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tbetcke committed Oct 18, 2024
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2 changes: 1 addition & 1 deletion _quarto.yml
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format:
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theme: morph
theme: default
css: styles.css
toc: false
smooth-scrolling: true
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1 change: 1 addition & 0 deletions index.qmd
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</div>
</div>

<br>


<section id="gallery">
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2 changes: 1 addition & 1 deletion phd_projects/entries/Benning_Hearing.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Improving impaired hearing through sound reconstruction from neural acti
institution: "UCL"
department: "Computer Science"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Martin Benning"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Benning_Paralift.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "PARALIFT – A PARAllel framework for LIFTed training of neural networks
institution: "UCL"
department: "Computer Science"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Martin Benning"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Berloff_Quasigeostrophic.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Developing Quasi-Geostrophic Coupled Ocean–Atmosphere Model"
institution: "Imperial"
department: "Mathematics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Pavel Berloff"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Beskos_bayesiancalibration.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Advanced Computational Methods for Bayesian Calibration of High-Dimensio
institution: "UCL"
department: "Statistics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Alexandros Beskos"

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2 changes: 1 addition & 1 deletion phd_projects/entries/BetckeM_inverseproblems.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "All-at-once deep learning methods for nonlinear PDE based inverse proble
institution: "UCL"
department: "Computer Science"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Marta Betcke"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Betcke_GPUarchitectures.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Fast Multipole Methods on modern architectures"
institution: "UCL"
department: "Maths and Advanced Research Computing Centre"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Timo Betcke"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Boulle_Koopman.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Koopman operator learning of nonlinear PDEs"
institution: "Imperial"
department: "Mathematics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Dr.Nicholas Boulle"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Bravi_cancerimmune.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "A machine learning-informed computational model of cancer-immune interac
institution: "Imperial"
department: "Mathematics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Dr. Barbara Bravi"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Briol_Bayesianinference.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Robust Bayesian Inference at Scale"
institution: "UCL"
department: "Statistical Science"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Dr.Francois-Xavier Briol"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Briol_Montecarlo.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Transfer Learning for Monte Carlo"
institution: "UCL"
department: "Statistical Science"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Dr.Francois-Xavier Briol"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Briol_simulation.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Simulation-based Inference for Expensive Scientific Simulators"
institution: "UCL"
department: "Statistical Science"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Dr.Francois-Xavier Briol"

---
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2 changes: 1 addition & 1 deletion phd_projects/entries/Burman_heterogeneouscoupling.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "A computational framework for heterogeneous coupling in large scale comp
institution: "UCL"
department: "Mathematics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Erik Burman"

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2 changes: 1 addition & 1 deletion phd_projects/entries/CotterKalise_Fieldgames.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "A Unified Solver for Optimal Transport, Schroedinger Bridges, and Variat
institution: "Imperial"
department: "Mathematics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Colin Cotter and Dr. Dante Kalise"

---
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2 changes: 1 addition & 1 deletion phd_projects/entries/Cotter_hybridmodelling.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "PDE-driven/data-driven hybrid modelling for data assimilation"
institution: "Imperial"
department: "Mathematics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Colin Cotter"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Coveney_HemeLB.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "HemeLB at the exascale and beyond: Implementing and studying whole human
institution: "UCL"
department: "Chemistry and Advanced Research Computing"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Peter V. Coveney"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Coveney_dynamicalsystems.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Quantifying and eliminating floating point pathologies in the simulation
institution: "UCL"
department: "Chemistry and Advanced Research Computing"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Peter V. Coveney"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Cox_kwave.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Grid-independent pseudospectral models of broadband acoustic wave propag
institution: "UCL"
department: "Medical Physics and Biomedical Engineering"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Ben Cox"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Cox_neuralODE.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Time Reversal Imaging and Learned Physics with Neural ODEs"
institution: "UCL"
department: "Medical Physics and Biomedical Engineering"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Ben Cox"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Deisenroth_dataassimilation.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Machine Learning for Low-Cost Data Assimilation"
institution: "UCL"
department: "Computer Science"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Marc Deisenroth"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Graham_Automatedbayesian.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Accelerated multi-level Bayesian calibration of expensive simulations on
institution: "UCL"
department: "Advanced Research Computing Centre"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Dr Matt Graham"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Graham_multilevelbayesian.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Automated Bayesian inference in stochastic differential equation models"
institution: "UCL"
department: "Advanced Research Computing Centre"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Dr Matt Graham"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Hewett_fractaldomains.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Numerical methods for PDEs in fractal domains"
institution: "UCL"
department: "Mathematics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof David Hewett"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Jensen_unifiedformlanguage.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "A Unified Form Language for PDEs in non-divergence form"
institution: "UCL"
department: "Mathematics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Dr Max Jensen"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Karin_tissue.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Agent-based simulations of tissue dynamics"
institution: "Imperial"
department: "Mathematics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Dr.Omer Karin"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Kovalchuk_healthcare.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Drift detection in graph streams and its applications in healthcare"
institution: "UCL"
department: "Computer Science and Advanced Research Computing Centre"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Dr. Yevgeniya Kovalchuk"

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2 changes: 1 addition & 1 deletion phd_projects/entries/MisenerHam_DAEinterface.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Algorithms and software for differentiable programming at the ML/PDE/DAE
institution: "Imperial"
department: "Computing and Mathematics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Ruth Misener and Prof David Ham"

---
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9 changes: 5 additions & 4 deletions phd_projects/entries/Ni_StochasticPDE.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Accelerating parabolic Stochastic PDE solver via a weak adversarial netw
institution: "UCL"
department: "Mathematics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Hao Ni"

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Expand All @@ -13,7 +13,7 @@ advisor: "Prof Hao Ni"


Stochastic partial differential equations (SPDEs) are power mathematical tools to model random spatiotemporal dynamics, with broader applications ranging from weather forecasting to fluid dynamics. Machine learning (ML)-based approaches are emerging as it can be used to effectively handle the curse of dimensionality of traditional numerical methods. It can lead to the high-performing SPDE solver with significant computational acceleration. Moreover, the generalization of physics- informed neural networks from PDEs to SPDEs may provide a novel family of neural networks for analysing noisy spatiotemporal data, which can be used to discover the hidden physics law and predict the future data evolution.
Most of ML algorithms for learning SPDEs fail into the supervised learning category, where the input and output pairs are “observable data” consisted of driving noise and the corresponding solution trajectories. These data are simulated by high quality numerical solver. One important aspect of improving ML algorithms is to design neural networks to better approximate the SPDE solution map [1 – 3]. Among them, our proposed Deep latent regularity network incorporates Regularity structure, a groundbreaking work on SPDEs by the Fields medallist Martin Hairer, to design neural networks. This model demonstrates superior performance in terms of accuracy and inferences time on various SPDEs such as the stochastic 2D Navier-Stokes equation.
Most of ML algorithms for learning SPDEs fall into the supervised learning category, where the input and output pairs are “observable data” consisted of driving noise and the corresponding solution trajectories. These data are simulated by high quality numerical solver. One important aspect of improving ML algorithms is to design neural networks to better approximate the SPDE solution map [1 – 3]. Among them, our proposed Deep latent regularity network incorporates Regularity structure, a groundbreaking work on SPDEs by the Fields medallist Martin Hairer, to design neural networks. This model demonstrates superior performance in terms of accuracy and inferences time on various SPDEs such as the stochastic 2D Navier-Stokes equation.


### Main objectives of the project
Expand All @@ -40,7 +40,8 @@ Reference

[3]. Gong, S., Hu, P., Meng, Q., Wang, Y., Zhu, R., Chen, B., Ma, Z., Ni, H. and Liu, T.Y., 2023, June. Deep latent regularity network for modeling stochastic partial differential equations. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 37, No. 6, pp. 7740-7747).

[4]. [1] Zang, Y., Bao, G., Ye, X. and Zhou, H., 2020. Weak adversarial networks for high-dimensional partial differential equations. Journal of Computational Physics, 411, p.109409.
[4]. Zang, Y., Bao, G., Ye, X. and Zhou, H., 2020. Weak adversarial networks for high-dimensional partial differential equations. Journal of Computational Physics, 411, p.109409.

[5]. Oliva, P.V., Wu, Y., He, C. and Ni, H., 2022. Towards fast weak adversarial training to solve high dimensional parabolic partial differential equations using XNODE-WAN. Journal of Computational Physics, 463, p.111233.

[5]. [2] Oliva, P.V., Wu, Y., He, C. and Ni, H., 2022. Towards fast weak adversarial training to solve high dimensional parabolic partial differential equations using XNODE-WAN. Journal of Computational Physics, 463, p.111233.
[6]. Chevyrev, Ilya, Andris Gerasimovics, and Hendrik Weber. "Feature engineering with regularity structures." arXiv preprint arXiv:2108.05879 (2021).
2 changes: 1 addition & 1 deletion phd_projects/entries/Parpas_moleculardynamics.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Efficient Computation of Transition States in Molecular Dynamics"
institution: "Imperial"
department: "Computing"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Dr. Panos Parpas"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Pavliotis_inference.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Inference and inverse problems for stochastic interacting particle syste
institution: "Imperial"
department: "Mathemetics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Greg A. Pavliotis"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Pearce_bacterialbiofilms.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Data-driven multi-scale modelling of bacterial biofilms"
institution: "UCL"
department: "Mathematics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Dr. Philip Pearce"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Salvi_Gillespie.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "A differentiable Gillespie algorithm for exact gradients through discret
institution: "Imperial"
department: "Mathematics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Dr.Cristopher Salvi"

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2 changes: 1 addition & 1 deletion phd_projects/entries/Tennyson_TROVE.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Re-griding the TROVE nuclear motion program"
institution: "UCL"
department: "Physics and Astronomy"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Jonathan Tennyson"

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2 changes: 1 addition & 1 deletion phd_projects/entries/ThomasShahrezaei_inference.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Inference of gene regulatory networks from single cell data"
institution: "Imperial"
department: "Mathematics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Prof Vahid Shahrezaei and Dr. Philipp Thomas "

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2 changes: 1 addition & 1 deletion phd_projects/entries/Tobar_machinelearning.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Optimal transport for probabilistic machine learning"
institution: "Imperial"
department: "Mathematics"
author: "Laura Beer"
date: "02/10/2024"
date: "10/02/2024"
advisor: "Dr.Felipe Tobar"

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2 changes: 1 addition & 1 deletion phd_projects/entries/burman_inverse.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Computational solution of inverse problems using large datasets of low r
institution: "UCL"
department: "Mathematics"
author: "Timo Betcke"
date: "30/09/2024"
date: "09/30/2024"
advisor: "Prof Erik Burman"

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2 changes: 1 addition & 1 deletion phd_projects/entries/cotter_parallel_time.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Data-driven preconditioning for parallel-in-time PDE solvers"
institution: "Imperial"
department: "Mathematics"
author: "Laura Beer"
date: "11/10/2024"
date: "10/11/2024"
advisor: "Prof Colin Cotter"

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2 changes: 1 addition & 1 deletion phd_projects/entries/gelat.qmd
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Expand Up @@ -3,7 +3,7 @@ title: "Large-scale high-performance solver for therapeutic ultrasound applicati
institution: "UCL"
department: "UCL Division of Surgery and Interventional Science"
author: "Timo Betcke"
date: "11/10/2024"
date: "10/11/2024"
advisor: "Dr Pierre Gélat"

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