Various Updates

phd_projects/entries/akyildiz.qmd

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+---
+title: "PDE-driven/data-driven hybrid modelling for data assimilation"
+institution: "Imperial"
+department: "Mathematics"
+author: "Timo Betcke"
+date: "10/20/2024"
+advisor: "Dr Deniz Akyildiz"
+
+---
+## Project Description
+
+Generative models display impressive abilities to simulate and generate realistic looking multimedia data, such as images and audio. However, when it comes to domains where many constraints are present, such as optimisation or physical modelling, they fall short of producing high-quality samples based on the training data alone. In these cases, samples often have unrealistic artefacts and unphysical behaviour. Therefore, it is of great interest to develop principled ways to incorporate constraints into generative models, e.g. diffusion models and flows. This project will first look at developing an optimisation-based methodology where one is interested in generating samples that minimise certain cost functions that can be described by constraints of the problem at hand. We aim to produce methodology and corresponding software to incorporate general constraints. Then the project will move ahead to incorporate constraints arising from physical modelling problems, e.g., described by a partial differential equation (PDE). All of this is envisioned to be converted to a modular software package, that can be interfaced with many popular software packages to improve its usability for researchers.
+
+### Existing background work
+
+Constraining generative models is a popular topic, since it is generally recognised that they cannot produce samples obeying, e.g., physical constraints well. Below is very recent work in this direction:
+
+Fishman, N., Klarner, L., De Bortoli, V., Mathieu, E., & Hutchinson, M. J. Diffusion Models for Constrained Domains. Transactions on Machine Learning Research, 2023.
+
+Kong, L., Du, Y., Mu, W., Neklyudov, K., De Bortoli, V., Wang, H., Wu, D., Ferber, A., Ma, Y.A., Gomes, C.P. and Zhang, C., 2024. Diffusion models as constrained samplers for optimization with unknown constraints. arXiv preprint arXiv:2402.18012.
+
+Fishman, N., Klarner, L., Mathieu, E., Hutchinson, M. and De Bortoli, V., 2024. Metropolis sampling for constrained diffusion models. Advances in Neural Information Processing Systems, 36.
+
+I have worked on diffusion models for inverse problems [1], which is a special case of constraining the generative model (instead of a loss function, one uses a likelihood – where the log-likelihood can be interpreted as a loss function). This worked really well for inverse problems, and we are already working on extensions of this idea using sequential Monte Carlo within my group for inverse problems as well as for general losses. Other relevant works include variational deep generative modelling with physics constraints, which can be seen from [2, 3, 4].
+
+[1] Boys, B., Girolami, M., Pidstrigach, J., Reich, S., Mosca, A. and Akyildiz, O.D., 2023. Tweedie moment projected diffusions for inverse problems. Transactions of Machine Learning Research, 2024.
+
+[2] Vadeboncoeur, A., Akyildiz, Ö.D., Kazlauskaite, I., Girolami, M. and Cirak, F., 2023. Fully probabilistic deep models for forward and inverse problems in parametric PDEs. Journal of Computational Physics, 491, p.112369.
+
+[3] Vadeboncoeur, A., Kazlauskaite, I., Papandreou, Y., Cirak, F., Girolami, M. and Akyildiz, O.D., 2023, July. Random grid neural processes for parametric partial differential equations. In International Conference on Machine Learning (ICML) (pp. 34759-34778).
+
+[4] Akyildiz, O.D., Girolami, M., Stuart, A.M. and Vadeboncoeur, A., 2024. Efficient Prior Calibration From Indirect Data. arXiv preprint arXiv:2405.17955.
+
+### Main objectives of the project
+
+This project aims at publishing two or three research articles with clear methodological improvements compared to the state-of-the-art. This will include first working on general optimisation problems and developing a methodology to solve optimisation problems using generative models, most notably, diffusion and flow models (but also potentially others). Once the methodology is developed, the methodology will be converted to a software package (written in JAX, as envisioned), properly documented, and aimed at general use. To improve then the usability of the software, we will incorporate physical constraints as ready-to-go functions which can be made to guide generative models.
+
+### Details of Software/Data Deliverables
+
+We aim at interfacing popular diffusion and flow model code (or incorporating into ours) with general purpose optimizers (again, can be modified) and PDE solvers. My earlier project as cited above [1] produced a mini software package, called DiffusionJAX: https://github.com/bb515/diffusionjax Further developments of this will be implementing general purpose optimisation methods as well as PDE solvers, such as the ones based on finite elements (see the relevant projects I worked in [5], [6] and software output: https://github.com/connor-duffin/ula-statfem). The final aim is to combine the strengths of the JAX and available generative modelling and scientific modelling code, combined into a coherent framework to work with the problem of generating data with complicated constraints that arise in real-world modelling.
+
+[5] Akyildiz, Ö.D., Duffin, C., Sabanis, S. and Girolami, M., 2022. Statistical finite elements via Langevin dynamics. SIAM/ASA Journal on Uncertainty Quantification, 10(4), pp.1560-1585.
+
+[6] Glyn-Davies, A., Duffin, C., Kazlauskaite, I., Girolami, M. and Akyildiz, Ö.D., 2024. Statistical Finite Elements via Interacting Particle Langevin Dynamics. arXiv preprint arXiv:2409.07101.
+

phd_projects/entries/casale_lupu.qmd

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+---
+title: "Mathematical and Computational Modeling of Resilience in Multilayer Networks"
+institution: "Imperial"
+department: "Computing"
+author: "Timo Betcke"
+date: "10/20/2024"
+advisor: "Dr. Giuliano Casale and Prof. Emil Lupu"
+
+---
+## Project Description
+
+### Existing background work
+
+The investigators work both in the Department of Computing at Imperial College London and have extensive expertise in the research topics that underpin the project. They have a running collaboration in the area of resilience, which intersects with their expertise in modelling enterprise systems and networks. Recent works relevant to the project include modelling and simulation of enterprise networks under cyber attacks (https://ieeexplore.ieee.org/document/9713988); mean-field ODE models for modelling networks evolving in randomly environments (https://ieeexplore.ieee.org/abstract/document/7843645); variational inference methods for inference of parameters in routing models (https://www.cambridge.org/core/journals/advances-in-applied-probability/article/abs/variational-inference-for-markovian-queueing-networks/D35E7DB62BE78D883730A04E617C3DB3); game theoretic analysis of stochastic agents modelling urban mobility (https://www.ifaamas.org/Proceedings/aamas2024/pdfs/p2462.pdf; a journal version is under submission). We have also built a software toolchain for multi-layer networks that will provide a software basis to this project.
+
+### Main objectives of the project
+
+The PhD project will develop advanced mathematical and computational models for studying the resilience of networks of networks. Specifically, the project will focus on the multilayer network formalism (MLN), which is used to describe networks consisting of multiple interconnected layers, each representing different types of interactions or relationships between nodes. MLNs are used to model systems where entities participate in various types of networks simultaneously, such as communication networks, social networks, and transportation systems, allowing for the analysis of interactions across different dimensions and their collective impact on the system's dynamics. Applications of MLNs include understanding information diffusion, analyzing infrastructure resilience, optimizing network traffic, and studying the spread of diseases or cyber threats across interconnected systems.
+
+This project focuses on the mathematical foundations of MLNs, exploring their dynamic properties and resilience to perturbations using advanced techniques such as Neural Ordinary Differential Equations (Neural ODEs) to model diffusion processes across network layers. A key aspect of the research will involve creating efficient analytical frameworks to capture the behavior of multimodal information flows and cascades within these networks. The aim is to understand how multilayered structures behave under various stresses, particularly in scenarios involving abrupt changes to the network structure (e.g., sudden failures, cyberattacks, etc.), developing new resilience metrics to quantify robustness. Although the project has a modelling focus, applications to mobility systems and network security (eg network segmentation) will be explored as use cases.
+
+### Details of Software/Data Deliverables
+
+Several public data sources are available to concretely assess the toolchain, we presently work with mobility datasets from Oslo and Austin and security data from enterprise networks. The focus of the deliverables will therefore be on open source software tools:
+
+- D1: Large-scale MLN simulation tool, Year 1
+- D2: Diffusion models and resilience metrics for MLN analysis, Year 2
+- D3: Use cases software applications in collaboration with external partners and companies, Year 3

phd_projects/entries/duncan.qmd

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+---
+title: "Smart Image-Based Sensor Optimisation for Fusion Simulation Validation"
+institution: "Imperial"
+department: "Mathematics"
+author: "Timo Betcke"
+date: "10/20/2024"
+advisor: "Dr Andrew Duncan"
+
+---
+## Project Description
+
+Fusion components need to sustain continuous extreme loads including: Steady state heat fluxes up to 20 MW/m2; strong local magnetic fields on the order of several Tesla imparting large Mega Newton body forces; and neutron bombardment leading to significant irradiation damage. The combination of extreme multi-physics conditions means that validation experiments are time and resource intensive, often yielding sparse data. Given that fusion component tests have a high cost in time and resources, a means of designing targeted and data-rich experiments that can be directly compared with engineering / physics simulations is highly desirable. 
+
+Combining advances in image-based diagnostics and machine learning to optimise their use is a route to reducing the number of experiments required for fusion component qualification. Large scale component validation experiments on UKAEA’s CHIMERA and LIBRTI facilities will cost on the order of £M’s. This cost means it is not possible to run the number of experiments required for uncertainty quantification but it is possible to simulate millions of experiments and use this information to run a targeted experimental campaign. Additionally, the cost in time and resources means that gaining high-fidelity data from an optimised array of imaging sensors has the potential to greatly reduce the required experimental effort for simulation validation. To enable this, new simulation tools are required that can accurately model image-based sensors applied to a multi-physics simulation. Furthermore, while optimisation algorithms exist for points sensors applied to single physics applications there are currently no methods for optimising arrays of image-based sensors applied to a realistic multi-physics experiment. 
+
+### Existing background work
+This project will leverage the expertise of Dr Andrew Duncan in machine learning methods for model calibration, uncertainty quantification and sensor placement optimization for expensive computational simulations subject to budget constraints.  The project will be co-supervised by Dr Dante Kalise, who has expertise in optimisation and optimal control of PDE driven systems.   The student will be based at Imperial College London but will spend up to a month each year working on-site at either Culham or FTF-Yorkshire to enhance interaction with UKAEA staff.
+
+
+
+### Main objectives of the project
+
+The aim of this project is to develop a series of robust optimisation methods that can be used to design optimal image-based sensor arrays for multi-physics validation experiments. These optimisations will use a multi-physics simulation as input and output an array of image-based diagnostics and their positions along with predicted measurement uncertainties. The first objective of this project will be to enable multi-physics sensor placement optimisation with a focus on ray-tracing algorithms for simulating camera sensors combined with other sensors. The second objective is to incorporate computationally efficient uncertainty propagation using machine learning and ensembles of multi-fidelity models.  The third objective will be to develop explainable approaches to sensor placement, leveraging multi-objective optimization methods obtain provide a justification of what aspects of an experiment will be informed by a particular sensor, and the associated tradeoffs against competing objectives.    The final objective of this project is to apply the developed optimization methods to a fusion-relevant test case such as the ‘Simple Test Case’ dataset being generated as part of UKAEA’s Key Challenge 4 on Digital Qualification.
+
+### Details of Software/Data Deliverables
+
+The final objective of this project is to develop a suite of computational optimization methods to be applied to a fusion-relevant test case such as the ‘Simple Test Case’ dataset being generated as part of UKAEA’s Key Challenge 4 on Digital Qualification.