predicting variations in the length of day with Physics Informed Neural Networks

summary :
Geodetic observations provide constraints on the rotation period of our Planet Earth, with variations in the length of day (LOD) of the order of a few ms on decadal periods. Such changes predominantly result from exchanges of angular momentum between the solid Earth and the fluid metallic core located 3000 km beneath our feet. Dynamics in the core are imaged from variations of the geomagnetic field, as recorded in ground-based stations and on board of low-Earth orbiting satellites, such as the Swarm constellation of ESA and the Macau Science Satellite [1]. Recently, Physics Informed Neural Networks (PINNs) have been considered for producing LOD predictions from magnetic observations over the past two centuries [2], using only the radial induction equation at the core surface in the frozen-flux approximation and yet providing very coherent results. In particular they show reduced bias on decadal periods, in comparison with previous estimates based on inverted core motions [1]. This may appear surprising given the crude approximations incorporated within the PINNs. The goal of the project is first to replicate this study, in order to understand where the information is captured, and which parameterizations of the PINN ensure convincing decadal and longer LOD predictions. This presents potentially important consequences as the evolution of the core angular momentum on long time-scales is key to disentangle the contribution of ice melting to the slowdown of Earth’s rotation rate [3]. Next, we will investigate whether PINNs can also help improve the subdecadal LOD budget, for which core flow inversions still today provide more accurate predictions [4]. This issue is timely, as on these shorter time-scales, it is difficult to disentangle core and atmospheric LOD contributions [5].

The candidate should have a background in applied maths, physics and/or scientific computing, with experience in artificial intelligence methods. She/he will interact with members of the “geodynamo” team at the ISTerre laboratory.

references :
[1] Finlay et al. (2023). Gyres, jets and waves in the Earth’s core. Nature Reviews Earth & Environment, 4(6), 377-392.
[2] Shahvandi et al. (2024). Length of day variations explained in a Bayesian framework. GRL, 51(22), e2024GL111148.
[3] Shahvandi et al. (2024). The increasingly dominant role of climate change on length of day variations. PNAS, 121(30), e2406930121.
[4] Rosat & Gillet (2023). Intradecadal variations in length of day : Coherence with models of the Earth’s core dynamics. PEPI, 341, 107053.
[5] Cazenave et al. (2025) Why is the Earth System oscillating at a 6-year period ? Surveys in Geophysics (accepted)