phlower is a deep learning framework based on PyTorch Ignite especially for physical phenomenon such as fluid dynamics.

Phlower Tensor Operation with physical dimension

Usually, physics values have physics dimensions. Phlower can consider it.

Let’s check what kind of items are treated as physics dimension There are many possible choices of base physical dimensions. Following to the SI standard, physical dimensions and corresponding dimension symbols are shown blelow.

time (T), length (L), mass (M), electric current (I), absolute temperature (Θ), amount of substance (N) and luminous intensity (J).

from phlower.utils.enums import PhysicalDimensionSymbolType

print(f"{[str(v) for v in PhysicalDimensionSymbolType]}")

['T (time)', 'L (length)', 'M (mass)', 'I (electric current)', 'Theta (thermodynamic temperature)', 'N (amount of substance)', 'J (luminous intensity)']

Create PhlowerTensor which is tensor object with physical dimension. There are several way to create PhlowerTensor, the most simple way is shown. PhlowerTensor is a wrapper of torch.Tensor. Call print to check values and dimensions.

import torch

from phlower import phlower_tensor

sample_velocity = torch.rand(3, 4)
dimension = {"L": 1, "T": -1}
physical_tensor = phlower_tensor(sample_velocity, dimension=dimension)

print(physical_tensor)

PhlowerTensor(tensor([[0.4986, 0.1072, 0.9929, 0.5529],
        [0.4707, 0.4580, 0.5383, 0.8241],
        [0.8728, 0.1017, 0.3627, 0.2145]]), Dimension: PhlowerDimensionTensor(T: -1.0, L: 1.0, M: 0.0, I: 0.0, Theta: 0.0, N: 0.0, J: 0.0)), is_time_series: False, is_voxel: False

Let’s calculate square of velocity. You can find that physical dimension is also converted to new dimension.

square_velocity = torch.pow(physical_tensor, 2)
print(square_velocity)

PhlowerTensor(tensor([[0.2486, 0.0115, 0.9858, 0.3058],
        [0.2216, 0.2098, 0.2898, 0.6791],
        [0.7617, 0.0104, 0.1315, 0.0460]]), Dimension: PhlowerDimensionTensor(T: -2.0, L: 2.0, M: 0.0, I: 0.0, Theta: 0.0, N: 0.0, J: 0.0)), is_time_series: False, is_voxel: False

Create PhlowerTensor without physical dimension if you do not pass information of dimension to phlower_tensor. Raise error when it comes to calculate PhlowerTensor with a physical dimension and that without it.

try:
    one_physical_tensor = phlower_tensor(
        torch.rand(3, 4), dimension={"L": 1, "T": -1}
    )
    another_physical_tensor = phlower_tensor(torch.rand(3, 4))
    _ = another_physical_tensor + one_physical_tensor
except Exception as ex:
    print(ex)

Cannnot calcualte PhlowerTensor with physics dimension and PhlowerTensor without it. PhlowerTensor(tensor([[0.8414, 0.1556, 0.0756, 0.5658],
        [0.7468, 0.6869, 0.0714, 0.8978],
        [0.3873, 0.5436, 0.0325, 0.4023]]), Dimension: None), is_time_series: False, is_voxel: False

Some calculation operations are not allowed when physics dimension value is not the same,

try:
    one_physical_tensor = phlower_tensor(
        torch.rand(3, 4), dimension={"L": 1, "T": -1}
    )
    another_physical_tensor = phlower_tensor(
        torch.rand(3, 4), dimension={"L": 1}
    )
    _ = another_physical_tensor + one_physical_tensor
except Exception as ex:
    print(ex)

Add operation for different physical dimensions is not allowed.

Some calculation operations are allowed even when physics dimension value is not the same,

one_physical_tensor = phlower_tensor(
    torch.rand(3, 4), dimension={"L": 1, "T": -1}
)
another_physical_tensor = phlower_tensor(
    torch.rand(3, 4), dimension={"Theta": 1}
)
print(another_physical_tensor * one_physical_tensor)

PhlowerTensor(tensor([[0.0245, 0.4689, 0.2952, 0.2262],
        [0.0606, 0.7343, 0.3823, 0.0156],
        [0.5988, 0.0511, 0.2306, 0.0387]]), Dimension: PhlowerDimensionTensor(T: -1.0, L: 1.0, M: 0.0, I: 0.0, Theta: 1.0, N: 0.0, J: 0.0)), is_time_series: False, is_voxel: False