DCDM

A Deep Conjugate Direction Method for Iteratively Solving Linear Systems

This repository is based on the paper [under review]. We accelerate fluid simulations by embedding a neural network in an existing solver for pressure, replacing an expensive pressure projection linked to a Poisson equation on a computational fluid grid that is usually solved with iterative methods (CG or Jacobi methods). We implemented our code with TensorFlow (keras) for training parts.

Requirements

Python 3.8
keras 2.8.0
tensorflow 2.3.0
CUDA 11

We are using virtual environments using conda.

Setting Up Environment for Running DCDM

Create and activate a conda environement:

conda create --name venvname[name of vertual env] python=3.8
conda activate venvname

Install tensorflow. Conda should install keras, numpy, and scipy automatically. If not, install them using conda.

conda install tensorflow

Download the data file here to the project source directory and extract all data files.

tar -zxvf icml2023data.tar.gz
cd icml2023data
tar -zxvf original_matA.tar.gz
tar -zxvf test_matrices_and_vectors.tar.gz
tar -zxvf trained_models.tar.gz

Once all the data are extracted, the files structures should look like the following:

.
└── (Project Source Directory)
    ├── src
    └── icml2023data
        ├── test_matrices_and_vectors  
        └── trained_models
        └── original_matA

test_matrices_and_vectors contains the RHS vectors and system matrices for different examples with different grid resolutions (N = 64, 128, 256).
- RHS (b) of the linear system (Ax = b): div_v_star_[frame].bin
- System matrix data: matrixA_[frame].bin (stored in compressed sparse row format).
trained_models includes pre-trained models. Each model is trained using a particular resolution K, and is designed for a particular simulation resolution N. Models are correspondingly named model_N[N]_from[K]_F32.

Running Tests

To compare the performance of different methods (DCDM, CG, DeflatedPCG, ICPCG),

cd src/
python3 test_all_cg.py --dataset_dir <dataset_path>

Note that dataset are located at ../icml2023data if users follow the steps in the previous section. To view all the command line options, users can find them using the following command:

python3 test_all_cg.py --help

Training

Dataset

We generated our dataset using Ritz vectors, and the dataset generating code is at src/datasetcreate.py. Note that our dataset for training for each dimention, here . Download to the project source directory and extract all data files.

tar -zxvf datasets.tar.gz
cd icml2023data
tar -zxvf datasets.tar.gz

.
└── (Project Source Directory)
    ├── src
    └── icml2023data
    └── <span style="color: red; ">datasets</span>

Dataset Creation

You can also generate the dataset by yourself with src/datasetcreate.py.

cd src/
python3 datasetcreate.py --dataset_dir <dataset_path> --output_dir <directory_to_save_the_newly_created_dataset>

After creating the new dataset, if you like to use it for the training, you should change the path(foldername) in line 171 and 181 in train.py

Training model

Pre-trained models can be found icml2023data/trained_models. If the you want to generate dataset by yourself, you can run the following commands:

cd src/
python train.py -N <dimention> --total_number_of_epochs <total epoch number> --epoch_each_number <epoch number for saved model> --batch_size <batch size> --loading_number <loading data size for once> --gpu_usage <gpu usage memory 1024*int> --data_dir <data path to the icml2023data>

ayano721/2023_DCDM