My research interests lie at the intersection of the mathematics of information, machine learning, deep learning, and numerical analysis. Specifically, my work focuses on areas such as the numerical perspective of information measures, dimensionality reduction, optimal transport, machine learning algorithms, generative models, and other advanced deep neural network architectures.

Current CAMaCS Projects:

Previous Projects:

• Stochastic Parareal: an application of probabilistic methods to time-parallelisation.

The project is focused on improving the rate of convergence (equivalently, computational efficiency) of Parareal (which is a time-parallel algorithm that provides speed-up for a broad variety of existing initial value problems (IVPs)) by applying stochastic methods. Certain classes of problems such as the Brusselator equations and the Lorenz systems were investigated.

The idea of stochastic methods is to generate, instead of deterministic solutions at each time interval, M solutions from a probability distribution (denoted as the 'sampling rule'), and piece together a continuous trajectory that minimises the errors at interval boundaries.

We presented in the experiments that, with the increasing number of samples M and larger variance in the sampling rule, our proposed methods tend to beat the deterministic Parareal with high probability. In chaotic systems such as the Lorenz, our methods also showed the potential to indicate multiple numerical solutions caused by small perturbations.

This project is supervised by Dr. Massimiliano TamborrinoLink opens in a new window, Dr. Debasmita Samaddar and Dr. Lynton Appel, and supported by UKAEA. (Mar. - Jun. 2020)

• Research paper classification using neural networks.

The project is focused on classifying research papers by disciplines using NLP techniques such as word embedding algorithms (word2vec & GloVe), convolutional neural networks and recurrent neural networks. Auto-optimization algorithms of hyper-parameters such as Bayesian optimization and Tree-structured Parzen estimator were implemented in the paper.

Although the training datasets are extremely small sized due to multiple difficulties in labelling research papers, the final model was successfully managed to classify more than 70000 research papers published by the Chinese Academy of Sciences (CAS). The accuracy of classification is averagely over 90% on test datasets.

This project is supported by Computer Network Information Center, CAS. (Jun. - Sep. 2019)

• Numerical estimation of information measures.Link opens in a new window

The project is focused on numerically estimating entropy and mutual information using k-th nearest neighbor estimators and its applications in related areas. Entropy and mutual information are defined as follows:

For continuous estimators, KSG, BI-KSG and G-knn estimators were reproduced. For discrete cases, Gao’s estimator and Multi-KL estimator were reproduced. We also improved the bias of G-knn method (not vanished yet) and proposed an approximate k-NN method which slightly outperforms the state-of-art KSG method in the paper.

The applications of these methods such as MIMO channel systems, quadrature amplitude modulation and feature selection were also discussed.

This project is supervised by Dr. Keith Briggs and supported by BT Wireless Research. (Jun. - Oct. 2018)