Mathematics and Statistics for Modelling and Prediction (MaP) projects
Please identify three projects of interest from this selection:
Bootstrap methods for hypothesis testing in non-linear models
Dr Simon Preston and Prof Andrew Wood
Hypothesis testing is an important way to draw scientific conclusions from experimental data. However, models relevant in industrial settings (for example models that characterise manufacturing processes) are almost invariably non-linear in the model parameters, and hypotheses of interest often involve parameters that lie on the boundary of the parameter space; these are challenging to standard (asymptotic) approaches to hypothesis testing. We will develop methods based on the "bootstrap" -- a powerful approach in computational statistics that involves computing null distributions using simulated data -- to address hypothesis testing in challenging non-linear settings.
Controlling bacterial biofilm formation with shape
Man-made materials play a major role in healthcare including extensive use as implants, which have an unfortunately significant rates of infection. The rise of antimicrobial resistance makes this problem pressing, in that the infections arising are often untreatable by antibiotics and therefore often fatal. Modification of the surface texture or topography has been found to control bacterial surface colonisation-we do not know why. This project will access a near infinite range of shapes formed at planar surfaces using 2 photon printing of polymers from a range of monomers. Through mining if this data, we aim to build a better understanding of the relationship between bacterial colonisation and shape that will enable better materials to be designed from first principles for use in healthcare. The student will develop and apply ideas and techniques from a variety of areas, including statistical shape analysis and machine learning, to address the questions of interest.
This project will be jointly supervised by Prof Morgan Alexander in the School of Pharmacy and Prof Ricky Wildman in the Faculty of Engineering.
Developing machine learning and statistical techniques to analyse large ground motion datasets to determine the changes in the state of global peatlands
Peatlands account for a third of all soil carbon and in good condition provides a clean water supply, flood control and biodiversity. To successfully manage this natural resource we need to understand its condition and response to change. To achieve this a new satellite imaging technique has been developed that uses the surface motion of the peat to monitor changes in peat condition over very large areas. Using the characteristics of surface motion time series this method has the capacity to determine the changing condition of peatland in space and time. The peatlands of interest are divided up into a large number of pixels of size 100 x 100 square metres, and each pixel is observed by the satellite every 6 days, resulting in a time series for each pixel. The challenge for this PhD is to develop statistical and machine learning techniques (e.g. high-dimensional time series modelling and classification) that can efficiently quantify the spatial and temporal changes in the condition of the peat from the huge data sets derived from the satellite data.
This project will be jointly supervised by Professor David Large in the Faculty of Engineering.
Bayesian inversion in resin transfer moulding
Dr Marco Iglesias, Prof Michael Tretyakov
This project will be based at the University of Nottingham in the School of Mathematical Sciences and the Faculty of Engineering.
The use of fibre-reinforced composite materials in aerospace and automotive industries and other areas has seen a significant growth over the last two decades. One of the main manufacturing processes for producing advanced composites is resin transfer moulding (RTM). The crucial stage of RTM is injection of resin into the mould cavity to fill empty spaces between fibres; the corresponding process is described by an elliptic PDE with moving boundaries. Imperfections of the preform result in uncertainty of its permeability, which can lead to defects in the final product. Consequently, uncertainty quantification (UQ) of composites’ properties is essential for optimal RTM. One of important UQ problems is quantification of the uncertain permeability. The objectives of this PhD project include (i) to construct, justify and test efficient algorithms for the Bayesian inverse problem within the moving boundary setting and (ii) to apply the algorithms to real data from composite laboratory experiments.
Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Mathematics, preferably at MMath/MSc level (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered). We are expecting that the successful applicant has a background in PDEs, Probability and Statistics and has exceptional computational skills.
For any enquiries please email: Marco.Iglesias@nottingham.ac.uk or Michael.Tretyakov@nottingham.ac.uk or Mikhail.Matveev@nottingham.ac.uk.
This project will be jointly supervised by Dr Mikhail Matveev in the Faculty of Engineering.
Electromagnetic compatibility in complex environments – predicting the propagation of electromagnetic waves using wave-chaos theory
Dr Stephen Creagh, Dr Gabriele Gradoni and Prof Gregor Tanner
Electromagnetic systems and devices are often complicated, irregular in their geometry and heterogeneous in their electrical characteristics. Such a system could be a PC, a mobile phone, or even an airplane cockpit. The prediction of the energy distribution becomes hard when using traditional analytical and numerical tools, especially if the wavelength is small compared to the size of the structure. Statistical methods are often more appropriate to describing the physical process under investigation in such cases. Appropriately chosen, such methods can lead to surprisingly simple and physically understandable characterization of the problem, which can be used to exploit complexity and turn collective behaviour into beneficial engineering technology.
This PhD project uses a phase-space representation of wave fields, the so-called Wigner distribution function (WDF), to unveiled transport properties of fields using tools of dynamical system theory. An exact evolution operator for the transport of these Wigner functions can be derived, and approximation schemes are obtained by using ray families that include reflections from irregular boundaries. The project will explore the possibility of linking the WDF operator to existing semiclassical approximations of quantum mechanics, used to transport densities of quantum particles. The challenge lies in constructing a phase space picture of those operators through the WDF before including the source operator.
Dr Gabriele Gradoni is also based at George Green Institute of Electromagnetics Research in the Faculty of Engineering.
Energy storage bed dynamics –the ever-expanding magnesium bed conundrum
Prof John King
In order to facilitate high penetration of renewable energy in to the grid, energy storage is needed to better manage the supply and demand for the grid. Hydrogen offers a high energy density solution and, rather than storing the hydrogen as a gas at high pressures, solid state storage of hydrogen in a metal like magnesium offers a low pressure and low cost technology. The hydrogenation of magnesium is very exothermic (74.5 kJ mol-1) and the material is also being investigated as a thermal energy store (i.e. using the exotherm of hydrogenation to liberate the stored thermal energy back as heat at 400°C).
A fear was that cycling a magnesium bed at high temperatures would lead to sintering and a loss of void space. However, the startling result was that the powdered magnesium bed when cycled at temperatures of 350-400°C, rather than losing porosity, gained porosity. The form of the bed had changed from a loose powder to a metal porous plug which had swelled in dimensions to fill the available head space in the vessel. Further cycling at temperature below 350°C results in the bed resorting back to a more densely packed loose powder.
The intriguing question is to uncover the fundamental mechanism(s) behind this process and to develop a predicative model based on the physical and chemical processes occurring. For the application, understanding these processes will enable optimisation of the porous structure for heat and mass flow; moreover, there is also concern the expanding bed may exert significant stress on the wall of the storage vessel eventually leading to failure of the vessel.
This challenging research project will develop new mathematical models based on the chemical and physical processes occurring in order to develop a model that simulates the expanding porous bed phenomenon. Some of these processes include: nucleation, growth of the metal hydride phase, crystal lattice expansion leading to defect formation, decrepitation, atomic diffusion and surface energy minimisation, annealing. The models developed will thus need to encompass a wide range of physical phenomena; the focus will be on partial-differential-equation/moving-boundary formulations, building on the established sintering literature but, for the reasons described above (specifically, to generate increased, rather than decreased, porosity), of necessity raising significant additional challenges. The project will accordingly equip the student with an unusually wide experience of experimental and modelling questions and of mathematical techniques, as applied in a context with clear energy and sustainability implications.
This project will be jointly supervised by Prof Gavin Walker in the Faculty of Engineering and Dr Richard Wheatley in the School of Chemistry.
Form, function and utility in small community energy networks
Dr Etienne Farcot and Dr Reuben O'Dea
This is a unique and exciting opportunity to undertake research that spans across the disciplines of energy engineering and mathematical sciences. Successful applicants will be joining a strong interdisciplinary team from academia and industry who are currently working on the delivery of the Energy Research Accelerator (ERA) Community Energy System (CES) demonstrator at the 15 acre Trent Basin site in Nottingham. The project will investigate the energy challenges and complexity science issues associated with heat and electrical power generation, storage and use arising from the connections between micro-generation output, grid/heat loads, weather, and energy/power demands (including occupant behavior) combined with variable load energy storage devices in order to provide energy stability, a reduction of cost and associated carbon emissions from fossil fuel use. The PhD research will develop new multi-vector CES models that utilise ‘big data’ obtained from a dedicated onsite monitoring platform at the housing development applied to a heterogeneous network of users. The work will ultimately help inform the design, implementation and operation of local community energy schemes in the UK. Applicants should have a Bachelor Science or Engineering (at least 2i) and/or a Master of Science or Engineering in Mathematical Sciences, Engineering or Energy related disciplines.
This project will be jointly supervised by Prof Mark Gillott and Dr Parham Mirzaei Ahrnjani in the School of Architecture & Built Environment.
Geometric statistical methods for curves and surfaces with applications in medical imaging
Dr Karthik Bharath
What is the average shape of a brain tumour in a cohort of patients? How might this evolve over time? Is it possible to associate the shape and its evolution with certain genetic and clinical characteristics of a patient? Advent of high-resolution imaging technologies have enabled meaningful answers to such questions based on continuous representations of tumours and organs as parametric curves and surfaces. These data objects typically reside on manifolds equipped with non-trivial geometries and symmetries (invariances). The project will focus on developing statistical methods for such data using tools from stochastic processes, differential geometry and group theory.
Inference for noisy ordinary differential equation models with application to "rust" modelling in sugar beet
Dr Theodore Kypraios and Prof Andrew Wood
There are many areas of science and technology where ordinary differential equations provide suitable models but the complication is that empirical observations contain measurement errors. The challenge is such situations is to develop inference techniques, such as maximum likelihood or Bayesian approaches, for "noisy" ordinary differential equation models. Ideas and techniques from the topic Uncertainty Quantification are relevant here. Various approaches will be developed and these will be applied to the modelling of "rust" in Sugar Beet, a form of disease in Sugar Beet which adversely affects growth and therefore yield. The methodology developed will be applied to a Sugar Beet dataset. Applications to other datasets from plant biology will be considered too.
This project will be jointly supervised by Prof Neil Crout and Prof Debbie Sparkes in the School of Biosciences.
Linking epidemiological and genomic data for infectious diseases
Prof Philip O'Neill and Dr Theodore Kypraios
In the past few years, advances in sequencing technology and the reduction in associated costs have enabled scientists to obtain highly detailed genomic data on disease-causing pathogens on a scale never seen before. In addition to the inherent phylogenetic information contained in such data, combining genomic data with traditional epidemiological data (such as time series of case incidence) also provides an opportunity to perform microbial source attribution, i.e. determining the actual transmission pathway of the pathogen through a population.
These advances have seen a corresponding surge of activity in the modelling and statistical analysis community, so that now a number of methods and associated computer packages exist to carry out source-attribution, i.e. estimating who-infected-whom in a particular outbreak. All the methods have their own limitations; a very common issue is that the models used to perform estimation are conditional upon the observed data, which can create estimation biases and lead to misleading results. In contrast, the method developed by Worby, Kypraios and O'Neill involves a model that can explain how the data arose, overcoming such problems. This project is concerned with developing this approach to both (i) extend the idea to more complex model settings, relaxing certain technical assumptions and (ii) improve computational efficiency. A highly-detailed data set on MRSA provided by collaborators at Guy's and St Thomas' hospital trust, London, provides one opportunity for applying such methods.
Relevant PublicationsWorby, C. J., O'Neill, P. D., Kypraios, T., Robotham, J. V., De Angelis, D., Cartwright, E. J. P., Peacock, S. J. and Cooper, B. S. (2016) Reconstructing transmission trees for communicable diseases using densely sampled genetic data. Annals of Applied Statistics 10(1), 395-417.
Machine learning for first-principles calculation of physical properties
Prof Richard Graham
The physical properties of all substances are determined by the interactions between the molecules that make up the substance. The energy surface corresponding to these interactions can be calculated from first-principles, in theory allowing physical properties to be derived ab-initio from a molecular simulation; that is by theory alone and without the need for any experiments. Recently we have focussed on applying these techniques to model carbon dioxide properties, such as density and phase separation, for applications in Carbon Capture and Storage. However, there is enormous potential to exploit this approach in a huge range of applications. A significant barrier is the computational cost of calculating the energy surface quickly and repeatedly, as a simulation requires. In collaboration with the School of Chemistry we have recently developed a machine-learning technique that, by using a small number of precomputed ab-initio calculations as training data, can efficiently calculate the entire energy surface.
This project will be jointly supervised by Dr Richard Wheatley in the School of Chemistry.
Mathematical Modelling of Lubrication in Grinding Wheels
Prof John Billingham
Grinding wheels are used to machine surfaces in many different manufacturing processes. Two key components of the process are: the fluid lubricant, which is sprayed into the point where the wheel meets the workpiece; the surface of the grinding wheel, which may be either random or patterned. Between them, the lubricant and the grinding wheel surface must fulfil the, often competing, requirements to remove material from the workpiece in a controlled manner, remove cuttings from between the wheel and the workpiece, and cool the wheel and workpiece. This aggressive engineering environment is hard to investigate experimentally, and mathematical modelling is in its infancy, so trial and error is the usual means of improving the process. Recent work has considered the flow outside the grinding wheel, , and a current PhD student is developing a basic model for the lubrication flow.
There are many possible extensions and uses of the simple models we have at the moment that can form the basis of a project, including: optimization of grinding surface patterns to promote even flow and cuttings removal; the use of homogenization to investigate periodic, slowly-varying periodic and random grinding surfaces; the use of uncertainty quantification techniques to characterise random grinding surfaces; inclusion of heat and cuttings transport into the model. **
Relevant Publications Textured grinding wheels: A review, Li, H.N and Axinte, D.A. 2016, Int. J. Machine Tools and Manuf.
Mathematical Modelling of Powder Snow Avalanches
Powder snow avalanches are fluidized suspensions of snow that can flow destructively in many parts of the world. Recent work, , has shown that a key mechanism that allows these avalanches to grow is the ingestion of fresh snow due to high pressure gradients at the head of the flow. A recent study of a simplified model of this process, , which treats the flow as inviscid and irrotational, captures several key features of these avalanches.
There are many possible extensions of this work that could form the basis of this project. For example, using a level set method to simulate the flow beyond the onset of Kelvin-Helmholz instability; including the effect of variable topography; extending the model to three dimensions to investigate lateral instability. Uncertainty quantification can be used in the context of this model to investigate the effect of, for example, uncertainties in the exact topography of the underlying snow.
 Role of pore pressure gradients in sustaining frontal particle entrainment in eruption currents: The case of powder snow avalanches, Louge, M. Y., Carroll, C. S. & Turnbull, B. 2011, Journal of Geophysical Research: Earth Surface 116 (F4).
 A dam-break driven by a moving source: a simple model for a powder snow avalanche, Billingham, J., submitted to J. Fluid Mech.
Mechanical modelling of the stability of Earth's peatland carbon reservoirs
The project involves the development of mechanical models of peatland growth and restoration. Peat is a soft multiphase (solid, liquid, gas) material that stores 1/3 of earth’s terrestrial carbon. Current models combine mass balance and hydrology but none consider the mechanical stability of the peat. This is a huge oversight as the extremely weak multiphase peat body should deform with ease and this deformation must influence gas emissions and long term stability. The project will develop novel numerical models of peat growth and the mechanical response of peat to the changes in loading, mass balance and hydrology. The student will have the opportunity to visit peatlands in the UK and Malaysia and to link their work to geospatial observations.
This project is jointly supervised by Dr David Large in the School of Chemical & Environmental Engineering, Dr Bagus Muljadi in the School of Chemical & Environmental Engineering and Professor Neil Crout in the School of Biosciences.
Modelling flow and crystallisation in polymers
Polymers are very long chain molecules and many of their unique properties depend upon their long chain nature. Like simple fluids many polymer fluids crystallise when cooled. However, the crystallisation process is complicated by the way the constituent chains are connected, leading to a multitude of unexplained phenomena. Furthermore, if a polymer fluid is placed under flow, this strongly affects both the ease with which the polymer crystallises and the arrangement of the polymer chains within the resulting crystal. This project will develop molecular models and simulations for polymer dynamics and phase transitions using a range of analytical, numerical and stochastic techniques, with the ultimate aim of improving our understanding of polymer crystallisation.
Modelling the environmental and genomic interactions in maize under changing climatic conditions
This student will develop mathematical models to understand the sensitivity of maize growth to hydroclimatic change. This project will use data produced by a related PhD project, and previous work, to identify environmental preferences and yield differences between maize varieties. The models will aim to establish the key factors for optimal yield, including agronomic practices, environmental conditions and genotypes. Predictions from the models will subsequently be tested using materials grown in controlled environment (CE) conditions.
The resulting mathematical models will be used to analyse the likelihood of crop success and system stability to small fluctuations in climate, and in water availability. The model can then be used predictively, to investigate the best crop mixtures and field configurations for future climate scenarios.
This project will be jointly supervised by Matt Jones in the School of Geography and Rahul Bhosale in the School of Biosciences with Medina [UADY, Mexico].
Modelling wave propagation in meta-materials: a graph network approach
A meta-material exhibits exotic properties, such as negative refraction, wave cloaking and non-reciprocal response, amongst others. These properties allow one to manipulate the propagation of waves in such a way as to, for example, realise an “invisible cloak”. Constructing meta-materials is not a trivial task, as one needs to judiciously design the material “atom-by-atom” in a periodic or aperiodic fashion using multiple-coupled geometrical and physical material parameters.
The fascinating properties of meta-materials occur at the interface where a continuum model can be used for the periodic structure (limit of large wave length) and the discrete “atomic” limit, where wave interference dominates (limit of small wave length). The aim of the project is to study this critical wavelength region using wave models on graph networks. The PhD project will develop such graph network models to study the dispersion relations of periodic meta-materials. The student will be introduced to the relevant electromagnetics theory and graph network techniques and will study the fundamental dynamics of rays and waves propagating through 1D and 2D meta-material structures modelling electromagnetic meta-surfaces, widely used for the manipulation of electromagnetic wave-front for fast signal processing and which can be realized in the laboratory. At a later stage of the project, the model parameters will be adjusted to mimic properties of meta-materials as they are produced in The Centre for Additive Manufacturing in Nottingham. Those structures are relevant for the next generation of electronics components and for cloaking of 3D objects.
Dr Gabriele Gradoni is also based at George Green Institute of Electromagnetics Research in the Faculty of Engineering.
Molecule comparison using electrostatic fields and 3D shape representation
In computational chemistry it is of great interest to search through libraries of molecules to extract molecules of similar shapes. The 3D shape and electrostatic field of a molecule are key to determining its function. Electrostatic feature maps predict locations of hydrophobic, H-bond acceptor and H-bond donor sites on a molecule from solutions of the Poisson-Boltzmann equation. The project will aim to develop new statistical shape analysis methodology that combines shape information from several conformations of a molecule with electrostatic potentials at different distances from a molecule. Bayesian methods based on Gaussian process models and fast approximations will be explored. Key low dimensional features will be extracted which can then be used to explore new compounds via machine learning methods.
This project will be jointly supervised by Mike Mazanetz of NovaData Solutions.
Object oriented data analysis of networks
Network data is now routinely available from a variety of applications, including in social media, corpus linguistics and neuroimaging. Less common is the study of samples of networks, for example collected over time or at random from a population. The project will take an object oriented data analysis approach, where the first questions of interest are what are the data objects, what space do they lie and how are they represented in feature space. Networks can be compared by using metrics on the space of graph Laplacians, with the Frobenius norm being used most commonly. We will develop statistical methodology using other metrics, and also develop statistical procedures in the resulting manifolds. Motivating applications include large social and financial datasets from developing economies. Such datasets are often very sparse and very noisy, and so the appropriate handling of uncertainty in the analysis of the networks is paramount.
This project will be jointly supervised by James Goulding (N/LAB, Business School).
Opening the black-box: understanding the mechanisms and behaviours of data-driven water resource models
Data-driven models are a class of inductive modelling methods that have emerged as an important category within water resource modelling over the last two decades; especially in areas such as rainfall-runoff modelling; river forecasting; ungauged catchment estimation and estimation of hydrological parameters. Data-driven models differ fundamentally from other modelling approaches because the responsibility for determining the form and strength of relationships between relevant variables, and for integrating these relationships into a functioning model, is handed to computationally-intelligent algorithms rather than a human modeller. This PhD will focus on the derivation, application and interpretation of partial derivatives for a suite of popular data-driven, water resource models so that their ‘black boxes’ are opened up – providing water resource modellers with a better understanding of which data-driven models are best suited for water-resource modelling tasks along with new insights into the process-representation of which they are capable.
This project will be jointly supervised by Nick Mount in the School of Geography.
Quantum tomography for high dimensional systems
Quantum Technology is a fast developing field which aims to harness quantum phenomena such as entanglement and superposition in a broad array of applications ranging from secure communication and faster computation to high precision metrology and imaging.
Building a successful quantum device relies on the ability to prepare quantum systems in specifically designed states, and to accurately manipulate and measure the different components of the device.
Since quantum measurements are intrinsically stochastic, statistical inference plays a key role, enabling the experimenter to interpret the measurement data and validate the functioning of the device.
An important component of the quantum engineering toolbox is quantum tomography: the estimation of unknown quantum states based on random outcomes of measurements performed on identically prepared quantum systems. Although many estimation methods have been explored theoretically and experimentally, there is currently a need for new techniques to deal with inference for high dimensional quantum states.
This PhD project aims to develop efficient methods for computing point estimators and confidence regions for multipartite quantum states. In particular we will be interested in statistical models which take into account prior information about the state, in the form of correlation structure, rank, or symmetry. The project involves both theoretical and computational work; prior knowledge of quantum mechanics is beneficial but is not an absolute requirement. The PhD student with work together with Dr Madalin Guta and Dr Theo Kypraios who have a leading expertise in statistical aspects of quantum theory and have developed a range of computational tools for quantum tomography, see [1,2,3,4]. The project builds on the group's prior work in the field and will benefit from contacts with external collaborations on both theoretical and practical aspects.
 M. Guta, T. Kypraios and I. Dryden, Rank based model selection for multiple ions quantum tomography, New Journal of Physics 14 105002 (2012).
 C. Butucea, M. Guta, T. Kypraios, Spectral thresholding quantum tomography for low rank states, New Journal of Physics 17 113050 (2015).
 A. Acharya, T. Kypraios, and M. Guta. Statistically efficient tomography of low rank states with incomplete measurements, New Journal of Physics, 18 043018 (2016).
 M. Guta, J. Kahn, R. Kueng, J. Tropp, Fast state tomography with optimal error bounds, arXiv:1809.11162.
This broad project is devoted to the construction of new efficient numerical methods for stochastic differential equations and stochastic numerical analysis of properties of the methods. Depending on the interest of the student, it can be focused, e.g. on numerics for stochastic partial differential equations, on methods which are efficient for computing ergodic limits, on stochastic geometric integration, etc.
We require an enthusiastic graduate with a 1st class degree in Mathematics, preferably at MMath/MSc level (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered). We are expecting that the successful applicant has a very good background in Probability and has good computational skills.
Milstein, G.N. and Tretyakov, M.V. (2004) Stochastic Numerics for Mathematical Physics. Series: Scientific Computation, Springer Web-page http://www.maths.nott.ac.uk/personal/pmzmt.
Text-Analytics for Major Event Detection
Social media such as microblogs (eg Twitter) and networking platforms (eg Facebook) are increasingly used for users to communicate breaking news and connect to each other anytime, from anywhere. Social media web sites contain various types of services and therefore different formats of data, including text, image, video etc are created. Among the various formats of data exchanged in social media, text plays a important role. The volume of textual data in social media is increasing exponentially, thus providing us with numerous opportunities for detecting the occurrence of an event in real-time (eg earthquakes, tsunami).
This project is concerned with developing computational statistics and machine learning methodology for text-analytics. In particular we are interested in detecting the occurrence of major events (eg. major train delay) when in the data (for example, tweets) there is often information about minor events too (eg someone tweeting/complaining because their train was 3 minutes late).
Thermal characterisation of the building fabric under uncertainty
The built environment is responsible for 45% of all UK carbon emissions with approximately 27% attributed to the domestic sector and 18% to non-domestic buildings. Reducing the energy demand in the built-environment is thus essential for the UK decarbonisation policy which legislates an 80% reduction of its 1990 greenhouse gas emissions by 2050. The existing housing stock is a primary target for reductions of the energy demand since it is estimated that up to 85% of existing buildings will be standing by 2050. An accurate characterisation of the thermal performance of the existing housing stock in the UK is thus needed to inform large-scale cost-effective policies for retrofit intervention that can effectively contribute towards achieving those decarbonisation targets. Unfortunately, existing approaches for the in-situ characterisation of the building fabric (including ISO standards) cannot accurately characterise the thermal performance of buildings in the presence of thermal bridge effects that arise from heterogeneities, irregularities and/or abrupt changes and discontinuities in the thermophysical properties of the building fabric. In particular, these approaches cannot capture thermal bridge effects due to fabric degradation and moisture condensation which are likely to be found in existing dwellings.
This challenging research will develop novel thermal imaging algorithms capable of characterising, with an accurate measure of uncertainty, the thermal performance of the building fabric in the presence of a general class of thermal bridge effects. This project will build upon state-of-the-art Bayesian algorithms for inverse problems that have been successfully applied for tomographic inversions in the context of groundwater flow , electrical impedance tomography , resin transfer moulding , and the characterisation of thermophysical properties of walls [3,4]. The techniques developed in this project will be validated with real experiments. Although highly ambitious, this proposed research has enormous potential to revolutionise current approaches for in-situ characterisation of the thermal performance of buildings thereby enhancing the predictive capabilities of existing housing stock models.
 Iglesias, M.A. 2016. “A Regularizing Iterative Ensemble Kalman Method for PDE-Constrained Inverse Problems.” Inverse Problems 32 (2):025002. http://stacks.iop.org/0266-5611/32/i=2/a=025002.
 Iglesias, M.A., M. Park, and M. Tretyakov. 2017. “Bayesian Inverse Problems in Resin Transfer Molding.” Submitted Preprint available at: https://arxiv.org/abs/1707.03575.
 Iglesias, M.A., Sawlan Z., Scavino M., Tempone R., and C. Wood. 2018. “Bayesian Inferences of the Thermal Properties of a Wall Using Temperature and Heat Flux Measurements.” International Journal of Heat and Mass Transfer 116 (Supplement C):417–31.
 De Simon,L. M. A. Iglesias, B. Jones and C. Wood. 2017. “Quantifying Uncertainty in Thermal Properties of Walls by Means of Bayesian Inversion.” Submitted Preprint available at: https://arxiv.org/abs/1710.02976.
This project will be jointly supervised by Dr Yupeng Wu in the Faculty of Engineering.
How to apply
To apply for the programme for 2019 entry please:
- identify three projects of interest,
- apply online using the University of Nottingham application page,
- in the personal statement section indicate that you are applying to the 'Mathematics and Statistics for Modelling and Prediction' programme,
- make sure to include a ranked list of your three preferred projects, together with a CV of no more than two pages.
For more information about a particular project please contact the named supervisor. For general enquiries about the programme, contact the academic lead Professor Andrew Wood.