Over the last few decades a large range of numerical dynamo models, simulating planetary fluid dynamics and the associated generation of a magnetic field, have been developed internationally. Although these models allowed the identification of some key physical principles involved, there is great potential to extract additional information about the dynamics using machine learning, a subfield of artificial intelligence.
One interesting application of this is the Earth, where its dynamo-generated magnetic field is undergoing decay and rapid change: there is speculation that we may be due for a global pole reversal.
The focus of this project is to apply a range of machine learning techniques to numerically simulated magnetic dynamos and historical geomagnetic datasets in order to better understand their underlying dynamics, and to assess whether they are predictable. 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. Such algorithms have been used with great success in, for example, spotting patterns in consumer spending, speech recognition and in recommending movies within Netflix (e.g. see the Wikipedia page). 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 apply well established techniques such as neural networks and data-driven model reduction to learn how a dynamo-generated magnetic field has changed, and to assess its predictability. Such analyses may be able to spot patterns in the data and supply accurate short-time forecasts.
Earth as a case study
Earth’s dynamo-generated magnetic field is very dynamic: exhibiting slow fluctuations and wandering magnetic poles. Yet the most global and significant changes are the multiple global reversals over its 3.5 billion year history, whose current rate of occurrence is about 2-3 times per million years (Stern, 2002). Because the last global reversal took place 780,000 years ago, some speculate that planet Earth is now “overdue”. True or not, it is certainly the case that change is afoot: 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 over northern Canada towards Siberia. Does this indicate that a period of significant change for the global field is upon us? By using a variety of global datasets that constrain the behaviour of the geomagnetic field, it has been possible to create time-dependent models of the geomagnetic field: such “movies” of the field cover the last 400 years. One aim of the project is to assess whether these movies can be used as a basis for a magnetic prediction.
The objectives of the PhD project are as follows:
1. Begin the investigation of the predictability of a dynamo-generated 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 output of a numerical dynamo model, and assess the ability to predict the last 10% (or so) of the time span of the model. The predictions will be compared with forecasts produced by other means (Aubert, 2013).
2. Apply data-driven techniques of model reduction, for example principal component analysis and dynamic mode decomposition (Schmid 2010) to dynamo simulations, in order to create simpler descriptions of the complex dynamics. The methods have been successfully applied in other areas of fluid dynamics but not yet to dynamo models, and can efficiently separate dynamics on different timescales: of relevance for the dynamo case is the separation and identification of waves from the slowly evolving background state.
3. 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. These methods essentially compress the images before prediction, thereby abstracting only the key components of the magnetic field that are changing. An additional benefit of these methods is that they can be used to detect anomalies in the movie, of particular interest being whether we can assess the predictability of features in the magnetic field such as geomagnetic jerks (e.g. Cox and Brown, 2013) which are regarded as “unpredictable”.
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