Comparison of gradient computation strategies for a differentiable Poisson solver. (a) Unrolled backpropagation: the Poisson solve Aϕ = F is implemented as an explicit sequence of multigrid (MG) iterations, and gradients of the loss ﹩{ \mathcal L }﹩ are obtained by backpropagating through the solver steps. This corresponds to differentiating the algorithm and requires storing or recomputing intermediate iterates, leading to memory and compute costs that scale with the number of solver iterations. (b) Adjoint method: the solver is treated as an implicit differentiable operator, and gradients are computed by solving a single adjoint system ﹩{A}^{T}{g}_{F}=\partial { \mathcal L }/\partial \phi ﹩. For symmetric Poisson operators A^T = A, allowing for reuse of the same MG solver. This yields gradients of the converged solution with constant memory overhead, independent of the forward iteration count.