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# Type Utilities
import enum
from typing import Dict, List, Tuple, Union
import numpy as np
import torch
from jaxtyping import Float, UInt8
class PDE(enum.Enum):
"""
Describes which PDE system currently being used.
The PDE system is used to determine the correct data loading and processing steps.
"""
ReactionDiffusion2D = "Reaction Diffusion 2D"
NavierStokes2D = "Navier Stokes 2D"
TurbulentFlow2D = "Turbulent Flow 2D"
KortewegDeVries1D = "Korteweg-de Vries 1D"
DarcyFlow2D = "Darcy Flow 2D"
"""Define a global dictionaries of PDE attributs."""
# Number of partial derivatives for each PDE system.
PDE_PARTIALS = {
PDE.ReactionDiffusion2D: 5,
PDE.NavierStokes2D: 3,
PDE.TurbulentFlow2D: 3,
PDE.KortewegDeVries1D: 4,
PDE.DarcyFlow2D: 4,
}
# Number of spatial dimensions for each PDE system.
PDE_NUM_SPATIAL = {
PDE.ReactionDiffusion2D: 2,
PDE.NavierStokes2D: 2,
PDE.TurbulentFlow2D: 2,
PDE.KortewegDeVries1D: 1,
PDE.DarcyFlow2D: 2,
}
# Spatial size of the grid for each PDE system.
PDE_SPATIAL_SIZE = {
PDE.ReactionDiffusion2D: [128, 128],
PDE.NavierStokes2D: [64, 64],
PDE.TurbulentFlow2D: [64, 64],
PDE.KortewegDeVries1D: [256],
PDE.DarcyFlow2D: [241, 241],
}
# Spatial size of the grid for each PDE system.
HIGH_RESOLUTION_PDE_SPATIAL_SIZE = {
PDE.ReactionDiffusion2D: [512, 512],
PDE.TurbulentFlow2D: [2048, 2048],
PDE.DarcyFlow2D: [421, 421],
PDE.NavierStokes2D: [256, 256],
}
# Number of parameters for each PDE system.
PDE_NUM_PARAMETERS = {
PDE.ReactionDiffusion2D: 3,
PDE.NavierStokes2D: 1,
PDE.TurbulentFlow2D: 1,
PDE.KortewegDeVries1D: 1,
PDE.DarcyFlow2D: 128, # NOTE: Incorrect, but we only use this in the forward problem?
}
# Range of parameter values for each PDE system.
PDE_PARAM_VALUES = {
PDE.ReactionDiffusion2D: {
"k": [
0.00544908,
0.01064798,
0.01446092,
0.01591103,
0.02190137,
0.02248171,
0.03376446,
0.04418002,
0.05103662,
0.05279494,
0.05734164,
0.06385121,
0.06426775,
0.06746974,
0.07166788,
0.07212561,
0.07438393,
0.08332919,
0.08620312,
0.08693649,
0.0880078,
0.08820963,
0.0905649,
0.09362309,
0.09649866,
0.09658253,
0.09808294,
0.09985239,
],
"Du": [
0.02219061,
0.07546761,
0.0816335,
0.117242,
0.1297511,
0.1470162,
0.1975422,
0.2052899,
0.2223661,
0.2351847,
0.238229,
0.3073048,
0.3356696,
0.3410229,
0.3570933,
0.3594401,
0.3844191,
0.4004743,
0.4182471,
0.4187508,
0.4282146,
0.4363962,
0.4394185,
0.4521105,
0.4605572,
0.4644799,
0.4954957,
0.4978229,
],
"Dv": [
0.01647486,
0.03266683,
0.03295169,
0.0336989,
0.04517053,
0.1197443,
0.1431938,
0.1512121,
0.1513326,
0.1761043,
0.1856076,
0.1935473,
0.2369018,
0.2541142,
0.2725704,
0.2871926,
0.2925416,
0.292952,
0.2959587,
0.3023561,
0.3132344,
0.3136975,
0.3793569,
0.4004971,
0.4271173,
0.4328981,
0.4949132,
],
},
PDE.NavierStokes2D: {
"re": [
83.0,
105.55940015,
134.25044531,
170.7397166,
217.14677189,
276.1672649,
351.22952801,
446.69371438,
568.10506678,
722.51602499,
918.89588194,
1168.65178436,
1486.29134153,
1890.26533093,
2404.03945141,
3057.45737879,
3888.47430005,
4945.36162206,
6289.51092016,
7999.0,
]
},
PDE.KortewegDeVries1D: {"delta": np.linspace(0.8, 5.0, 100, endpoint=True)},
PDE.TurbulentFlow2D: {
"nu": [
1.00000000e-05,
1.42792351e-05,
2.03896555e-05,
2.91148685e-05,
4.15738052e-05,
5.93642139e-05,
8.47675566e-05,
1.21041587e-04,
1.72838128e-04,
2.46799626e-04,
3.52410989e-04,
5.03215936e-04,
7.18553866e-04,
1.02603996e-03,
1.46510658e-03,
2.09206013e-03,
2.98730184e-03,
4.26563853e-03,
6.09100555e-03,
8.69749003e-03,
]
},
PDE.DarcyFlow2D: {
# NOTE: This should not be used since coeff is a scalar field
"coeff": []
},
}
# Number of data channels for each PDE system.
PDE_NUM_CHANNELS = {
PDE.ReactionDiffusion2D: 2,
PDE.NavierStokes2D: 1,
PDE.TurbulentFlow2D: 1,
PDE.KortewegDeVries1D: 1,
PDE.DarcyFlow2D: 1,
}
# Number of timesteps in the trajectory for each PDE system.
PDE_TRAJ_LEN = {
PDE.ReactionDiffusion2D: 101,
PDE.NavierStokes2D: 64,
PDE.TurbulentFlow2D: 60,
PDE.KortewegDeVries1D: 140,
# This value is only used to pass some assertions so any non-zero value works
PDE.DarcyFlow2D: 101,
}
class DataMetrics(enum.Enum):
"""
Describes various data loss metrics, removing the need for metrics based on strings.
"""
MSE = "Mean Squared Error"
Relative_Error = "Relative Error"
class ParamMetrics(enum.Enum):
"""
Describes various parameter loss metrics, removing the need for metrics based on strings.
"""
MSE = "Mean Squared Error"
Relative_Error = "Relative Error"
########################
# common types
TypeBatchSolField1D = Float[torch.Tensor, "batch time xspace"]
TypeBatchSolField2D = Float[torch.Tensor, "batch time channel xspace yspace"]
TypeUnBatchSolField2D = Float[torch.Tensor, "time channel xspace yspace"]
TypeXGrid = Float[torch.Tensor, "batch xspace"]
TypeYGrid = Float[torch.Tensor, "batch yspace"]
# Navier Stokes has different grid input shape
TypeNSGrid = Float[torch.Tensor, "xspace yspace"]
TypeTimeGrid = Float[torch.Tensor, "batch timesteps"]
TypeParam = Dict[
str, Float[torch.Tensor, "batch 1"] | Float[torch.Tensor, "batch xspace yspace 1"]
]
TypeBatch = Float[torch.Tensor, "batch"]
########################
# types for logging_utils
# input dimensions for scaling functions
TypeScaleInputField1D = Float[np.ndarray, "time xspace"]
TypeScaleInputField2D = Float[np.ndarray, "time xspace yspace"]
# output dimensions for return value of scaling functions
TypeScaledField1D = UInt8[np.ndarray, "time xspace"]
TypeScaledField2D = UInt8[np.ndarray, "time 3 xspace yspace"]
# output type for return value of scaling functions
TypeLoggingField1D = Tuple[
TypeScaledField1D,
TypeScaledField1D,
TypeScaledField1D,
]
TypeLoggingField2D = Tuple[
TypeScaledField2D,
TypeScaledField2D,
TypeScaledField2D,
]
########################
# types for pde_module
TypeCollapsedInputSolField1D = Float[torch.Tensor, "batch channels_conditioning xspace"]
TypeCollapsedTargetSolField1D = Float[torch.Tensor, "batch channels_target xspace"]
TypeCollapsedInputSolField2D = Float[
torch.Tensor, "batch channels_conditioning xspace yspace"
]
TypeCollapsedTargetSolField2D = Float[
torch.Tensor, "batch channels_target xspace yspace"
]
TypeTimeFrames = Float[torch.Tensor, "batch n_past"]
TypeICIndex = Float[torch.Tensor, "batch 1"]
# input batch types for pde module
TypeBatch1D = List[
Union[
List[TypeXGrid],
TypeTimeGrid,
TypeCollapsedInputSolField1D,
TypeCollapsedTargetSolField1D,
TypeTimeFrames,
TypeICIndex,
TypeParam,
]
]
TypeBatch2D = List[
Union[
List[Union[TypeXGrid, TypeYGrid]],
TypeTimeGrid,
TypeCollapsedInputSolField2D,
TypeCollapsedTargetSolField2D,
TypeTimeFrames,
TypeICIndex,
TypeParam,
]
]
# output prediction types for pde module
TypePredict1D = Tuple[
TypeBatchSolField1D,
TypeBatchSolField1D,
# Dict of dict so that we may store auxillary metrics during tailoring
Dict[str, Union[torch.Tensor, Float[torch.Tensor, "batch"], Dict]],
]
TypePredict2D = Tuple[
TypeBatchSolField2D,
TypeBatchSolField2D,
# Dict of dict so that we may store auxillary metrics during tailoring
Dict[str, Union[torch.Tensor, Float[torch.Tensor, "batch"], Dict]],
]
TypeLossDict = Dict[str, Union[Dict, torch.Tensor, Float[torch.Tensor, "batch"]]]
# input and output types for autoregressive rollout in pde module
TypeAutoRegressiveInitFrames = Union[
Float[torch.Tensor, "batch n_past xspace"],
Float[torch.Tensor, "batch n_pastxchannels xspace yspace"],
]
TypeAutoRegressivePredFrames = Union[
Float[torch.Tensor, "batch n_fut xspace"],
Float[torch.Tensor, "batch n_futxchannels xspace yspace"],
]
########################
# types for pde_residual
# Shape of partial differentials computed for 1d and 2d systems
TypePartials1D = TypeBatchSolField1D
TypePartials2D = Float[torch.Tensor, "batch time xspace yspace"]
TypeNSPartials2D = Float[torch.Tensor, "batch 3 time xspace yspace"]
# return type for advection residual + partials
TypeAdvectionPartialsReturnType = Union[
TypePartials1D,
Tuple[
TypePartials1D,
Float[torch.Tensor, "batch 2*time xspace"],
],
]
# return type for burgers residual + partials
TypeBurgersPartialsReturnType = Union[
TypePartials1D,
Tuple[
TypePartials1D,
Float[torch.Tensor, "batch 3*time xspace"],
],
]
# return type for 1drd residual + partials
Type1DRDPartialsReturnType = Union[
TypePartials1D,
Tuple[
TypePartials1D,
Float[torch.Tensor, "batch 2*time xspace"],
],
]
# Return type for 1D KDV residual + partials
Type1DKDVPartialsReturnType = Union[
TypePartials1D,
Tuple[
TypePartials1D,
Float[torch.Tensor, "batch 4*time xspace"],
],
]
# return type for 2drd residual + partials
Type2DRDPartialsReturnType = Union[
TypeBatchSolField2D,
Tuple[
TypeBatchSolField2D,
Float[torch.Tensor, "batch time*5 channels xspace yspace"],
],
]
# return types for 2dns residual + partials
TypeUnBatchedNSPartials2D = Float[torch.Tensor, "3 time xspace yspace"]
TypeUnBatchedNSResiduals2D = Float[torch.Tensor, "time xspace yspace"]
##################################
# types for finite_differences
# Return type after computing all needed partials
Type1DRPartialsTuple = Tuple[
TypeBatchSolField1D,
TypeBatchSolField1D,
TypeBatchSolField1D,
TypeBatchSolField1D,
]
Type2DRDPartialsTuple = Tuple[
TypePartials2D,
TypePartials2D,
TypePartials2D,
TypePartials2D,
TypePartials2D,
]
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