# (C) Copyright IBM Corp. 2019, 2020, 2021, 2022.
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import importlib
from typing import Dict, List, Union
import numpy as np
import sympy
import torch
from sympy import sympify
from sympy.parsing.sympy_parser import parse_expr
from torch.autograd import grad
from torch.autograd.functional import jacobian
from torch.nn.parameter import Parameter
from simulai.io import MakeTensor
from simulai.tokens import D
[docs]
class SymbolicOperator(torch.nn.Module):
"""The SymbolicOperatorClass is a class that constructs tensor operators using symbolic expressions written in PyTorch.
Returns:
object: An instance of the SymbolicOperatorClass.
"""
def __init__(
self,
expressions: List[Union[sympy.Expr, str]] = None,
input_vars: List[Union[sympy.Symbol, str]] = None,
output_vars: List[Union[sympy.Symbol, str]] = None,
function: callable = None,
gradient: callable = None,
keys: str = None,
inputs_key=None,
constants: dict = None,
trainable_parameters: dict = None,
external_functions: dict = dict(),
processing: str = "serial",
device: str = "cpu",
engine: str = "torch",
auxiliary_expressions: list = None,
) -> None:
if engine == "torch":
super(SymbolicOperator, self).__init__()
else:
pass
self.engine = importlib.import_module(engine)
self.constants = constants
if trainable_parameters is not None:
self.trainable_parameters = trainable_parameters
else:
self.trainable_parameters = dict()
self.external_functions = external_functions
self.processing = processing
self.periodic_bc_protected_key = "periodic"
self.protected_funcs = ["cos", "sin", "sqrt", "exp"]
self.protected_operators = ["L", "Div", "Identity", "Kronecker"]
self.protected_funcs_subs = self._construct_protected_functions()
self.protected_operators_subs = self._construct_implict_operators()
# Configuring the device to be used during the fitting process
if device == "gpu":
if not torch.cuda.is_available():
print("Warning: There is no GPU available, using CPU instead.")
device = "cpu"
else:
device = "cuda"
print("Using GPU.")
elif device == "cpu":
print("Using CPU.")
else:
raise Exception(f"The device must be cpu or gpu, but received: {device}")
self.device = device
self.expressions = [self._parse_expression(expr=expr) for expr in expressions]
if isinstance(auxiliary_expressions, dict):
self.auxiliary_expressions = {
key: self._parse_expression(expr=expr)
for key, expr in auxiliary_expressions.items()
}
else:
self.auxiliary_expressions = auxiliary_expressions
self.input_vars = [self._parse_variable(var=var) for var in input_vars]
self.output_vars = [self._parse_variable(var=var) for var in output_vars]
self.input_names = [var.name for var in self.input_vars]
self.output_names = [var.name for var in self.output_vars]
self.keys = keys
if inputs_key != None:
self.inputs_key = self._parse_inputs_key(inputs_key=inputs_key)
else:
self.inputs_key = inputs_key
self.all_vars = self.input_vars + self.output_vars
if self.inputs_key is not None:
self.forward = self._forward_dict
else:
self.forward = self._forward_tensor
self.function = function
self.diff_symbol = D
self.output = None
self.f_expressions = list()
self.g_expressions = dict()
self.feed_vars = None
for name in self.output_names:
setattr(self, name, None)
# Defining functions for returning each variable of the regression
# function
for index, name in enumerate(self.output_names):
setattr(
self,
name,
lambda data: self.function.forward(input_data=data)[..., index][
..., None
],
)
# If no external gradient is provided, use the core gradient evaluator
if gradient is None:
gradient_function = self.gradient
else:
gradient_function = gradient
subs = {self.diff_symbol.name: gradient_function}
subs.update(self.external_functions)
subs.update(self.protected_funcs_subs)
for expr in self.expressions:
if not callable(expr):
f_expr = sympy.lambdify(self.all_vars, expr, subs)
else:
f_expr = expr
self.f_expressions.append(f_expr)
if self.auxiliary_expressions is not None:
for key, expr in self.auxiliary_expressions.items():
if not callable(expr):
g_expr = sympy.lambdify(self.all_vars, expr, subs)
else:
g_expr = expr
self.g_expressions[key] = g_expr
# Method for executing the expressions evaluation
if self.processing == "serial":
self.process_expression = self._process_expression_serial
else:
raise Exception(f"Processing case {self.processing} not supported.")
def _construct_protected_functions(self):
"""This function creates a dictionary of protected functions from the engine object attribute.
Returns:
dict: A dictionary of function names and their corresponding function objects.
"""
protected_funcs = {
func: getattr(self.engine, func) for func in self.protected_funcs
}
return protected_funcs
def _construct_implict_operators(self):
"""This function creates a dictionary of protected operators from the operators engine module.
Returns:
dict: A dictionary of operator names and their corresponding function objects.
"""
operators_engine = importlib.import_module("simulai.tokens")
protected_operators = {
func: getattr(operators_engine, func) for func in self.protected_operators
}
return protected_operators
def _parse_key_interval(self, intv: str) -> List:
begin, end = intv.split(",")
end = int(end[:-1])
begin = int(begin)
end = int(end + 1)
return np.arange(begin, end).astype(int).tolist()
def _parse_inputs_key(self, inputs_key: str = None) -> dict:
# Sentences separator: '|'
sep = "|"
# Index identifier: ':'
inx = ":"
# Interval identifier
intv = "["
# Removing possible spaces in the inputs_key string
inputs_key = inputs_key.replace(" ", "")
try:
split_components = inputs_key.split(sep)
except ValueError:
split_components = inputs_key
keys_dict = dict()
for s in split_components:
try:
if len(s.split(inx)) > 1:
key, index = s.split(inx)
if not key in keys_dict:
keys_dict[key] = list()
keys_dict[key].append(int(index))
else:
keys_dict[key].append(int(index))
elif len(s.split(intv)) > 1:
key, interval_str = s.split(intv)
interval = self._parse_key_interval(interval_str)
keys_dict[key] = interval
else:
raise ValueError
except ValueError:
keys_dict[s] = -1
return keys_dict
def _collect_data_from_inputs_list(self, inputs_list: dict = None) -> list:
data = list()
for k, v in self.inputs_key.items():
if v == -1:
if inputs_list[k].shape[1] == 1:
data_ = [inputs_list[k]]
else:
data_ = list(torch.split(inputs_list[k], 1, dim=1))
else:
data_ = [inputs_list[k][:, i : i + 1] for i in v]
data += data_
return data
def _parse_expression(self, expr=Union[sympy.Expr, str]) -> sympy.Expr:
"""Parses the input expression and returns a SymPy expression.
Args:
expr (Union[sympy.Expr, str], optional, optional): The expression to parse, by default None. It can either be a SymPy expression or a string.
Returns:
sympy.Expr: The parsed SymPy expression.
Raises:
Exception: If the `constants` attribute is not defined, and the input expression is a string.
"""
if isinstance(expr, str):
try:
expr_ = sympify(
expr, locals=self.protected_operators_subs, evaluate=False
)
if self.constants is not None:
expr_ = expr_.subs(self.constants)
if self.trainable_parameters is not None:
expr_ = expr_.subs(self.trainable_parameters)
except ValueError:
if self.constants is not None:
_expr = expr
for key, value in self.constants.items():
_expr = _expr.replace(key, str(value))
expr_ = parse_expr(_expr, evaluate=0)
else:
raise Exception("It is necessary to define a constants dict.")
elif callable(expr):
expr_ = expr
else:
if self.constants is not None:
expr_ = expr.subs(self.constants)
else:
expr_ = expr
return expr_
def _parse_variable(self, var=Union[sympy.Symbol, str]) -> sympy.Symbol:
"""Parse the input variable and return a SymPy Symbol.
Args:
var (Union[sympy.Symbol, str], optional, optional): The input variable, either a SymPy Symbol or a string. (Default value = Union[sympy.Symbol, str])
Returns:
sympy.Symbol: A SymPy Symbol representing the input variable.
"""
if isinstance(var, str):
return sympy.Symbol(var)
else:
return var
def _forward_tensor(self, input_data: torch.Tensor = None) -> torch.Tensor:
"""Forward the input tensor through the function.
Args:
input_data (torch.Tensor, optional): The input tensor. (Default value = None)
Returns:
torch.Tensor: The output tensor after forward pass.
"""
return self.function.forward(input_data=input_data)
def _forward_dict(self, input_data: dict = None) -> torch.Tensor:
"""Forward the input dictionary through the function.
Args:
input_data (dict, optional): The input dictionary. (Default value = None)
Returns:
torch.Tensor: The output tensor after forward pass.
"""
return self.function.forward(**input_data)
def _process_expression_serial(self, feed_vars: dict = None) -> List[torch.Tensor]:
"""Process the expression list serially using the given feed variables.
Args:
feed_vars (dict, optional): The feed variables. (Default value = None)
Returns:
List[torch.Tensor]: A list of tensors after evaluating the expressions serially.
"""
return [f(**feed_vars).to(self.device) for f in self.f_expressions]
def _process_expression_individual(
self, index: int = None, feed_vars: dict = None
) -> torch.Tensor:
"""Evaluates a single expression specified by index from the f_expressions list with given feed variables.
Args:
index (int, optional): Index of the expression to be evaluated, by default None
feed_vars (dict, optional): Dictionary of feed variables, by default None
Returns:
torch.Tensor: Result of evaluating the specified expression with given feed variables
"""
return self.f_expressions[index](**feed_vars).to(self.device)
def __call__(
self, inputs_data: Union[np.ndarray, dict] = None
) -> List[torch.Tensor]:
"""Evaluate the symbolic expression.
This function takes either a numpy array or a dictionary of numpy arrays as input.
Args:
inputs_data (Union[np.ndarray, dict], optional): Union (Default value = None)
Returns:
List[torch.Tensor]: List[torch.Tensor]: A list of tensors containing the evaluated expressions.
Raises:
Raises:
does: not match with the inputs_key attribute
"""
constructor = MakeTensor(
input_names=self.input_names, output_names=self.output_names
)
inputs_list = constructor(input_data=inputs_data, device=self.device)
output = self.forward(input_data=inputs_list)
output = output.to(self.device) # TODO Check if it is necessary
outputs_list = torch.split(output, 1, dim=-1)
outputs = {key: value for key, value in zip(self.output_names, outputs_list)}
if type(inputs_list) is list:
inputs = {key: value for key, value in zip(self.input_names, inputs_list)}
elif type(inputs_list) is dict:
assert (
self.inputs_key is not None
), "If inputs_list is dict, \
it is necessary to provide\
a key."
inputs_list = self._collect_data_from_inputs_list(inputs_list=inputs_list)
inputs = {key: value for key, value in zip(self.input_names, inputs_list)}
else:
raise Exception(
f"Format {type(inputs_list)} not supported \
for inputs_list"
)
feed_vars = {**outputs, **inputs}
# It returns a list of tensors containing the expressions
# evaluated over a domain
return self.process_expression(feed_vars=feed_vars)
def eval_expression(self, key, inputs_list):
"""This function evaluates an expression stored in the class attribute 'g_expressions' using the inputs in 'inputs_list'. If the expression has a periodic boundary condition, the function evaluates the expression at the lower and upper boundaries and returns the difference. If the inputs are provided as a list, they are split into individual tensors and stored in a dictionary with the keys as the input names. If the inputs are provided as an np.ndarray, they are converted to tensors and split along the second axis. If the inputs are provided as a dict, they are extracted using the 'inputs_key' attribute. The inputs, along with the outputs obtained from running the function, are then passed as arguments to the expression using the 'g(**feed_vars)' syntax.
Args:
key (str): the key used to retrieve the expression from the 'g_expressions' attribute
inputs_list (list): either a list of arrays, an np.ndarray, or a dict containing the inputs to the function
Returns:
the result of evaluating the expression using the inputs.:
"""
try:
g = self.g_expressions.get(key)
except:
raise Exception(f"The expression {key} does not exist.")
# Periodic boundary conditions
if self.periodic_bc_protected_key in key:
assert isinstance(inputs_list, list), (
"When a periodic boundary expression is used,"
" the input must be a list of arrays."
)
# Lower bound
constructor = MakeTensor(
input_names=self.input_names, output_names=self.output_names
)
tensors_list = constructor(input_data=inputs_list[0], device=self.device)
inputs_L = {
key: value for key, value in zip(self.input_names, tensors_list)
}
output = self.function.forward(input_data=tensors_list)
output = output.to(self.device) # TODO Check if it is necessary
outputs_list = torch.split(output, 1, dim=-1)
outputs_L = {
key: value for key, value in zip(self.output_names, outputs_list)
}
feed_vars_L = {**inputs_L, **outputs_L}
# Upper bound
constructor = MakeTensor(
input_names=self.input_names, output_names=self.output_names
)
tensors_list = constructor(input_data=inputs_list[-1], device=self.device)
inputs_U = {
key: value for key, value in zip(self.input_names, tensors_list)
}
output = self.function.forward(input_data=tensors_list)
output = output.to(self.device) # TODO Check if it is necessary
outputs_list = torch.split(output, 1, dim=-1)
outputs_U = {
key: value for key, value in zip(self.output_names, outputs_list)
}
feed_vars_U = {**inputs_U, **outputs_U}
# Evaluating the boundaries equality
return g(**feed_vars_L) - g(**feed_vars_U)
# The non-periodic cases
else:
constructor = MakeTensor(
input_names=self.input_names, output_names=self.output_names
)
inputs_list = constructor(input_data=inputs_list, device=self.device)
output = self.function.forward(input_data=inputs_list)
outputs_list = torch.split(output, 1, dim=-1)
outputs = {
key: value for key, value in zip(self.output_names, outputs_list)
}
if type(inputs_list) is list:
inputs = {
key: value for key, value in zip(self.input_names, inputs_list)
}
elif type(inputs_list) is np.ndarray:
arrays_list = np.split(inputs_list, inputs_list.shape[1], axis=1)
tensors_list = [torch.from_numpy(arr) for arr in arrays_list]
for t in tensors_list:
t.requires_grad = True
inputs = {
key: value for key, value in zip(self.input_names, tensors_list)
}
elif type(inputs_list) is dict:
assert (
self.inputs_key is not None
), "If inputs_list is dict, \
it is necessary to provide\
a key."
inputs = {
key: value
for key, value in zip(
self.input_names, inputs_list[self.inputs_key]
)
}
else:
raise Exception(
f"Format {type(inputs_list)} not supported \
for inputs_list"
)
feed_vars = {**inputs, **outputs}
return g(**feed_vars)
@staticmethod
def gradient(feature, param):
"""Calculates the gradient of the given feature with respect to the given parameter.
Args:
feature (torch.Tensor): Tensor with the input feature.
param (torch.Tensor): Tensor with the parameter to calculate the gradient with respect to.
Returns:
torch.Tensor: Tensor with the gradient of the feature with respect to the given parameter.
Example:
>>> feature = torch.tensor([1, 2, 3], dtype=torch.float32)
>>> param = torch.tensor([2, 3, 4], dtype=torch.float32)
>>> gradient(feature, param)
tensor([1., 1., 1.], grad_fn=<AddBackward0>)
"""
grad_ = grad(
feature,
param,
grad_outputs=torch.ones_like(feature),
create_graph=True,
allow_unused=True,
retain_graph=True,
)
return grad_[0]
def jac(self, inputs):
"""Calculates the Jacobian of the forward function of the model with respect to its inputs.
Args:
inputs (torch.Tensor): Tensor with the input data to the forward function.
Returns:
torch.Tensor: Tensor with the Jacobian of the forward function with respect to its inputs.
Example:
>>> inputs = torch.tensor([[1, 2, 3], [2, 3, 4]], dtype=torch.float32)
>>> jac(inputs)
tensor([[1., 1., 1.],
[1., 1., 1.]], grad_fn=<MulBackward0>)
"""
def inner(inputs):
return self.forward(input_data=inputs)
return jacobian(inner, inputs)
def diff(feature: torch.Tensor, param: torch.Tensor) -> torch.Tensor:
"""Calculates the gradient of the given feature with respect to the given parameter.
Args:
feature (torch.Tensor): Tensor with the input feature.
param (torch.Tensor): Tensor with the parameter to calculate the gradient with respect to.
Returns:
torch.Tensor: Tensor with the gradient of the feature with respect to the given parameter.
Example:
>>> feature = torch.tensor([1, 2, 3], dtype=torch.float32)
>>> param = torch.tensor([2, 3, 4], dtype=torch.float32)
>>> gradient(feature, param)
tensor([1., 1., 1.], grad_fn=<AddBackward0>)
"""
grad_ = grad(
feature,
param,
grad_outputs=torch.ones_like(feature),
create_graph=True,
allow_unused=True,
retain_graph=True,
)
return grad_[0]