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Just as a tangent-linear computes a general directional derivative (a JAX jvp) the adjoint computes a (conjugate) derivative of a general dual element evaluation (the conjugate of a JAX vjp).
For a state $u \in V$ the generalization is defined by a functional
$J (u) = \eta (u)$,
for some $\eta \in V^*$, and the adjoint then computes (the conjugate of) the derivative of the reduced functional $\hat{J} = J \circ \hat{u}$ where $\hat{u}$ defines the forward (mapping from the control to the state).
compute_gradient is currently the case where $u$ is a scalar-valued output and $\eta$ is the identity.
This is already possible using InnerProduct or DotProduct to define the functional, and this is already used for the Gauss-Newton approximation. A simple interface could be added, and a new marker might be added to allow $\eta$ to be changed without re-evaluating the forward.
The text was updated successfully, but these errors were encountered:
Just as a tangent-linear computes a general directional derivative (a JAX
jvp
) the adjoint computes a (conjugate) derivative of a general dual element evaluation (the conjugate of a JAXvjp
).For a state$u \in V$ the generalization is defined by a functional
for some$\eta \in V^*$ , and the adjoint then computes (the conjugate of) the derivative of the reduced functional $\hat{J} = J \circ \hat{u}$ where $\hat{u}$ defines the forward (mapping from the control to the state).
compute_gradient
is currently the case whereThis is already possible using$\eta$ to be changed without re-evaluating the forward.
InnerProduct
orDotProduct
to define the functional, and this is already used for the Gauss-Newton approximation. A simple interface could be added, and a new marker might be added to allowThe text was updated successfully, but these errors were encountered: