In this project, the mathematical background of so-called Generative Adversarial Neural Networks is investigated and analyzed. Generative approaches have become very influential recently, due to quite impressive results in a variety of applications, including natural language processing and image generation. In this project, we investigate in particular so-called Deep Convolutional Generative Adversarial Networks (DCGANS).
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In this project, a Deep Convolutional Generative Adversarial Network (DCGAN) model is used for data from the well-known MNIST database. The performance of the model was analyzed and evaluated for various steering parameters of the method.
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Train punctuality is a necessity for a free flowing transport system where commuters can travel without the worry of missed connections or being behind schedule themselves. Reliable prediction of delays not only allows passengers to have a more enjoyable experience but gives train operators greater control of running a railway system efficiently. This project seeks to gain an understanding of machine learning methods, specifically support vector machines, and then use support vector classification and regression to predict train delays between London Euston and Manchester Piccadilly using a two-level method.
Convolutional Neural Networks (CNNs) are specialized deep learning algorithms for processing data which has spatial correlation between neighboring data points. The objective of this project is to outline and discuss the mathematics behind CNNs and to draw conclusions about their successes and limitations. For this purpose, the well-known Fashion MNIST dataset is used. All codes are written in Python using the Tensorflow library.
In this project, a recent approach is investigated for approximating the solution to partial differential equations arising in mathematical physics by specially designed physics-informed neural networks.
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This project discusses the mathematics behind Recurrent Neural Networks. These are often used for predicting sequential data (for example in natural language processing) due to their ability to retain information from previous predictions. As an example, a Long Short Term Memory (LSTM) Network is described and its detailed working explained.
This project discusses some recently proposed techniques for shape recognition using Artificial Neural Networks. We are in particular interested in the internal functioning of these algorithms, including the underlying optimization approaches employed when training the network. We discuss various techniques, such as Stochastic Gradient Descent (SGD), Adam, AMSGrad and L-BFGS.
In this project, Convolutional Neural Networks (CNNs) are investigated with respect of their performance in image classification. An emphasis is on the mathematical details of the underlying optimization routines when training the neural networks. We investigate and analyze in particular the approaches taken in Stochastic Gradient Descent (SGD) with momentum, AdaGrad, RMSProp and the Adam algorithm. Examples are presented using the well-established Fashion-MNIST data base and the Python computing environment.
The Kalman Filter (KF) presents a recursive algorithm of two steps: prediction under current measurements and update by comparison between predictions and the next measurements. Classically, the technique of KF is often investigated for its use in Tracking and Navigation using a stochastic model for the movement of physical objects. In this project, however, the technique of KF is applied to financial data for Crude Oil Price Estimation. We will also discuss some variants of the KF, namely the Extended Kalman Filter and the Ensemble Kalman Filter.
Reinforcement Learning (RL) has gained immense traction in the past decade for example in the application of robotics and autonomous systems. Unlike many other domains of Machine Learning, the purpose of RL is to achieve or approach some form of General Artificial Intelligence. In this project, we will exclusively look into the development of Algorithms for Autonomous Self-Driving Cars. The RL and Optimal Control algorithms developed here are written in Python and based on the open source package CARLA, an Autnomous Driving Simulator.
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This project investigates the use of image segmentation and radial basis function parameterisation for the identification of precipitation bands in the UK Radar based rain rate composites. Different methods of image segmentation are discussed, including the Chan-Vese model. The latter one is then implemented by using the so-called level set method for shape characterization. The numerical codes are written in Python and make use of the UK Met Office Rain Radar Data from the NIMROD system.
This project investigates and compares mathematical details of Deep Forward Neural Networks and Convolutional Neural Networks. The main application considered here is classification using examples from the MNIST data set. We also compare with more classical approaches such as Support Vector Machines.
Forecasting models predicting stock prices are lucrative if they are accurate and robust enough to make profits. In this project, we look at three machine learning algorithms and apply them to predict the closing price of the S&P 500 index. The algorithms we will be investigating are K-Nearest Neighbors, Artificial Neural Networks and Support Vector Machines.
This project discusses several variants of the Kalman Filter (KF) approach for forecasting, including the linear and nonlinear KF, Gauss-Hermite KF and cubature KF. Their performance is studied when applied to various typical forecasting problems in Finance.
The use of different flavors of the Kalman Filter, as well as the Kalman Smoother, is examined for applications from object tracking in 1D and 2D situations. In particular, the Rauch-Tung-Striebel (RTS) Kalman Smoother is considered and compared to the other variants. Numerical experiments are presented using the Matlab toolbox.
Nowcasting is a technique of predicting certain weather phenomena, such as heavy rainfall, for the next hour or so from observed rainfall data during the last one to three hours. This can help warning residents and authorities of imminent floods. UK rainfall Data are provided every five minutes by the Met Office using their NIMROD data system. The task considered in this project is to first automatically segment obtained rainfall data maps using the Chan-Vese model combined with a level set approach for interface tracking. Afterwards, the results are entered into a Kalman Filter in order to predict the movement and intensity of regions with high rainfall for the next half an hour or so. This approach is fast since it relies completely on image processing techniques, and does not require a complicated fluid flow model of the atmosphere.