File size: 2,722 Bytes
484b847 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 |
from typing import Dict, List, Tuple, Union
import torch
import typeguard
from jaxtyping import Float, jaxtyped
from pdeinvbench.utils.types import (
Type1DRPartialsTuple,
Type2DRDPartialsTuple,
TypeBatchSolField1D,
TypePartials2D,
TypeXGrid,
TypeYGrid,
)
@jaxtyped(typechecker=typeguard.typechecked)
def partials_torch_1d_systems(
solution_field: TypeBatchSolField1D,
x: TypeXGrid,
dt: torch.Tensor,
) -> Type1DRPartialsTuple:
"""
Compute the spatial and temporal partial differentials for 1d systems.
solution field: solution field
x: spatial grid
dt: time differential
Returns:
data_x: X spatial gradient (du/dx)
data_x_usqr: spatial gradient of u^2/2 (du^2/dx)
data_xx: X spatial second gradient (d^2u/dx^2)
data_t: temporal gradient (du/dt)
(All return arguments are same shape as data)
"""
x_axis = -1
t_axis = -2
# take first batch element of spatial and time grids (all the same, artifact of dataloader)
if len(x.shape) == 2:
x = x[0]
data_x = torch.gradient(solution_field, spacing=(x,), dim=x_axis)[0]
data_x_usqr = torch.gradient(
solution_field * solution_field / 2, spacing=(x,), dim=x_axis
)[0]
data_xx = torch.gradient(data_x, spacing=(x,), dim=x_axis)[0]
data_t = torch.gradient(solution_field, spacing=dt, dim=t_axis)[0]
return data_x, data_x_usqr, data_xx, data_t
@jaxtyped(typechecker=typeguard.typechecked)
def partials_torch_2d_systems(
solution_field: TypePartials2D,
x: TypeXGrid,
y: TypeYGrid,
dt: torch.Tensor,
) -> Type2DRDPartialsTuple:
"""
Compute the spatial and temporal partial differentials for 2D systems.
solution_field: solution field
x, y: spatial grids
dt: time differential
Returns:
data_x: X spatial gradient (du/dx)
data_y: Y spatial gradient (du/dy)
data_xx: X spatial second gradient (d^2u/dx^2)
data_yy: Y spatial second gradient (d^2u/dy^2)
data_t: temporal gradient (du/dt)
"""
# take first batch element of spatial grids (all the same, artifact of dataloader)
if len(x.shape) == 2:
x = x[0]
if len(y.shape) == 2:
y = y[0]
y_axis = -1
x_axis = -2
t_axis = -3
data_x = torch.gradient(solution_field, spacing=(x,), dim=x_axis)[0]
data_xx = torch.gradient(data_x, spacing=(x,), dim=x_axis)[0]
data_y = torch.gradient(solution_field, spacing=(y,), dim=y_axis)[0]
data_yy = torch.gradient(data_y, spacing=(y,), dim=y_axis)[0]
data_t = torch.gradient(solution_field, spacing=dt, dim=t_axis)[0]
return data_x, data_y, data_xx, data_yy, data_t
|