Our series of departmental seminars and colloquia will be of interest to all academic staff, postdoctoral researchers and PhD students. Contact Abhishek Pal Majumder for further information.
20 May 2025
13:00 to 14:00 Maths113
Speaker: Dr. Reetha Thomas (Indian Institute of Management, Bangalore)
Title: PIGNN-GPR: A Hybrid Machine Learning Framework for Spatio-Temporal PM2.5 Prediction
Abstract: Accurate prediction of pollutant concentration is critical for both environmental sustainability and public health. While numerous studies have integrated the physics-based and data-driven approaches in deep learning for air quality forecasting, neural networks still face challenges with interpretability and explainability due to their hidden nature. Among the various air pollutants, PM2.5 stands out as one of the most hazardous, making its precise monitoring and forecasting a complex task. In this study, we present an innovative and efficient approach for forecasting hourly PM2.5 concentrations using a hybrid Physics-Informed Graph Neural Network– Gaussian Process Regression (PIGNN-GPR) model. The physics-informed component integrates fundamental principles from the reaction-diffusion-advection equation, ensuring adherence to physical constraints, while the Graph Neural Network captures complex spatial dependencies by leveraging wind speed and wind direction across multiple locations. To improve forecast reliability, we incorporate Gaussian Process Regression to refine the PM2.5 predictions from the Physics-Informed Graph Neural Network, offering confidence intervals that quantify prediction uncertainty. Additionally, we apply the Inverse Distance Weighting spatial interpolation method to estimate PM2.5 concentrations at unmonitored sites. For better model interpretability, we use SHapley Additive exPlanations to assess the contribution of key input variables, latitude, longitude, wind speed, and wind direction, to predictions. The model is evaluated using real-world air quality data from multiple locations in the Delhi region, India. This hybrid PIGNN-GPR framework marks a significant step forward in improving both the explainability and accuracy of air quality predictions, providing a powerful tool for environmental monitoring and decision making. (Joint work with Soudeep Deb)
Math-Stat Colloquium:
23 April 2025
15:00 to 16:00 JJ Thomson, Slingo Lecture Theatre
Speaker: (University of Bristol)
Title: Random matrices and number theory
Abstract: The purpose of this lecture will be to review some of the classical connections between random matrix theory and number theory, specifically the modelling of the value distribution of the Riemann zeta function near the critical line, and to explain some recent results concerning complex-valued joint moments of the Riemann zeta function and their evaluation in terms of . The talk is intended for a broad maths audience, including graduate students, and does not require any prerequisites. Towards the end we will touch upon some ongoing joint work of the speaker with Fei Wei (Sussex).
7 April 2025
14:00 to 15:00 Maths314
Speaker: Prof. Tao Tang (President of Nanfang College, Guangzhou, China)
Title: Deep adaptive sampling for numerical PDEs
Abstract: In this talk, we shall propose a deep adaptive sampling method for solving PDEs where deep neural networks are utilized to approximate the solutions. In particular, we propose the failure informed PINNs (FI-PINNs), which can adaptively refine the training set with the goal of reducing the failure probability. Compared to the neural network approximation obtained with uniformly distributed collocation points, the developed algorithms can significantly improve the accuracy, especially for low regularity and high-dimensional problems.
5 March 2025
16:00 to 17:00 Maths314
Speaker: Sandipan Roy (University of Bath)
Title: Multi-response linear regression estimation based on low-rank pre-smoothing
Abstract: Pre-smoothing is a technique aimed at increasing the signal-to-noise ratio in data to improve subsequent estimation and model selection in regression problems. However, pre-smoothing has thus far been limited to the univariate response regression setting. Motivated by the widespread interest in multi-response regression analysis in many scientific applications, a technique for data pre-smoothing is proposed in this setting based on low-rank approximation. Theoretical results are established on the performance of the proposed methodology and quantify its benefit empirically in a number of simulated experiments. The proposed low-rank pre-smoothing technique is also demonstrated on real data arising from the environmental sciences.
26 February 2025
14:00 to 15:00 Maths314
Speaker: Sylvain Rubenthaler
Title: A central limit theorem for conservative fragmentation chains
Abstract: We are interested in a fragmentation process. We observe fragments that are frozen when their sizes fall below $\varepsilon (\varepsilon>0)$. It is known (Bertoin and Marinez 2005) that the empirical measure of these fragments converges in law, under some renormalization. In (Hoffman and Krell 2011), the authors establish a bound for the rate of convergence. I proved a central-limit theorem, under some assumptions, providing an exact rate of convergence. In the talk, I will present the tools used in the proof : fragmentation, tagged fragments, elements of renewal theory, as well as my favorite tricks for obtaining central-limit results.
16 October 2024
14:30 to 15:30 Maths 113
Speaker: Dr. Mona Azadkia (LSE)
Title: A simple measure of conditional dependence
Abstract: We propose a coefficient of conditional dependence between two random variables Y and Z given a set of other variables X1,…,Xp, based on an i.i.d. sample. The coefficient has a long list of desirable properties, the most important of which is that under absolutely no distributional assumptions, it converges to a limit in [0,1], where the limit is 0 if and only if Y and Z are conditionally independent, given X1,…,Xp, and is 1 if and only if Y is equal to a measurable function of Z given X1,…,Xp. Moreover, it has a natural interpretation as a nonlinear generalization of the familiar partial R2 statistic for measuring conditional dependence by regression. Using this statistic, we devise a new variable selection algorithm called Feature Ordering by Conditional Independence (FOCI), which is model-free, has no tuning parameters, and is provably consistent under sparsity assumptions. A number of applications to synthetic and real datasets are worked out.
7 October 2024
13:00 to 14:00 Maths 100
Speaker: Reyk Boerner
Chair: Dr. Chris Daw
Title: Edge state of metastable ocean currents and its role for climate tipping
Abstract: Earth's climate system is multistable, implying the risk of abrupt transitions between competing climatic states under random fluctuations or parametric forcing (e.g. increasing greenhouse gas concentrations). There is growing concern that ongoing climate change could trigger a rapid and potentially irreversible shutdown of the Atlantic Meridional Overturning Circulation (AMOC), a major ocean current that transports vast amounts of heat northward and is thus responsible for the UK's mild climate. However, the likelihood and mechanism of such a critical transition, or 'tipping', remain highly uncertain. In this talk, we explore the predictability and pathways of tipping in climate models through the study of edge states, or Melancholia states. These unstable invariant sets, saddles embedded in the basin boundary between different attractors, often act as gateways for transitions where trajectories can sometimes spend long transient periods. Using first a conceptual and then a more complex climate model, I will illustrate a) how edge states can be computed numerically, b) what their dynamical and physical properties tell us about tipping risk, and c) what role they might play in future climate change. From a dynamical systems perspective, the results are directly transferable to other metastable systems of interest in applied mathematics.
1 October 2024
Eviatar's Inaugural Talk (Joint Met-Mathstat Seminar)
13:00 to 14:00 Brian Hoskins GU01 lecture theatre
Speaker: Dr. Eviatar Bach
Title: Machine learning for data assimilation and forecasting
Abstract: