on the matter density and velocity divergence fields.

Scientific details

Coming soon...

Installation

The installation instructions are the same as mentioned in the original BicycleGAN repository.

Usage

Preparing the data

• Our approach requires aligned pairs of images, one from the $\Lambda$ CDM simulation and the other from the f(R) simulation for training the model. The simulation data in this study is obtained from $N$-body simulations of the MG-GLAM code.
• We have then used DTFE to interpolate the particle positions onto a uniform grid. The resulting density fields can be stored in various formats; consult the DTFE documentation for details; here we save them as npy.gz files, which are read in the script scripts/prepare_data.py. An example command used is:

./DTFE example_F4n1_L128Np256Ng512_Run1_0157.hdf5 test --grid 512 -i 105 --output 101 --field density_a velocity_a divergence_a --periodic

• The script scripts/prepare_data.py provides a template code to arrange the simulation data in a manner that can be used with the BicycleGAN code. It reads the DTFE densities (which we have processed into npy.gz files) and combines the GR and the corresponding f(R) 2D fields (in this study, we use 512x512 grid size when using DTFE) into a single array and saves them. For example, with GR and F6 velocity divergence data, this script will store numpy binary files (.npy) in official_pix2pix_data_velDiv_F6n1_GR/train, official_pix2pix_data_velDiv_F6n1_GR/val, and official_pix2pix_data_velDiv_F6n1_GR/test directories. There is code to additionally save 256x256 cutouts from the 512x512 fields, which is used in this work.

Note: prepare_data.py hardcodes the code assuming GR and F6 velocity divergence, velDiv, is used, but the code can be modified for any other case, such as GR and F4 density. More details about the simulation can be found in our paper (see the Scientific details section).

Training, validation, and testing

• The script scripts/train.sh can be used for training (which itself runs BicycleGAN/train.py), and contains the hyperparameters used. During training, paired simulated fields from $\Lambda$ CDM and f(R) gravity are used.
• scripts/testing.sh can be used for testing the model - uncomment the line that needs to be run for testing (i.e., if you want to run the script testing_for_den_F4den_test_Bicycle.py, uncomment the corresponding line in scripts/testing.sh). The description of some of the testing python scripts is as follows (for the below description, we assume the model is trained to learn the $\Lambda$ CDM to F4 mapping; F4 means f(R) with $|f_{R0}| = 10^{-4}$, see the paper for detailed description):
  • testing_for_den_F4den_test_Bicycle.py: for testing the model on the $\Lambda$ CDM-F4 case.
  • testing_for_den_F4den_test_Bicycle_latent_interp.py: for performing latent extrapolation for $\Lambda$ CDM-F5 / $\Lambda$ CDM-F6 cases (change dataroot accordingly). Note that this script does not in itself perform latent extrapolation, it runs BicycleGAN/test_latent_interpolate.py instead of BicycleGAN/test.py. Latent extrapolation is added as an option in BicycleGAN/models/bicycle_gan_model.py called latent_interpolate (the name latent_interpolate should actually have been latent_extrapolate since we perform latent extrapolation and latent interpolation, so this name is a slight mismatch).
  • testing_for_den_F4den_validation_Bicycle.py: for validating the model on the $\Lambda$ CDM-F4 case. This will run all saved checkpoints that were stored during training on the validation data.
  • testing_for_den_F4den_validation_Bicycle_latent_interp.py: for validating the model when using latent extrapolation for the $\Lambda$ CDM-F5 / $\Lambda$ CDM-F6 cases.

and similarly for the velocity divergence.

• At test time, given a simulated $\Lambda$ CDM field, the model will generate the corresponding f(R) field. In BicycleGAN, the generator network takes two inputs: the input field (from $\Lambda$ CDM, in this case) and a latent vector. In our study, we had the simulated f(R) fields (ground-truth) available to evaluate the model's prediction, so the latent vector used during test time was obtained from encoding the ground-truth through the encoder network component of BicycleGAN, which is also trained during training. However, if the ground truth is unavailable, the latent vector can be a randomly sampled vector from some known distribution, such as Gaussian. The BicycleGAN code contains options to handle this. For example, see the get_z_random method used in this line as a starting point.
• The evaluation metrics used to select the best model based on the validation set and for evaluating the selected model on the test set can be found in scripts/evaluation_metrics.py. To select the best model, we select the model that generally performs well on the metrics used in this study (2D power spectrum, histogram of values, cumulants of the distribution). This script contains the driver function, which is used in all the validation/testing scripts described above.

Interpretation

• BicycleGAN/spat_attn_scalar_field.py contains code to store some intermediate outputs of the discriminator network of the BicycleGAN model. These outputs are then used in BicycleGAN/interpretation_with_scalar_field.ipynb to visualize the attention weights learned by the discriminator network.
• Note that BicycleGAN/interpretation_with_scalar_field.ipynb also uses output_F6_Run62.dat, which is the full (512x512x512) 3D scalar field array for a particular run (Run62) of the F6 simulations of MG-GLAM. The scalar field is obtained from the MG-GLAM simulation code. Due to its large disk usage (~512 MB), it is not stored here.
• The notebook visually compares the attention weights and the scalar field for possible correlations (see the paper for detailed discussion).

Execution time

• The script used to calculate the inference time of the emulator is BicycleGAN/time_bicyclegan.py. The script loads the trained generator model and calculates the time required for a forward pass in inference mode using a CPU or a GPU. time_bicyclegan.sh was used to run all our experiments.
• BicycleGAN/timing_GR.log and BicycleGAN/timing_F4.log are example logs of the execution time of the GR and F4 simulation output by MG-GLAM (the Tot/min column gives the elapsed time for each step in the simulation; simulations are run for 157 steps corresponding to z = 0).

Bugs or issues

If you find something not working as expected or want to discuss a feature, we would like to know about it. Please feel free to open an issue in the issue tracker or send an email.

License

MIT