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    <description>Recent content on </description>
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      <title>Curriculum Vitae</title>
      <link>https://mbuze.github.io/cv/</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
      
      <guid>https://mbuze.github.io/cv/</guid>
      <description>Career and Education  January 2025 - Present  Lecturer in Mathematics and AI at MARS: Mathematics for AI in Real-world Systems, within School Of Mathematical Sciences, Lancaster University, UK; A permanent post (equivalent to Assistant Professor) as part of MARS, a newly-formed applied maths / AI research group at Lancaster. See here for more details.   February 2023 - January 2025  Research Associate at School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, UK; A postdoctoral position funded by EPSRC grant</description>
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      <title>Discrete modelling of nucleation and migration of defects in materials</title>
      <link>https://mbuze.github.io/research/materials/</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
      
      <guid>https://mbuze.github.io/research/materials/</guid>
      <description>Atomistic numerical continuation and deflation techniques Modern high-throughput molecular and atomistic simulations rely on sophisticated optimisation tools to effectively explore the severely non-convex energy landscapes. Bifurcation theory-based techniques such as numerical continuation and deflation are well-developed mathematical approaches already used in a range of nonlinear settings (see e.g., [AG90], [FBF15]), but remain underutilised in atomistic and molecular simulations. The broader adoption of such tools at atomistic scales has been identified as highly desirable in a recent white paper, a summary document of the IPAM Long Program New Mathematics for the Exascale: Applications to Materials Science [*].</description>
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    <item>
      <title>Events</title>
      <link>https://mbuze.github.io/events/</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
      
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      <description>Future events   Computational Materials Science and Mathematics at the Particle and Atomistic Scales ICMS, Edinburgh, UK, 10-14 November 2025 I am on the organising committee and will run a one-day session devoted to numerical continuation/deflation and optimisation techniques at the atomistic scale. More info to follow. website. --    Singularities in Discrete Systems Oberwolfach, Germany 4-9 May 2025. website    Past events  (30 talks, including 9 in the last year)  Visit to Kanazawa Kanazawa University, Japan, 16 - 20 December 2024 Hosted by Patrick van Meurs, I also gave a seminar talk.</description>
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      <title>Optimal transport - theory and applications</title>
      <link>https://mbuze.github.io/research/ot/</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
      
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      <description>[7], [9] and [10]. -- In its basic version, the optimal transport (OT) problem is to solve $$ \min_{\gamma} \left\{ \int_{X \times X} c(x_1,x_2) d\gamma(x_1,x_2)\, \Bigm\vert \, \gamma \in \mathcal{P}(X \times X),\; \gamma_i = \mu_i\right\}, $$ where $\mu_1 \in \mathcal P(X)$ is the source measure, $\mu_2 \in \mathcal P(X)$ is the target measure, ${c \,\colon\, X \times X \to \mathbb{R}\cup \{+\infty\}}$ is the cost function, and $\gamma_i$ is the $i$th marginal of the transport plan $\gamma$.</description>
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    <item>
      <title>Publications</title>
      <link>https://mbuze.github.io/publications/</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
      
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      <description>[10]   J.&amp;nbsp;Braun and M.&amp;nbsp;Buze. Incompleteness of Sinclair-type continuum flexible boundary conditions for atomistic fracture simulations. arXiv e-prints, 2403.05462, 2024 (accepted for publication in SIAM MMS). [&amp;nbsp;bib&amp;nbsp;| http&amp;nbsp;| .pdf&amp;nbsp;]   [9]   M.&amp;nbsp;Buze, J.&amp;nbsp;Feydy, S.R. Roper, K.&amp;nbsp;Sedighiani, and D.&amp;nbsp;Bourne. Anisotropic power diagrams for polycrystal modelling: Efficient generation of curved grains via optimal transport, Computational Materials Science, Volume 245, 2024. [&amp;nbsp;bib&amp;nbsp;| DOI&amp;nbsp;| http&amp;nbsp;| .pdf&amp;nbsp;]   [8]   M.</description>
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      <title>Teaching</title>
      <link>https://mbuze.github.io/teaching/</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
      
      <guid>https://mbuze.github.io/teaching/</guid>
      <description>Summer School on Deep Learning for Mathematical Imaging
July 2024 I was invited by Dr Andreas Alpers to deliver a short course on machine learning approaches to microstructure modelling in Python, including a hands-on showcase of my library PyAPD, to research interns at The Centre for Mathematical Imaging Techniques. Materials related to this are available here.
 Teaching at Heriot-Watt 2023/2024   Lecturer for F17XB Mathematics for Engineers and Scientists 2; A big service course for 500+ students across three campuses.</description>
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      <title>Uncertainty quantification for machine learning interatomic potentials</title>
      <link>https://mbuze.github.io/research/uqip/</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
      
      <guid>https://mbuze.github.io/research/uqip/</guid>
      <description>Interatomic potentials approximate the potential energy of systems of atoms as a function of their positions and are seen as a computationally feasible alternative to electronic structure calculations, which additionally model the motion of electrons around atomic nuclei. Empirical potentials have between $2$ and $11$ parameters, rising to $1000$ for modern machine-learning potentials, and the highly nonlinear nature of the overall model necessitates quantifying the uncertainty in their choice and how this propagates to quantities of interest, such as mechanical or chemical properties of materials.</description>
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