Department of Civil and Environmental Engineering (CEE)

1. Optimising large-scale flood defence management in response to evolving climate scenarios
   As climate change intensifies, the impact of rainfall variation on flood defence assets becomes increasingly severe, requiring accurate predictions with uncertainty quantification and adaptive asset management under uncertain scenarios. This PhD project aims to develop a rigorous mathematical framework for optimizing the maintenance and performance metrics of existing flood defences to extend their lifespan in response to evolving climate conditions.

   The project will focus on the application of Probabilistic Graphical Models (PGMs) for data assimilation, health monitoring, prediction, planning, and optimization. PGMs will be trained to predict key climate-related variables, such as rainfall and evapotranspiration, over the next 100 years. These models will incorporate both real-world spatial-temporal data and synthetic data generated by Finite Element models.
   The resulting framework will facilitate the analysis of life-extension measures for flood defence assets, allowing for the development of optimal maintenance strategies in the face of uncertain climate scenarios, including rare and extreme events (black swan events). This project provides a unique opportunity to contribute to both the mathematical and environmental sciences by addressing critical challenges in climate resilience and infrastructure management.

   This project will be carried out in partnership with the Environment Agency (EA), the national body responsible for maintaining England’s extensive flood defences. Leveraging critical data from the EA, this project will harness advanced analytical tools to enhance the precision and effectiveness of decision-making processes for key stakeholders.
   
   

2. Real-time traffic emissions monitoring for climate change mitigation
   This project aims to develop an integrated system for monitoring and predicting network-wide traffic emissions, combining data-driven learning models and traffic simulation. The system will feature two key components: a prediction model that forecasts emissions trends based on historical data and Macroscopic Fundamental Diagram (MFD)-based traffic dynamics, and a monitoring model that implements perimeter control to minimize both total travel time and emissions. The project will investigate the trade-offs in emissions estimation across different scales, develop a learning-based emissions prediction model, and evaluate system performance based on sensor data quality and spatial distribution. Using the London metropolitan area as a testbed, the project seeks to provide real-time emissions monitoring and control, offering critical insights for urban climate change mitigation policies, particularly in low-emission zone development. This interdisciplinary project will combine expertise in traffic modelling, environmental science, mathematical optimization, and control theory.
   
   

3. Data-assimilation for Lagrangian atmospheric dispersion models
   The idea behind this project is to incorporate data-assimilation methods to the Met Office atmospheric dispersion model NAME, which is – among other applications – used for operational ash predictions above the Atlantic and Western Europe. NAME is a Lagrangian dispersion model, implying that standard data assimilation techniques are not appropriate. We will use LES to generate a scalar field from a point source and the associated flow field. We will partition this data into data to be assimilated and ‘independent observations’. We will use a Lagrangian random walk model such as NAME to generate a parallel plume that we will want to adjust to fit the observations using the first data set mentioned above. This will be done using nudging or particle filtering or some combination. Continuous nudging of the scalar field would prevent the model plume simply returning to its previous position while conserving mass and maintaining continuity of the flow field. Having in mind volcanoes, the NAME source will be a 1d vertical line source (with a known height) but we may want to investigate a surface source (we are also interested in such problems eg release of radiological species). We will adjust how much of the data will be used for assimilation and how much for independent observations bearing in mind that real observations of plumes are typically quite sparse (in both time and space; bearing in mind too that the plume itself may occupy only a very limited part of the domain especially close to the source).
   
   

4. Understanding the socioeconomic implications of resource emergencies and associated mitigation policies using Bayesian material flow analysis
   This PhD project will focus on improving the capability of Bayesian material flow analysis methodology to include multi-regional systems and energy stocks and flows (by incorporating energy balances). This will include application of statistics and scientific programming in our
   existing Python code.
   The improved methodology and code will be applied to analyse the supply/demand balance of energy materials in UK and its major trading partners. We plan to focus on the current ‘energy crisis’ and understand the landscape of energy material supply scenarios available to the UK and how these marry up to its demand. This will include the major energy production sites (and their processing steps) that supply (refined) energy materials to the UK.
   
   This will require the following objectives to be met:
   1. Development of datasets describing the material and energy compositions of products and production/waste treatment/recycling process inputs and outputs
   2. Improvement of our Python code (on our Imperial-hosted github repository) so it can ingest both material and energy data, and splice its outputs by region (e.g. UK), material
   or energy cycle, and product (or product category, e.g. electricity generation).
   3. We expect that these advancements will be demonstrated by modelling different competing technology options within the same product category, e.g. different energy sources for electricity generation, to understand their resource implications.
   Dissemination of these research outcomes to key stakeholders such as policymakers will also be key.
   
   

Mathematics Department 

1. Medium-term modelling of meteorological variables and electricity prices using (multivariate) trawl processes and ambit fields 
   Due to climate change and the growing share of renewable energy production, there is a strong and increasing link between electricity prices and meteorological variables, as weather conditions directly influence energy generation from sources like wind and solar. This project aims to develop a new stochastic model based on trawl processes or ambit fields that captures these dynamics over a medium-term time horizon (5-10 years), allowing for simulation studies to better understand and forecast fluctuations in supply and demand. By modelling the inherent volatility in renewable energy generation, the project will help optimise the balance between energy supply and demand, enhancing grid stability and financial planning in an increasingly variable energy landscape.
   Project Partner: EDF
   
   
2. Hydrodynamics and motility of marine larvae
   Many animals living in our oceans, including corals, spend the early part of their lives in a larval state before developing into their more recognisable adult form. One advantage of this, and this is especially true for corals, is that the simple, often microscopic larval state allows for effective spreading and dispersal of these animals by ocean currents, allowing them to reach and populate new environments. The purpose of this project is to understand larva motility, both how they are able to propel themselves using arrays of slender appendages called cilia, but also how they interact and move in external flows. The project aims to combine theoretical and numerical techniques from fluid mechanics with experimental techniques from biophysics to track and measure larval trajectories. The project is based on a collaboration between Imperial College London and the Living Systems Institute at the University of Exeter.
   Project Partner: University of Exeter
   
   
3. Dynamical measures of uncertainty in neural networks with application to climate dynamics
   
   Neural networks have become a predominant modelling paradigm in many applications, including climate dynamics [1,2]. Standard neural network models do not capture measures of uncertainty, which is problematic since neural networks have been shown to behave sensitively with respect to changes in input data [3]. Traditional approaches to quantify uncertainty use statistical methods. In this project, we propose to use dynamical systems quantities such as (finite-time) Lyapunov exponents to understand sensitivity with respect to inputs and parameters. We aim to collaborate with Potsdam Institute for Climate Impact Research (PIK), to apply this to network and machine-learning-based prediction of extreme events [4].
   [1] Guo, Q., He, Z. & Wang, Z. Monthly climate prediction using deep convolutional neural network and long short-term memory. Sci Rep 14, 17748 (2024). https://doi.org/10.1038/s41598-024-68906-6
   [2] Nauck, C., Lindner, M., Schürholt, K., & Hellmann, F. Toward dynamic stability assessment of power grid topologies using graph neural networks, Chaos 33 (2023).
   [3] I. J. Goodfellow, J. Shlens, C. Szegedy, Explaining and Harnessing Adversarial Examples. ICLR 2015
   [4] PIK Working Group Network and Machine-Learning-Based Prediction of Extreme Events https://www.pik-potsdam.de/en/institute/departments/complexity-science/research/network-and-machine-learning-based-prediction-of-extreme-events.
   Project Partner: PIK (Potsdam Institute for Climate Impact Research)
    
4. Statistical Inference for Pairs of Paths of Stochastic Processes
   
   We will use tools from stochastic analysis to motivate, build, and analyze tests of independence, or dependence, of pairs of paths ofstochastic processes, both in discrete and in continuous time, including asymptotic exactness and power. The basic question is to test the null hypothesis of independence for two sequences of time-dependent observations. We will pay special attention to the starkly different asymptotic properties of test statistics, for largely stationary processes, like mean-reverting ones, or for highly non-stationary ones, such as random
   walks and Wiener processes.
   Project Partner: Royal Society
    
5. Data Assimilation in Misspecified Models with Applications to Geophysical Models
   This project will consider the problem of data assimilation and stochastic filtering when the assumed physical models are imperfect which is the case in the real world. It will explore statistical theory and practical mitigation of model misspecification (or model mismatch). The produced insights and algorithmic innovation will be tested on geophysical models arising in ocean modelling.
   
   
6. Statistics for Stochastic transport equations 

   Stochastic transport equations robustify deterministic PDEs by adding random forcing terms to account for model errors. While such equations are essential for describing the complex dynamics in climate data, there are only few methods for parameter estimation. The application of classical methods developed for deterministic equations leads to wrong conclusions.

   In this project we want to build upon recent ideas from statistics for stochastic PDEs to develop mathematically rigorous and statistically optimal estimators. Ultimately, these estimators will be implemented by researchers and engineers to validate models based on stochastic transport equations on real data. Moreover, our results will provide ways for quantifying the uncertainty in the estimates, which is crucial for downstream processing tasks.

   The intersection of statistics and PDEs has attracted tremendous interest from many researchers in recent years. Combining theoretical tools from different mathematical areas opens up exciting opportunities for the PhD candidate to contribute to a quickly growing research area, and to collaborate with research groups worldwide.

   Besides proving mathematical theorems, there will be opportunities for exploring numerical simulations and for applying the developed methods to real data within the CDT but also, for example, in collaboration with the ERC project “Stochastic transport in upper ocean dynamics” which is partly hosted at Imperial College

    

7. Turbulence in stratified flows
   This project will tackle the stochastic parameterisation of mixing processes and tracer transport in density-stratified flows. Computational, experimental and theoretical approaches can be developed with applications to ocean dynamics and the built environment.
   
   
8. Bayesian causal inference
   Causal inference aims to understand the challenging question of ‘what would happen’ in different scenarios, thus helping decision-makers make reliable choices. Bayesian methods are increasingly used for such tasks, especially for uncertainty quantification. This project will investigate such methods in theory and practice, seeking to improve their reliability and performance.
   
   
9. Next generation numerics for ocean modelling
   This project will take the first steps towards a new ocean model based upon innovative numerical methods that allow the use of unstructured meshes that can resolve coastlines, topography and have spatially varying resolution to focus on specific regions of interest (to study e.g. global climate impacts on regional processes). These numerical methods (based on compatible finite element methods) have already been introduced into the next generation Met Office forecasting system (LFRic), and in this project we take on the challenge of designing an efficient, accurate, scalable ocean modelling system using them.
   
   
10. Reconciling the Eulerian and Lagrangian Models for Turbulent Transport
    The underlying idea is both fundamental and highly practical: to close the profound gap between the existing approaches for characterizing turbulent transport, which is ubiquitous in geophysical fluids and climate-type models. One approach is based on observing turbulence at fixed spatial locations, and the other one follows trajectories of elementary fluid particles. The former approach is more suitable for modelling purposes, whereas the latter approach is more suitable for experimental observations of the turbulence. We don’t fully understand the differences between these approaches, and we don’t yet know how to translate one into the other.
    
    
11. Time varying parameter models: theory and applications
    The project is concerned with the wide area of models for time-varying parameters, that find applications in climate econometrics and environmental risk management:
    i) Robust models and filters for time-varying location parameters
    ii) Score-driven filters, quasi score-driven filters and their properties
    iii) Dynamic models for multiple quantiles.