An approximate second-order adjoint for the shallow-stream ice sheet equations produces Hessians whose leading ~4 eigenvector modes match the exact AD-computed Hessian, but whose subspaces diverge beyond that rank.
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Exact vs approximate second-order derivatives in vertically-integrated ice sheet models
An approximate second-order adjoint for the shallow-stream ice sheet equations produces Hessians whose leading ~4 eigenvector modes match the exact AD-computed Hessian, but whose subspaces diverge beyond that rank.