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<!DOCTYPE HTML>
<html lang="en">
<head>
<title>Timon S. Gutleb</title>
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<meta name="description" content="Personal website of Timon S. Gutleb, Lecturer in Scientific Computing at the University of Leeds">
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<section id="header">
<header>
<p></p>
<div class="image avatar"><img src="images/profile.webp" alt="Picture of Timon S. Gutleb." />
</div>
<h1 id="logo">Timon S. Gutleb</h1>
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<ul>
<li><a href="#about" class="active">About Me</a></li>
<li><a href="#research">Research</a></li>
<li><a href="#papers">Publications</a></li>
<li><a href="#talks">Selected Talks</a></li>
<li><a href="#teaching">Teaching</a></li>
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title="Link to Timon's LinkedIn profile"><span class="label">LinkedIn</span></a></li>
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<section id="about">
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<h2>About Me</h2>
<p align="left">I am a Lecturer in Scientific Computing at the University of Leeds. </p>
<p align="left"> My research focus is the development of computational algorithms and tools for natural science applications such as molecular quantum physics and collective behavior in biology, including specifically also machine learning models thereof. I am also interested in computational orthogonal polynomials and their applications in spectral methods as well as the aforementioned machine learning models. </p>
<p align="left"> Previously I was a PIMS-Simons postdoctoral fellow at the University of British Columbia and a postdoctoral research associate at the University of Oxford after having completed a PhD in applied mathematics at the Imperial College London. </p>
</div>
</section>
<section id="research">
<div class="container">
<h2>Research</h2>
<p>The following is a non-exhaustive list of things I have worked on and am currently interested in.</p>
<div class="features">
<article>
<img class="image" style="padding-top:30px;" src="images/GrapheneSpin.webp"
alt="Dirac cones in the conduction and valence bands of graphene reconstructed from smooth interpolants by learning invariants instead of the surfaces themselves."
title="Dirac cones in the conduction and valence bands of graphene reconstructed from smooth interpolants by learning invariants instead of the surfaces themselves." />
<div class="inner">
<h3>Machine learning conical intersections</h3>
<p align="left">Conical intersections play a crucial role in determining the dynamics of molecules and materials upon light excitation, molecular orbitals and material band structure.
In the relevant context of high-dimensional non-smooth hyper-surfaces, common machine learning models perform poorly.</p>
<p align="left">
I have worked on overcoming these issues by learning globally smooth invariant quantities from which the desired conical intersections can be reconstructed accurately.</p>
</div>
<p></p>
</article>
<article>
<img class="image" style="padding-top:30px;" src="images/alalala-molsim.webp"
alt="Molecular dynamics simulation of an Ala-Ala-Ala molecule (C₉H₁₇N₃O₄)."
title="Molecular dynamics simulation of an Ala-Ala-Ala molecule (C₉H₁₇N₃O₄)." />
<div class="inner">
<h3>Machine learning of interaction models</h3>
<p align="left">Many physical and biological systems can be accurately modeled using
atomistic many body interactions. Machine learning based methods allow one to infer
succesful models for otherwise prohibitively large and complex systems. </p>
<p align="left">
I work on novel methodologies and applications of such frameworks as well as the
closely related problem of analyzing their theoretical foundations.</p>
</div>
<p></p>
</article>
<article>
<img class="image" style="padding-top:30px;" src="images/timefractionaldampeningwave.webp"
alt="Wave equation on a disk dampened by a time-fractional Caputo derivative term."
title="Wave equation on a disk dampened by a time-fractional Caputo derivative term." />
<div class="inner">
<h3>Fractional Differential Equations</h3>
<p align="left">Fractional differential equations generalize ODEs and PDEs to include
derivative operators of non-integer order. The resulting operators are generally
nonlocal and thus pose several challenges to conventional numerical approaches. </p>
<p align="left"> Fractional derivatives and closely related objects such as Riesz potentials appear in applications featuring memory
effects, e.g. photoacoustic imaging in medical physics or in the continuous limit of classical particle swarms.</p>
</div>
<p></p>
</article>
<article>
<img class="image" style="padding-top:30px;" src="images/forced-helmholtz-rho-0-5.webp"
alt="Numerical solution to an inhomogeneous Helmholtz equation with k = 80 and right-hand side f(x,y) = sin(100x) on an annular domain with inner radius 0.5."
title="Numerical solution to an inhomogeneous Helmholtz equation with k = 80 and right-hand side f(x,y) = sin(100x) on an annular domain with inner radius 0.5." />
<div class="inner">
<h3>Orthogonal Polynomials and Spectral Methods</h3>
<p align="left">Orthogonal polynomials can be used to accurately and efficiently
approximate functions.</p>
<p align="left"> With appropriate orthogonal polynomials for a given domain and weight function in hand one can construct quadrature methods as well as spectral methods for solving integral and partial differential equations with
sparse discretisations and spectral convergence.</p>
</div>
<p></p>
</article></div>
</section>
<section id="papers">
<div class="container">
<h2>Publications</h2>
<p>See also the automated listings at <a target="_blank"
href="https://scholar.google.com/citations?hl=en&user=4uZ9qhIAAAAJ">Google Scholar</a> or <a
target="_blank" href="https://www.semanticscholar.org/author/148200620">Semantic
Scholar</a>.</p>
<article>
<ol reversed class="pdf-list">
<li><em>Modelling Power-Law Ultrasound Absorption Using a Time-Fractional, Static Memory, Fourier Pseudo-Spectral Method</em> </br> <a target="_blank" href="https://arxiv.org/abs/2408.02541"
class="primary button small icon fa-external-link tight">arXiv</a> <a href="http://bug.medphys.ucl.ac.uk/matthew-king">M. J. King</a>, T. S. Gutleb, <a href="http://bug.medphys.ucl.ac.uk/bradley-treeby">B. E. Treeby</a>, <a href="http://bug.medphys.ucl.ac.uk/ben-cox">B. T. Cox</a>.
(2024).</li>
<li><em>Parameterizing Intersecting Surfaces via Invariants</em> </br> <a target="_blank" href="https://arxiv.org/abs/2407.03731"
class="primary button small icon fa-external-link tight">arXiv</a> T. S. Gutleb, <a
target="_blank" href="https://scholar.google.com/citations?user=N8HRUpQAAAAJ&hl=en">R. Barrett</a>, <a
target="_blank" href="https://www.chemie.uni-leipzig.de/en/wilhelm-ostwald-institute-for-physical-and-theoretical-chemistry/juniorprofessur-westermayr">J. Westermayr</a>, <a
target="_blank" href="https://personal.math.ubc.ca/~ortner/">C. Ortner</a>.
(2024).</li>
<li><em>Atomic Cluster Expansion Without Self-Interaction</em> </br> <a target="_blank" href="https://arxiv.org/abs/2401.01550"
class="primary button small icon fa-external-link tight">arXiv</a> <a
target="_blank" href="https://doi.org/10.1016/j.jcp.2024.113271"
class="primary button small icon fa-external-link tight">DOI</a> <a target="_blank"
href="https://cheukhinhojerry.github.io/">C.H. Ho</a>, T. S. Gutleb, <a
target="_blank" href="https://personal.math.ubc.ca/~ortner/">C. Ortner</a>.
<em>Journal of Computational Physics (2024)</em>.</li>
</li>
<li><em>A Frame Approach for Equations Involving the Fractional Laplacian</em> </br> <a
target="_blank" href="https://arxiv.org/abs/2311.12451"
class="primary button small icon fa-external-link tight">arXiv</a> <a
target="_blank" href="https://ioannispapapadopoulos.github.io/">Ioannis P. A.
Papadopoulos</a>, T. S. Gutleb, <a target="_blank"
href="https://carrilloja.org/">J. A. Carrillo</a>, <a target="_blank"
href="http://wwwf.imperial.ac.uk/~solver/">S. Olver</a>. (2023)</li>
<li><em>Explicit Fractional Laplacians and Riesz Potentials of Classical Functions</em>
</br> <a target="_blank" href="https://arxiv.org/abs/2311.10896"
class="primary button small icon fa-external-link tight">arXiv</a> T. S. Gutleb, <a target="_blank"
href="https://ioannispapapadopoulos.github.io/">Ioannis P. A. Papadopoulos</a>.
(2023)</li>
<li><em>A Static Memory Sparse Spectral Method for Time-Fractional PDEs</em> </br> <a target="_blank"
href="https://arxiv.org/abs/2304.06855"
class="primary button small icon fa-external-link tight">arXiv</a> <a
target="_blank" href="https://doi.org/10.1016/j.jcp.2023.112522"
class="primary button small icon fa-external-link tight">DOI</a> T. S.
Gutleb, <a target="_blank" href="https://carrilloja.org/">J. A. Carrillo</a>.
<em>Journal of Computational Physics (2023)</em>.</li>
<li><em>Building Hierarchies of Semiclassical Jacobi Polynomials for Spectral Methods In Annuli</em> </br> <a target="_blank" href="https://arxiv.org/abs/2310.07541"
class="primary button small icon fa-external-link tight">arXiv</a> <a
target="_blank" href="https://doi.org/10.1137/23M160846X"
class="primary button small icon fa-external-link tight">DOI</a> <a target="_blank"
href="https://ioannispapapadopoulos.github.io/"> I. P. A. Papadopoulos</a>, T. S.
Gutleb, <a target="_blank" href="https://home.cc.umanitoba.ca/~slevinrm/">R. M.
Slevinsky</a>, <a target="_blank" href="http://wwwf.imperial.ac.uk/~solver/">S.
Olver</a>. <em>SIAM Journal on Scientific Computing (2024)</em>.</li>
<li><em>Polynomial and Rational Measure Modifications of Orthogonal Polynomials via Infinite-Dimensional Banded Matrix Factorizations</em> </br> <a target="_blank" href="https://arxiv.org/abs/2302.08448"
class="primary button small icon fa-external-link tight">arXiv</a> <a
target="_blank" href="https://doi.org/10.1007/s10208-024-09671-w"
class="primary button small icon fa-external-link tight">DOI</a> T. S. Gutleb, <a
target="_blank" href="http://wwwf.imperial.ac.uk/~solver/">S. Olver</a>, <a
target="_blank" href="https://home.cc.umanitoba.ca/~slevinrm/">R. M.
Slevinsky</a>. <em>Foundations of Computational Math. (2024)</em></li>
<li><em>Computation of Power Law Equilibrium Measures on Balls of Arbitrary
Dimension</em> </br> <a target="_blank"
href="https://arxiv.org/abs/2109.00843"
class="primary button small icon fa-external-link tight">arXiv</a> <a
target="_blank" href="https://doi.org/10.1007/s00365-022-09606-0"
class="primary button small icon fa-external-link tight">DOI</a> T. S. Gutleb, <a target="_blank"
href="https://carrilloja.org/">J. A. Carrillo</a>, <a target="_blank"
href="http://wwwf.imperial.ac.uk/~solver/">S. Olver</a>. <em>Constructive
Approximation (2022)</em>.</li>
<li><em>Computing Equilibrium Measures with Power Law Kernels</em></br> <a target="_blank"
href="https://arxiv.org/abs/2011.00045"
class="primary button small icon fa-external-link tight">arXiv</a> <a
target="_blank" href="https://doi.org/10.1090/mcom/3740"
class="primary button small icon fa-external-link tight">DOI</a> T. S. Gutleb, <a
target="_blank" href="https://carrilloja.org/">J. A. Carrillo</a>, <a
target="_blank" href="http://wwwf.imperial.ac.uk/~solver/">S. Olver</a>.
<em>Mathematics of Computation (2022)</em>. </li>
<li><em>A Fast Sparse Spectral Method for Nonlinear Integro-differential Volterra
Equations with General Kernels</em></br> <a target="_blank"
href="https://arxiv.org/abs/2005.06081"
class="primary button small icon fa-external-link tight">arXiv</a> <a
target="_blank" href="https://doi.org/10.1007/s10444-021-09866-7"
class="primary button small icon fa-external-link tight">DOI</a> T. S. Gutleb. <em>Advances in
Computational Mathematics (2021)</em>. </li>
<li><em>A Time Splitting Method for the Three-Dimensional Linear Pauli Equation</em>
</br> <a target="_blank"
href="https://arxiv.org/abs/2005.06072"
class="primary button small icon fa-external-link tight">arXiv</a> <a
target="_blank" href="https://doi.org/10.1515/cmam-2023-0094"
class="primary button small icon fa-external-link tight">DOI</a> T. S. Gutleb, N. Mauser, M. Ruggeri, H. Stimming. <em>Comp.
Meth. in Appl. Math. (2023)</em>.</li>
<li><em>A Sparse Spectral Method for Volterra Integral Equations Using Orthogonal
Polynomials on the Triangle</em></br> <a target="_blank"
href="https://arxiv.org/abs/1906.03907"
class="primary button small icon fa-external-link tight">arXiv</a> <a
target="_blank" href="https://doi.org/10.1137/19M1267441"
class="primary button small icon fa-external-link tight">DOI</a> T. S. Gutleb, <a target="_blank"
href="http://wwwf.imperial.ac.uk/~solver/">S. Olver</a>. <em>SIAM Journal on
Numerical Analysis (2020)</em>.</li>
</ol>
</article>
</div>
</section>
<section id="talks">
<div class="container">
<h2>Selected Talks</h2>
<p>Below is a selection of my conference talks. I'll update the website with a more complete list
soon.</p>
<ul class="pdf-list">
<li><a target="_blank"
href="https://numericalanalysisconference.org.uk/meetings/2023/minisymposia">29th
Biennial Numerical Analysis Conference</a>, Glasgow, UK, 2023. <a target="_blank"
href="files/Gutleb_NACONF2023.pdf"
class="primary button small icon fa-download tight">Slides (PDF)</a></li>
<li><a target="_blank" href="https://www.siam.org/conferences/cm/conference/cse23">SIAM
CSE23</a>, Amsterdam, Netherlands, 2023. <a target="_blank"
href="files/Gutleb_SIAM_CSE23.pptx"
class="primary button small icon fa-download tight">Slides (PPTX)</a></li>
<li><a target="_blank" href="http://faculty.washington.edu/trogdon/RMT+NLA/index.html">Random
Matrix Theory and Numerical Linear Algebra</a>, Seattle, USA, 2022. <a
target="_blank" href="files/Gutleb_RMT+NLAConference_poster.pdf"
class="primary button small icon fa-download tight">Poster (PDF)</a></li>
<li><a target="_blank" href="https://www.icosahom2020.org/">ICOSAHOM</a>, Vienna, Austria, 2021.
</li>
<li><a target="_blank" href="https://winter20.cms.math.ca/">CMS 2020 Winter Meeting</a>, Canada,
2020.</li>
<li><a target="_blank" href="http://www.csrc.ac.cn/en/event/workshop/2020-01-10/103.html">4th
Conference on Numerical Methods for Fractional-Derivative Problems</a>, Beijing, China,
2020.</li>
<li><a target="_blank"
href="https://numericalanalysisconference.org.uk/meetings/2019/minisymposia">28th
Biennial Numerical Analysis Conference</a>, Glasgow, UK, 2019. <a target="_blank"
href="files/Gutleb_NACONF2019_SparseSpectralVolterra_slides.pdf"
class="primary button small icon fa-download tight">Slides (PDF)</a></li>
</li>
</ul>
</div>
</section>
<section id="teaching">
<div class="container">
<h2>Teaching</h2>
<p>If you are a student of ongoing teaching at the University of Leeds, please use the module's <a href="https://minerva.leeds.ac.uk/">Minerva page</a> or reach out with questions via the module-associated Teams channel.</p>
<ul class="pdf-list">
<li>Small Class Instructor for Integral Calculus with Applications</br>Jun 2024 - Aug 2024, University of
British Columbia, Canada</li>
<li>Intercollegiate Tutor for Numerical Linear Algebra</br>Oct 2022 - Jan 2023, University of
Oxford, UK</li>
<li>Senior GTA for Numerical Analysis</br>Jan 2022 - Apr 2022, Imperial College London, UK</li>
<li>GTA and student project mentor for Mathematical Modeling</br>Mar 2021 - Jun 2021 & May 2022
- August 2022, Wolfgang Pauli Institute, University of Vienna, Austria</li>
<li>Graduate Teaching Assistant (GTA) in Analysis 1 and 2 for Physicists </br> <a
target="_blank" href="https://ufind.univie.ac.at/en/person.html?id=59491&teaching=true">
Oct 2015 - Jul 2018 </a>, University of Vienna, Austria</li>
</ul>
</div>
</section>
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<script type="text/javascript">document.write((new Date()).getFullYear())</script> Timon S.
Gutleb
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