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Navierstokes

continuiti.benchmarks.navier_stokes

Navier-Stokes benchmark.

NavierStokes(dir=None)

Bases: Benchmark

Navier-Stokes benchmark.

This benchmark contains a dataset of turbulent flow samples taken from neuraloperator/graph-pde that was used as illustrative example in the FNO paper:

Li, Zongyi, et al. "Fourier neural operator for parametric partial differential equations." arXiv preprint arXiv:2010.08895 (2020).

The dataset loads the NavierStokes_V1e-5_N1200_T20 file which contains 1200 samples of Navier-Stokes flow simulations at a spatial resolution of 64x64 and 20 time steps.

The benchmark exports operator datasets where both input and output function are defined on the space-time domain (periodic in space), i.e., \((x, y, t) \in [-1, 1] \times [-1, 1] \times (-1, 0]\) for the input function and \((x, y, t) \in [-1, 1] \times [-1, 1] \times (0, 1]\) for the output function.

The input function is given by the vorticity field at the first ten time steps \((-0.9, -0.8, ..., 0.0)\) and the output function by the vorticity field at the following ten time steps \((0.1, 0.2, ..., 1.0)\).

Visualization of first training sample.

The datasets have the following shapes:

    len(benchmark.train_dataset) == 1000
    len(benchmark.test_dataset) == 200

    x.shape == (3, 64, 64, 10)
    u.shape == (1, 64, 64, 10)
    y.shape == (3, 64. 64, 10)
    v.shape == (1, 64, 64, 10)
PARAMETER DESCRIPTION
dir

Path to data set. Default is data/navierstokes in the root directory of the repository.

TYPE: Optional[str] DEFAULT: None

Source code in src/continuiti/benchmarks/navierstokes.py 
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def __init__(self, dir: Optional[str] = None):
    if dir is None:
        # Get root dir relative to this file
        root_dir = pathlib.Path(continuiti.__file__).parent.parent.parent
        dir = root_dir / "data" / "navierstokes"
    else:
        dir = pathlib.Path(dir)

    # Create space-time grids (x_1, x_2, t)
    ls = torch.linspace(-1, 1, 64)
    tx = torch.linspace(-0.9, 0.0, 10)
    grid_x = torch.meshgrid(ls, ls, tx, indexing="ij")
    x = torch.stack(grid_x, axis=0).unsqueeze(0).expand(1200, -1, -1, -1, -1)
    x = x.reshape(1200, 3, 64, 64, 10)

    ty = torch.linspace(0.1, 1.0, 10)
    grid_y = torch.meshgrid(ls, ls, ty, indexing="ij")
    y = torch.stack(grid_y, axis=0).unsqueeze(0).expand(1200, -1, -1, -1, -1)
    y = y.reshape(1200, 3, 64, 64, 10)

    # Load vorticity
    data = scipy.io.loadmat(dir / "NavierStokes_V1e-5_N1200_T20.mat")
    vort0 = torch.tensor(data["a"], dtype=torch.float32)
    vort = torch.tensor(data["u"], dtype=torch.float32)
    assert vort0.shape == (1200, 64, 64)
    assert vort.shape == (1200, 64, 64, 20)

    # Input is vorticity for t \in [0, 10]
    u = torch.cat(
        (vort0.reshape(-1, 64, 64, 1), vort[:, :, :, :9]),
        axis=3,
    ).reshape(1200, 1, 64, 64, 10)

    # Output is vorticity for t \in [10, 20]
    v = vort[:, :, :, 10:].reshape(1200, 1, 64, 64, 10)

    # Split train/test
    train_indices = torch.arange(1000)
    test_indices = torch.arange(1000, 1200)

    train_dataset = OperatorDataset(
        x=x[train_indices],
        u=u[train_indices],
        y=y[train_indices],
        v=v[train_indices],
    )

    test_dataset = OperatorDataset(
        x=x[test_indices],
        u=u[test_indices],
        y=y[test_indices],
        v=v[test_indices],
    )

    super().__init__(train_dataset, test_dataset, [RelativeL1Error()])
Last update: 2024-08-20
Created: 2024-08-20