### Set up Conda environment for DiffusionPDE

Source: https://github.com/jhhuangchloe/diffusionpde/blob/main/README.md

Instructions to create and activate the Conda environment using the provided `environment.yml` file, installing all necessary Python libraries for the DiffusionPDE project.

```bash
conda env create -f environment.yml -n DiffusionPDE
conda activate DiffusionPDE
```

--------------------------------

### Recover PDE Solution Over Time Interval

Source: https://github.com/jhhuangchloe/diffusionpde/blob/main/README.md

Command to recover the solution of a PDE throughout a time interval, utilizing sparse sensor data, with an example for Burgers' equation.

```python
python3 generate_pde.py --config configs/burgers.yaml
```

--------------------------------

### Train Diffusion Models for PDE Solving

Source: https://github.com/jhhuangchloe/diffusionpde/blob/main/README.md

Steps to prepare training data by merging `.npy` files and then train a new diffusion model using `torchrun`. Raw data in the datasets should be scaled to (-1, 1) before training.

```python
python3 merge_data.py # Darcy Flow
```

```bash
torchrun --standalone --nproc_per_node=3 train.py --outdir=pretrained-darcy-new --data=/data/Darcy-merged/ --cond=0 --arch=ddpmpp --batch=60 --batch-gpu=20 --tick=10 --snap=50 --dump=100 --duration=20 --ema=0.05
```

--------------------------------

### Solve PDE with Observations on Both Coefficient and Solution Spaces

Source: https://github.com/jhhuangchloe/diffusionpde/blob/main/README.md

Command to simultaneously solve for both coefficient (initial state) and solution (final state) spaces, given sparse observations on both sides, using a specific configuration file (e.g., for Darcy Flow).

```python
python3 generate_pde.py --config configs/darcy.yaml
```

--------------------------------

### BibTeX Citation for DiffusionPDE Research Paper

Source: https://github.com/jhhuangchloe/diffusionpde/blob/main/README.md

This BibTeX entry provides the necessary information to cite the 'DiffusionPDE: Generative PDE-Solving Under Partial Observation' research paper in academic publications. It includes authors, title, year, eprint, archive prefix, primary class, and URL for the arXiv preprint.

```bibtex
@misc{huang2024diffusionpdegenerativepdesolvingpartial,
      title={DiffusionPDE: Generative PDE-Solving Under Partial Observation}, 
      author={Jiahe Huang and Guandao Yang and Zichen Wang and Jeong Joon Park},
      year={2024},
      eprint={2406.17763},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
      url={https://arxiv.org/abs/2406.17763}, 
}
```

--------------------------------

### Solve Forward PDE Problem

Source: https://github.com/jhhuangchloe/diffusionpde/blob/main/README.md

Command to solve the forward problem, which involves sparse observation on the coefficient or initial state space, using a specified configuration file (e.g., for Darcy Flow).

```python
python3 generate_pde.py --config configs/darcy-forward.yaml
```

--------------------------------

### Solve Inverse PDE Problem

Source: https://github.com/jhhuangchloe/diffusionpde/blob/main/README.md

Command to solve the inverse problem, which involves sparse observation on the solution or final state space, using a specified configuration file (e.g., for Darcy Flow).

```python
python3 generate_pde.py --config configs/darcy-inverse.yaml
```

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