jax_sn.variance_reduction.continuous_adjoint module

Continuous adjoint of the multi-group operator.

The continuous adjoint \(\mathbf{A}^\dagger\) is the discretisation of the adjoint transport equation: it negates the streaming direction (\(\Omega \to -\Omega\)) but keeps the moment/discrete operators \(\mathbf{M}, \mathbf{D}\) at \(+\Omega\), and gathers the transposed group scatter. It is therefore not the algebraic transpose \(\mathbf{A}^T\) (which reverses the whole operator chain); see MultiGroupOperator.

Because the harmonics wk_ylm/ylm are frozen at AngularData construction and only the transport sweep re-reads quadrature_set.angles, negating the angles after that freeze flips only the streaming, leaving \(\mathbf{M}, \mathbf{D}\) at \(+\Omega\). Combined with (a) reversing the sweep ordering to match the negated direction and (b) transposing the group axes of the scatter tensor (so the forward incoming_gather computes the outgoing sum), the ordinary forward MultiGroupOperator run on this transformed data is \(\mathbf{A}^\dagger\). No new operator/strategy/solver is introduced.

The transformed data is deliberately kept private and consumed immediately inside solve_continuous_adjoint(): it is a valid computational object but internally inconsistent (its angles no longer match its frozen harmonics; its scatter tensor is transposed), so it must never escape into general use.

solve_continuous_adjoint(operator: MultiGroupOperator, rhs, solver: AbstractLinearSolver)

Solve \(\mathbf{A}^\dagger \psi^\dagger = \mathbf{C}^\dagger[b]\) for the continuous adjoint of operator, where the source is conditioned by the adjoint chain \(\mathbf{C}^\dagger = \mathbf{M}\,(\mathbf{T}^\dagger)^{-1}\mathbf{H}\mathbf{D}\) (built automatically because the chain strategy runs on the adjoint-transformed data).

The adjoint operator is the ordinary forward MultiGroupOperator run on _continuous_adjoint_data(); it is built inside the jit so gradients w.r.t. cross sections / geometry still flow through the adjoint solve.

Parameters:

• operator (MultiGroupOperator) – The forward multi-group operator whose continuous adjoint is solved.

• rhs (RightHandSide) – The (physical) adjoint source.

• solver (AbstractLinearSolver) – An iterative solver (GMRES / BiCGStab). The direct block solver is rejected: for downscattering the continuous adjoint is upper-triangular, which that solver does not handle.

Return type:

lx.LinearSolveOutput