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from typing import Dict, List, Tuple, Union |
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import torch |
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import typeguard |
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from jaxtyping import Float, jaxtyped |
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from pdeinvbench.utils.types import ( |
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Type1DRPartialsTuple, |
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Type2DRDPartialsTuple, |
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TypeBatchSolField1D, |
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TypePartials2D, |
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TypeXGrid, |
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TypeYGrid, |
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) |
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@jaxtyped(typechecker=typeguard.typechecked) |
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def partials_torch_1d_systems( |
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solution_field: TypeBatchSolField1D, |
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x: TypeXGrid, |
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dt: torch.Tensor, |
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) -> Type1DRPartialsTuple: |
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""" |
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Compute the spatial and temporal partial differentials for 1d systems. |
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solution field: solution field |
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x: spatial grid |
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dt: time differential |
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Returns: |
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data_x: X spatial gradient (du/dx) |
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data_x_usqr: spatial gradient of u^2/2 (du^2/dx) |
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data_xx: X spatial second gradient (d^2u/dx^2) |
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data_t: temporal gradient (du/dt) |
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(All return arguments are same shape as data) |
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""" |
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x_axis = -1 |
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t_axis = -2 |
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if len(x.shape) == 2: |
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x = x[0] |
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data_x = torch.gradient(solution_field, spacing=(x,), dim=x_axis)[0] |
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data_x_usqr = torch.gradient( |
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solution_field * solution_field / 2, spacing=(x,), dim=x_axis |
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)[0] |
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data_xx = torch.gradient(data_x, spacing=(x,), dim=x_axis)[0] |
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data_t = torch.gradient(solution_field, spacing=dt, dim=t_axis)[0] |
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return data_x, data_x_usqr, data_xx, data_t |
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@jaxtyped(typechecker=typeguard.typechecked) |
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def partials_torch_2d_systems( |
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solution_field: TypePartials2D, |
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x: TypeXGrid, |
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y: TypeYGrid, |
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dt: torch.Tensor, |
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) -> Type2DRDPartialsTuple: |
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""" |
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Compute the spatial and temporal partial differentials for 2D systems. |
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solution_field: solution field |
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x, y: spatial grids |
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dt: time differential |
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Returns: |
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data_x: X spatial gradient (du/dx) |
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data_y: Y spatial gradient (du/dy) |
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data_xx: X spatial second gradient (d^2u/dx^2) |
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data_yy: Y spatial second gradient (d^2u/dy^2) |
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data_t: temporal gradient (du/dt) |
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""" |
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if len(x.shape) == 2: |
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x = x[0] |
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if len(y.shape) == 2: |
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y = y[0] |
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y_axis = -1 |
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x_axis = -2 |
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t_axis = -3 |
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data_x = torch.gradient(solution_field, spacing=(x,), dim=x_axis)[0] |
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data_xx = torch.gradient(data_x, spacing=(x,), dim=x_axis)[0] |
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data_y = torch.gradient(solution_field, spacing=(y,), dim=y_axis)[0] |
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data_yy = torch.gradient(data_y, spacing=(y,), dim=y_axis)[0] |
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data_t = torch.gradient(solution_field, spacing=dt, dim=t_axis)[0] |
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return data_x, data_y, data_xx, data_yy, data_t |
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