The geomagnetic field is a fundamental component of Earth. Wrapping around our planet like an invisible force-field, it protects life on the surface along with modern electrical infrastructure from harmful solar radiation. Far from being a constant presence, the field is very dynamic, exhibiting significant recent change: a patch of weak field in the south Atlantic (the south Atlantic anomaly) is spreading; the global field (expressed by the dipole strength) is weakening at a rate of 5% per century; and very recent measurements over the last few decades have shown that the magnetic north pole has begun a sprint away from its historical position.
Predicting the magnetic field is challenging, not the least because we do not yet have a model that describes how the magnetic field changes. However, a variety of global datasets constrain the time-dependent behaviour of the geomagnetic field. Sparse information about the ancient magnetic field, as recorded by very old rocks and archeological artefacts, informs us how its larger-scales have changed over the last few thousand years.
The novel aspect of this project is to apply recent advances in artificial intelligence, in particular a technique called machine learning to the prediction of Earth’s magnetic field. Machine learning is a technique in which computers ‘learn’ to interpret data via an explicit training process, using statistical models and (deep) neural networks for example. In some studies, machine learning has been shown to predict the next frames of video starting from a static image (Vondrick et al. 2016). In this project, we will train neural networks to learn how the magnetic field has changed, and to assess its predictability.
The objectives of the PhD project are as follows:
1. Begin the investigation of the predictability of the magnetic field using a simple recurrent neural network such as an “echo state” neural network, which has been shown to model and predict complex dynamical systems with surprising accuracy. We will base our study on both the 400-yr observation-derived model (gufm1, Jackson et al. 2000), and more recent models based on satellite data over the last few decades.
2. Considering the observations now as a movie with many hundreds of frames, we will apply techniques based on learning algorithms, such as auto-encoders (e.g. Vondrick et al. 2016) or other manifold learning and representation learning methods (such as Variational AutoEncoder or Generative Adversarial Networks) that can be used to guess the next few frames in the sequence and doing so predict the future structure.
3. Is the present state-of-the-art in numerical models of the geomagnetic field consistent with the real observations? This can be assessed by training a neural network on the output of a numerical simulation of Earth’s magnetic field: for example, the coupled Earth model of Aubert et al., 2013 or the database of simulated magnetic reversals under development at Leeds. Comparing a prediction from the trained network and the true evolution of the field will provide an important measure on whether or not the numerical models are a faithful representation of the Earth’s core.
Year 1: Familiarisation with geomagnetic observations, the theory of the dynamics of Earth’s core and models of the geodynamo. Hands-on experiments of basic machine learning with application to predicting the Earth’s magnetic field.
Year 2: Application of frame-prediction techniques to movies of the geomagnetic field derived from observations.
Year 3: Application of machine learning algorithms applied to the output of numerical simulations of the Earth’s core; comparison to the real geomagnetic signal.
The student will learn techniques of machine learning using both Matlab and Python, with standard deep learning libraries such as Keras, Caffe, Pytorch and Tensorflow, and will have the opportunity to take relevant specific undergraduate or masters level courses. The student will also have access to a broad spectrum of training workshops at Leeds. The student will be a part of the world-leading deep Earth research group, a vibrant part of the Institute of Geophysics and Tectonics.
Although the project will be based at Leeds, there are project partners in both Edinburgh and Copenhagen who the student will visit. There will also be opportunities to attend international conferences (UK, Europe, US and elsewhere), and other possible collaborative visits within Europe.
Movies showing the historical change in the geomagnetic field can be found at https://sos.noaa.gov/datasets/earths-magnetic-declination/ https://www.youtube.com/watch?v=NHRMxH3M2po
Stern, D. A (2002) Millennium of Geomagnetism, online material: http://www.phy6.org/earthmag/mill_1.htm
Aubert, J., Finlay, C. C., & Fournier, A. (2013). Bottom-up control of geomagnetic secular variation by the Earth’s inner core. Nature, 502(7470), 219–223. http://doi.org/10.1038/nature12574
Cox, G A, and Brown, W J. 2013. Rapid dynamics of the Earth's core Astronomy and Geophysics, 54(5)5.32-5.37
Finlay, C. C., Olsen, N., Kotsiaros, S., Gillet, N., & Tøffner-Clausen, L. (2016). Recent geomagnetic secular variation from Swarm and ground observatories as estimated in the CHAOS-6 geomagnetic field model. Earth Planets and Space, 68(1), 1–18. http://doi.org/10.1186/s40623-016-0486-1
Jackson, A., Jonkers, A., & Walker, M. (2000). Four centuries of geomagnetic secular variation from historical records. Philosophical Transactions of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 358(1768), 957–990.
Vondrick, C., Pirsiavash, H. & Torralba, A. (2016) Generating Videos with Scene Dynamics, NIPS https://arxiv.org/abs/1609.02612