Code for "DeltaPhi: Learning Physical Trajectory Residual for PDE Solving".
Create and activate an Anaconda Environment:
conda create -n DeltaPhi python=3.9
conda activate DeltaPhi
Install Pytorch with following commands (refer to Other Versions for additional cuda versions.):
# for CUDA 11.8
conda install pytorch==2.3.0 torchvision==0.18.0 torchaudio==2.3.0 pytorch-cuda=11.8 -c pytorch -c nvidia
# for CUDA 12.1
conda install pytorch==2.3.0 torchvision==0.18.0 torchaudio==2.3.0 pytorch-cuda=12.1 -c pytorch -c nvidia
Install additional required packages with following commands:
pip install -r requirement.txt
Download the dataset from Google Driver.
Put Composites.zip in datasets/ and unzip it.
cd datasets
unzip Composites.zipThe directory structure is as follows:
datasets/Composites/Composites_LBO_basis/Composites_LBO_basis.mat
datasets/Composites/Data/Composites.mat
Run the experiment using the following scripts:
cd Composites
# The code for NORM (Previous):
CUDA_VISIBLE_DEVICES=0 python norm.py
# The code for NORM (DeltaPhi):
CUDA_VISIBLE_DEVICES=0 python norm_DeltaPhi.py Download the dataset from Google Driver.
Put HeatTransfer.zip in datasets/ and unzip it.
cd datasets
unzip HeatTransfer.zipThe directory structure is as follows:
datasets/HeatTransfer/Data/HeatTransfer.mat
datasets/HeatTransfer/HeatTransfer_LBO_basis/lbe_ev_input.mat
datasets/HeatTransfer/HeatTransfer_LBO_basis/lbe_ev_output.mat
Run the experiment using the following scripts:
cd HeatTransfer
# The code for NORM (Previous):
CUDA_VISIBLE_DEVICES=0 python norm.py
# The code for NORM (DeltaPhi):
CUDA_VISIBLE_DEVICES=0 python norm_DeltaPhi.py Codes for additional simulation cases will be released later.
You can create a residual neural operator based on an existing direct neural operator by modifying the original Dataset and Model class.
All other configurations keep unchanged.
-
Dataset. Implement the
Datasetclass in which the__getitem__()function returns not only the original input-output function$(a_i,u_i)$ , but also the randomly sampled auxiliary sample$(a_{k_i}, u_{k_i}, score_{k_i})$ . -
Model. Modify the
Modelclass in two aspects: (a) Auxiliary sample integration: Concatenate original inputs with auxiliary sample$(a_{k_i}, u_{k_i}, score_{k_i})$ . (b) Trajectory residual connection: Take the summation of the auxiliary output function$u_{k_i}$ and original model outputs, as the final model outputs.
We greatly appreciate the following open-source works, as they form the foundation of our work.