Data-driven modelling and computation-improving the efficiency of computations in applied mathematics through scientific machine learning

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Evidently, for many problems, computers have the capacity to outperform humans in classifications. I am intrigued by the contrary case where humans can predict or classify outcomes well and where computers might struggle. An obvious example of this comes in the form of image or text data. These types of problems are often trivial for humans to analyse but add a layer of complexity for a machine- how does one teach a machine to dissect a picture and analyse patterns? How does a machine learn to draw inference and emotion from a tweet consisting only of text? Perhaps what interests me most about these problems is the ability of a machine to learn an inherently human trait, albeit in a very different way- it so purely and explicitly imitates a learning process, relatable to that of a human. In talking with Professor David Large and Doctor Christopher Fallaize, I learned that classifying image data captured by satellites using InSAR could be crucial in determining the condition of peatlands across the world, without the need to conduct prior large scale field research. Management of peatlands is vital in carbon sequestration, as well as maintaining the diverse ecosystems that inhabit them, and disturbing them releases huge amounts of greenhouse gases into the atmosphere. In developing machine learning methods on these images, particularly through the use of time series, the conditions of peat can be classified by tracking their annual and sub-annual surface motion. These classifications could be used to identify areas of concern that could require restoration programmes. I am interested in the application of time series to image data, especially in the context of diagnosing the condition of peatlands. This work could prove vital in ensuring their conservation, which has been threatened by climate change.