GAFD Seminar: Calum Skene (University of Edinburgh)

Wednesday, 14 October 2026 at 12:30

Automatic Differentiation and Adjoints for Dynamo Problems: A Dynamical-Systems View of the Geodynamo

Event details

Speaker: Dr Calum Skene, University of Edinburgh

Title: Automatic Differentiation and Adjoints for Dynamo Problems: A Dynamical-Systems View of the Geodynamo

Abstract: Adjoint methods provide an efficient way to obtain gradient information and have therefore become powerful tools for sensitivity analysis and gradient-based optimisation across many areas of science. Because the sensitivity of a quantity to many parameters can be computed with a single additional adjoint solve, at a cost comparable to that of the original calculation, these methods are particularly well suited to nonlinear optimisation problems in geophysical and astrophysical fluid dynamics, where the parameter spaces are often very high-dimensional. However, deriving the adjoint of a complex model is usually a lengthy, tedious, and error-prone process, which has limited their uptake in research. In this talk, I will show how adjoint-based optimisation can reveal nonlinear pathways to magnetic-field generation in models of the geodynamo, and how recent advances in automatic differentiation are making these techniques much easier to apply.

In 1978, Roberts suggested that the Earth’s magnetic field, which is generated by a dynamo process in its outer core, could originate from a subcritical dynamo instability. This means that a finite-amplitude seed magnetic field could trigger dynamo action in parameter regimes where small magnetic fields decay. A natural question is then: what is the smallest magnetic field that can initiate this process? Finding this minimal seed places a bound on the magnetic energy required to start the geodynamo and provides a systematic procedure for finding subcritical dynamo states. I will describe how adjoint-based nonlinear optimisation can solve this problem, and how it uncovers dynamically important invariant states that illuminate the dynamical landscape governing this nonlinear pathway.

I will then discuss recent progress in automating this procedure in the open-source spectral PDE solver Dedalus by leveraging techniques from reverse-mode automatic differentiation. This framework enables the automatic computation of the discrete adjoint of a Dedalus model without the need for the user to rewrite their forward code, systematically opening a wide range of scientific computing studies to adjoint-based techniques.

Organiser

Mathematics and Statistics

Location

Laver 320