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Inverse problem implementation (#177)

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* inverse problem implementation

* add tutorial7 for inverse Poisson problem

* fix doc in equation, equation_interface, system_equation

---------

Co-authored-by: Dario Coscia <dariocoscia@dhcp-015.eduroam.sissa.it>
This commit is contained in:
Anna Ivagnes
2023-11-15 14:02:16 +01:00
committed by Nicola Demo
parent a9f14ac323
commit 0b7a307cf1
21 changed files with 967 additions and 40 deletions
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27
pina/equation/system_equation.py
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@@ -11,14 +11,14 @@ class SystemEquation(Equation):
System of Equation class for specifing any system
of equations in PINA.
Each ``equation`` passed to a ``Condition`` object
must be an ``Equation`` or ``SystemEquation``.
A ``SystemEquation`` is specified by a list of
must be an ``Equation`` or ``SystemEquation``.
A ``SystemEquation`` is specified by a list of
equations.
:param Callable equation: A ``torch`` callable equation to
evaluate the residual
:param str reduction: Specifies the reduction to apply to the output:
``none`` | ``mean`` | ``sum`` | ``callable``. ``none``: no reduction
``none`` | ``mean`` | ``sum`` | ``callable``. ``none``: no reduction
will be applied, ``mean``: the sum of the output will be divided
by the number of elements in the output, ``sum``: the output will
be summed. ``callable`` a callable function to perform reduction,
@@ -43,19 +43,28 @@ class SystemEquation(Equation):
raise NotImplementedError(
'Only mean and sum reductions implemented.')
def residual(self, input_, output_):
def residual(self, input_, output_, params_=None):
"""
Residual computation of the equation.
Residual computation for the equations of the system.
:param LabelTensor input_: Input points to evaluate the equation.
:param LabelTensor output_: Output vectors given my a model (e.g,
:param LabelTensor input_: Input points to evaluate the system of
equations.
:param LabelTensor output_: Output vectors given by a model (e.g,
a ``FeedForward`` model).
:return: The residual evaluation of the specified equation,
:param dict params_: Dictionary of parameters related to the inverse
problem (if any).
If the equation is not related to an ``InverseProblem``, the
parameters are initialized to ``None`` and the residual is
computed as ``equation(input_, output_)``.
Otherwise, the parameters are automatically initialized in the
ranges specified by the user.
:return: The residual evaluation of the specified system of equations,
aggregated by the ``reduction`` defined in the ``__init__``.
:rtype: LabelTensor
"""
residual = torch.hstack(
[equation.residual(input_, output_) for equation in self.equations])
[equation.residual(input_, output_, params_) for equation in self.equations])
if self.reduction == 'none':
return residual