Pointwise adjoint operator

[nbouziani]

This PR is an update of the deprecated PointwiseOperator PR. It is the Firedrake bit of the ExternalOperator concept introduced in UFL.

It handles the practical implementation thereof, especially it implements some of the subclasses covered by this concept :

• PointexprOperator: Operator defined through an externally defined expression (e.g. lambda expression) passed in. This evaluation of this operator is done by merely evaluate this expression pointwise.

• PointsolveOperator: Solve an externally defined algebraic relationship pointwise. For instance one can think to an implicit constitutive law that is part of a given PDE-based model.

• PointnetOperator: Represents neural networks. Evaluation is associated to a forward-pass and gradient computation to a gradient of the output wrt inputs. So far, only PyTorch has been covered (it should be straightforward to extend this to TensorFlow).

There are more classes of function that could be derived from the AbstractPointwiseOperator base class.

This PR also cover the implementation of the adjoint capability of pointwise operators enabling to tackle more generally all the PDE-constrained optimization problems containing pointwise operators in the PDE-constraint and/or in the cost function.

Examples of applications cover:

• Implicit constitutive relations (e.g. Glen's flow law in glaciology)
• Regularizer for inverse problems (e.g. seismic inversion)
• Subgrid parametrization

This PR is associated to several other PRs:

UFL: firedrakeproject/ufl#16
Pyadjoint: dolfin-adjoint/pyadjoint#15
TSFC: firedrakeproject/tsfc#201
PyOP2: OP2/PyOP2#579

[dham]

Superseded by ExternalOperator.