dynabench 0.4.4

Benchmark dataset for learning dynamical systems from data

DynaBench

The DynaBench package started as a benchmark dataset for learning dynamical systems from low-resolution data. It has since evolved into a full-fledged package for generating synthetic data, training models, and evaluating them on various tasks concerning partial differential equations. The package is designed to be easy to use and flexible, allowing for easy extension and modification of the existing models, data generation algorithms and physical equations.

Take a look at the documentation for more details on the package and how to use it.

⚡️ Getting Started

To get started with the package, you can install it via pip:

pip install dynabench

Additional dependencies

To use some of the components of dynabench (models, solvers etc.) additional dependencies are required. It is recommended to use a virtual environment. Then install:

# install dependencies needed for Point Transfomer V3 model with e.g. ${CUDA} as cu118
pip install addict spconv-${CUDA} torch-scatter -f https://data.pyg.org/whl/torch-2.4.0+${CUDA}.html

For further information check out the pytorch_scatter and spconv repos. Moreover, the Point Transformer model V3 CAN be used with flash-attention which may be installed according to their guide. Note, that the model requires cuda and the requirements need to be installed according to the PyTorch installation.

Downloading data

The DynaBench package contains dozens of different equations that can be used to generate synthetic data. The easiest way to get started, however, is to use one of the original benchmark equations. These can be downloaded using the following command:

from dynabench.dataset import download_equation

download_equation(equation='advection', structure='cloud', resolution='low')

The original benchmark dataset consists of simulations of the following equations:

Equation	Components	Time Order	Spatial Order
Advection	1	1	1
Burgers'	2	1	2
Gas Dynamics	4	1	2
Kuramoto-Sivashinsky	1	1	4
Reaction-Diffusion	2	1	2
Wave	1	2	2

Loading data

To easily load the data the dynabench package provides the DynabenchIterator iterator:

from dynabench.dataset import DynabenchIterator

advection_iterator = DynabenchIterator(equation='advection', 
                                        structure='cloud', 
                                        resolution='low',
                                        lookback=4,
                                        rollout=16)

This will iterate through all downloaded simulation of the advection dataset with observation points scattered (cloud) and low resolution. Each sample will be a tuple containing a snapshot of the simulation at the past 4 time steps, the future 16 time steps as target as well as the coordinates of the observation points:

for sample in advection_iterator:
    x, y, points = sample

    # x is the input data with shape (lookback, n_points, n_features)
    # y is the target data with shape (rollout, n_points, n_features)
    # points are the observation points with shape (n_points, dim)
    # for the advection equation n_features=1 and dim=2

⚙️ Usage

More advanced use cases include generating data for different equations, training models, and evaluating them. The package provides a simple interface for all these tasks.

Example: Generating data for Cahn-Hilliard equation

The DynaBench package provides a simple interface for generating synthetic data for various physical systems. For example data for the Cahn-Hilliard equation can be generated by running:

from dynabench.equation import CahnHilliardEquation
from dynabench.initial import RandomUniform
from dynabench.grid import Grid
from dynabench.solver import PyPDESolver



# Create an instance of the CahnHilliardEquation class with default parameters
pde_equation = CahnHilliardEquation()

# Create an instance of grid with default parameters
grid = Grid(grid_limits=((0, 64), (0, 64)), grid_size=(64, 64))

# generate an initial condition as a sum of 5 gaussians
intitial = RandomUniform()


# Solve the Cahn-Hilliard equation with the initial condition
solver = PyPDESolver(equation=pde_equation, grid=grid, initial_generator=intitial, parameters={'method': "RK23"})
solver.solve(t_span=[0, 100], dt_eval=1)

Example: Training NeuralPDE

The DynaBench package provides several models that can be used to forecast the physical system. For example, to train the NeuralPDE model on the advection equation, you can use the following code snippet:

from dynabench.dataset import DynabenchIterator
from torch.utils.data import DataLoader
from dynabench.model import NeuralPDE

import torch.optim as optim
import torch.nn as nn

advection_train_iterator = DynabenchIterator(split="train",
                                             equation='burgers',
                                             structure='grid',
                                             resolution='low',
                                             lookback=1,
                                             rollout=4)

train_loader = DataLoader(advection_train_iterator, batch_size=32, shuffle=True)

model = NeuralPDE(input_dim=2, hidden_channels=64, hidden_layers=3,
                  solver={'method': 'euler', 'options': {'step_size': 0.1}},
                  use_adjoint=False)

optimizer = optim.Adam(model.parameters(), lr=1e-3)
criterion = nn.MSELoss()

for epoch in range(10):
    model.train()
    for i, (x, y, p) in enumerate(train_loader):
        x, y = x[:,0].float(), y.float() # only use the first channel and convert to float32
        optimizer.zero_grad()
        y_pred = model(x, range(0, 5))
        y_pred = y_pred.transpose(0, 1)
        loss = criterion(y_pred, y)
        loss.backward()
        optimizer.step()
        print(f"Epoch: {epoch}, Batch: {i}, Loss: {loss.item()}")

Further Models

In Dynabench there are several SOTA-models already implemented and ready to train. The models are altered to fit the data structure of dynabench. The source code can be found in src/dynabench/model/_grid or /point respectively and include the NeuralPDE model, Neural Operator model, Point Transformer model, and Point Transformer model V3. The first three models can be trained from scratch by simply starting the respective script in /examples. For the Point Transformer V3 some additional packages need to be installed. These can be found in Additional dependencies.

To try a model first change the intrinsic parameters of the model as needed and then run the example training script of the model with:

python3 examples/example_{model}.py

📈 Benchmark Results

The original six equations have been used to evaluate the performance of various models on the task of forecasting the physical system. For this 900 spatial points have been used. The results are shown below:

• 1-step MSE

model	Advection	Burgers	Gas Dynamics	Kuramoto-Sivashinsky	Reaction-Diffusion	Wave
CNN	5.30848e-05	0.0110988	0.00420368	0.000669837	0.00036918	0.00143387
FeaSt	0.000130351	0.0116155	0.0162	0.0117867	0.000488848	0.00523298
GAT	0.00960113	0.0439986	0.037483	0.0667057	0.00915208	0.0151498
GCN	0.026397	0.13899	0.0842611	0.436563	0.164678	0.0382004
GraphPDE	0.000137098	0.0107391	0.0194755	0.00719822	0.000142114	0.00207144
KernelNN	6.31157e-05	0.0106146	0.013354	0.00668698	0.000187019	0.00542925
NeuralPDE	8.24453e-07	0.0112373	0.00373416	0.000536958	0.000303176	0.00169871
Persistence	0.0812081	0.0367688	0.186985	0.142243	0.147124	0.113805
Point Transformer	4.41633e-05	0.0103098	0.00724899	0.00489711	0.000141248	0.00238447
PointGNN	2.82496e-05	0.00882528	0.00901649	0.00673036	0.000136059	0.00138772
ResNet	2.15721e-06	0.0148052	0.00321235	0.000490104	0.000156752	0.00145884

• 16-step rollout MSE:

model	Advection	Burgers	Gas Dynamics	Kuramoto-Sivashinsky	Reaction-Diffusion	Wave
CNN	0.00161331	0.554554	0.995382	1.26011	0.0183483	0.561433
FeaSt	1.48288	0.561197	0.819594	3.74448	0.130149	1.61066
GAT	41364.1	0.833353	1.21436	5.68925	3.85506	2.38418
GCN	3.51453e+13	13.0876	7.20633	1.70612e+24	1.75955e+07	7.89253
GraphPDE	1.07953	0.729879	0.969208	2.1044	0.0800235	1.02586
KernelNN	0.897431	0.72716	0.854015	2.00334	0.0635278	1.57885
NeuralPDE	0.000270308	0.659789	0.443498	1.05564	0.0224155	0.247704
Persistence	2.39393	0.679261	1.457	1.89752	0.275678	2.61281
Point Transformer	0.617025	0.503865	0.642879	2.09746	0.0564399	1.27343
PointGNN	0.660665	1.04342	0.759257	2.82063	0.0582293	1.30743
ResNet	8.64621e-05	1.86352	0.480284	1.0697	0.00704612	0.299457

📃 Citing

If you use DynaBench for your research, please cite:

@inproceedings{dulny2023dynabench,
    author = {Dulny, Andrzej and Hotho, Andreas and Krause, Anna},
    title = {DynaBench: A Benchmark Dataset for Learning Dynamical Systems from Low-Resolution Data},
    year = {2023},
    isbn = {978-3-031-43411-2},
    publisher = {Springer-Verlag},
    address = {Berlin, Heidelberg},
    doi = {10.1007/978-3-031-43412-9_26},
    booktitle = {Machine Learning and Knowledge Discovery in Databases: Research Track: European Conference, ECML PKDD 2023, Turin, Italy, September 18–22, 2023, Proceedings, Part I},
    pages = {438–455},
    numpages = {18},
    keywords = {neuralPDE, dynamical systems, benchmark, dataset},
    location = {Turin, Italy}
}

📚 More resources

• The documentation for the package can be found here.
• The original benchmark paper can be found here.

How to contribute to dynabench

This guide has been largely adapted from the findiff contribution guide

Did you find a bug?

• Ensure the bug was not already reported by searching on GitHub under Issues.

• If you're unable to find an open issue addressing the problem, open a new one. Be sure to include a title and clear description, as much relevant information as possible, and a code sample or an executable test case demonstrating the expected behavior that is not occurring.

Did you write a patch that fixes a bug?

• Open a new GitHub pull request with the patch.

• Ensure the PR description clearly describes the problem and solution. Include the relevant issue number if applicable.

Do you intend to add a new feature or change an existing one?

• Suggest your change in the dynabench discussion forum and start writing code.

• Do not open an issue on GitHub until you have collected positive feedback about the change. GitHub issues are primarily intended for bug reports and fixes.

Do you have questions about the source code?

• Ask any question about how to use dynabench in the discussion forum.

Thank you for your support! :heart:

The dynabench Team

License

The content of this project itself, including the data and pretrained models, is licensed under the Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0). The underlying source code used to generate the data and train the models is licensed under the MIT license.

References

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