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

显然，对于许多问题，计算机在分类方面有能力胜过人类。我对相反的情况很感兴趣，在这种情况下，人类可以很好地预测或分类结果，而计算机可能会遇到困难。一个明显的例子是图像或文本数据的形式。这类问题对人类来说通常是微不足道的，但对机器来说却增加了一层复杂性——如何教会机器解剖图片并分析模式？机器是如何从一条只有文字的推文中学习推断和情感的？也许这些问题中最让我感兴趣的是机器学习人类固有特征的能力，尽管是以一种非常不同的方式——它如此纯粹和明确地模仿人类的学习过程，与人类的学习过程相关。在与David Large教授和Christopher Fallaize博士的交谈中，我了解到使用InSAR对卫星捕获的图像数据进行分类对于确定世界各地泥炭地的状况至关重要，而无需事先进行大规模的实地研究。泥炭地的管理对固碳至关重要，对维持栖息于泥炭地的多样化生态系统至关重要，对泥炭地的干扰会向大气中释放大量温室气体。在对这些图像开发机器学习方法时，特别是通过使用时间序列，泥炭的状况可以通过跟踪其年度和次年度表面运动来分类。这些分类可用于确定可能需要恢复方案的令人关切的领域。我对时间序列在图像数据中的应用很感兴趣，特别是在泥炭地状况诊断方面。这项工作对于确保它们受到气候变化威胁的保护至关重要。

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.