Efficient adjoint mantle reconstructions

Last updated: August 2026

About

Adjoint methods allow observations to constrain otherwise inaccessible properties and histories of Earth's interior. G-ADOPT can automatically derive adjoint equations for mantle-convection models, but realistic inversions remain computationally demanding and can be sensitive to initial conditions, parameter scaling, and nonlinear behaviour.

This project will develop efficient optimisation methods for adjoint geodynamic inversions. It will use curvature information, Hessian-vector products, and Newton-Krylov methods to identify better search directions and reduce the number of expensive forward and adjoint calculations.

Research questions

• When do Hessian-informed methods improve adjoint mantle reconstructions?
• How can preconditioning, scaling, checkpointing, and trust-region methods improve convergence?
• Which numerical diagnostics distinguish a genuine physical reconstruction from an optimisation artefact?

Methods and data

Projects can use G-ADOPT, automatic differentiation, Newton-Krylov methods, Hessian-vector products, high-performance computing, and synthetic or observational mantle-convection inversions.

Possible projects

Possible directions include implementing a second-order optimisation method, testing it with controlled twin experiments, improving checkpointing and preconditioning, or applying it to a time-dependent mantle reconstruction.

Essential background

Useful preparation includes applied mathematics, computational science, physics, geophysics, programming, or numerical optimisation.