About Me

I am a Lecturer in Scientific Computing at the University of Leeds.

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.

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.

Research

The following is a non-exhaustive list of things I have worked on and am currently interested in.

Dirac cones in the conduction and valence bands of graphene reconstructed from smooth interpolants by learning invariants instead of the surfaces themselves.

Machine learning conical intersections

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.

I have worked on overcoming these issues by learning globally smooth invariant quantities from which the desired conical intersections can be reconstructed accurately.

Molecular dynamics simulation of an Ala-Ala-Ala molecule (C₉H₁₇N₃O₄).

Machine learning of interaction models

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.

I work on novel methodologies and applications of such frameworks as well as the closely related problem of analyzing their theoretical foundations.

Wave equation on a disk dampened by a time-fractional Caputo derivative term.

Fractional Differential Equations

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.

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.

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.

Orthogonal Polynomials and Spectral Methods

Orthogonal polynomials can be used to accurately and efficiently approximate functions.

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.

Publications

See also the automated listings at Google Scholar or Semantic Scholar.

  1. Modelling Power-Law Ultrasound Absorption Using a Time-Fractional, Static Memory, Fourier Pseudo-Spectral Method
    arXiv   M. J. King, T. S. Gutleb, B. E. Treeby, B. T. Cox. (2024).
  2. Parameterizing Intersecting Surfaces via Invariants
    arXiv   T. S. Gutleb, R. Barrett, J. Westermayr, C. Ortner. (2024).
  3. Atomic Cluster Expansion Without Self-Interaction
    arXiv   DOI   C.H. Ho, T. S. Gutleb, C. Ortner. Journal of Computational Physics (2024).
  4. A Frame Approach for Equations Involving the Fractional Laplacian
    arXiv   Ioannis P. A. Papadopoulos, T. S. Gutleb, J. A. Carrillo, S. Olver. (2023)
  5. Explicit Fractional Laplacians and Riesz Potentials of Classical Functions
    arXiv   T. S. Gutleb, Ioannis P. A. Papadopoulos. (2023)
  6. A Static Memory Sparse Spectral Method for Time-Fractional PDEs
    arXiv  DOI  T. S. Gutleb, J. A. Carrillo. Journal of Computational Physics (2023).
  7. Building Hierarchies of Semiclassical Jacobi Polynomials for Spectral Methods In Annuli
    arXiv   I. P. A. Papadopoulos, T. S. Gutleb, R. M. Slevinsky, S. Olver. (2023).
  8. Polynomial and Rational Measure Modifications of Orthogonal Polynomials via Infinite-Dimensional Banded Matrix Factorizations
    arXiv   DOI   T. S. Gutleb, S. Olver, R. M. Slevinsky. Foundations of Computational Math. (2024)
  9. Computation of Power Law Equilibrium Measures on Balls of Arbitrary Dimension
    arXiv  DOI   T. S. Gutleb, J. A. Carrillo, S. Olver. Constructive Approximation (2022).
  10. Computing Equilibrium Measures with Power Law Kernels
    arXiv   DOI  T. S. Gutleb, J. A. Carrillo, S. Olver. Mathematics of Computation (2022).
  11. A Fast Sparse Spectral Method for Nonlinear Integro-differential Volterra Equations with General Kernels
    arXiv   DOI  T. S. Gutleb.   Advances in Computational Mathematics (2021).
  12. A Time Splitting Method for the Three-Dimensional Linear Pauli Equation
    arXiv   DOI   T. S. Gutleb, N. Mauser, M. Ruggeri, H. Stimming. Comp. Meth. in Appl. Math. (2023).
  13. A Sparse Spectral Method for Volterra Integral Equations Using Orthogonal Polynomials on the Triangle
    arXiv   DOI   T. S. Gutleb, S. Olver. SIAM Journal on Numerical Analysis (2020).

Selected Talks

Below is a selection of my conference talks. I'll update the website with a more complete list soon.

Teaching

If you are a student of ongoing teaching at the University of Leeds, please use the module's Minerva page or reach out with questions via the module-associated Teams channel.

  • Small Class Instructor for Integral Calculus with Applications
    Jun 2024 - Aug 2024, University of British Columbia, Canada
  • Intercollegiate Tutor for Numerical Linear Algebra
    Oct 2022 - Jan 2023, University of Oxford, UK
  • Senior GTA for Numerical Analysis
    Jan 2022 - Apr 2022, Imperial College London, UK
  • GTA and student project mentor for Mathematical Modeling
    Mar 2021 - Jun 2021 & May 2022 - August 2022, Wolfgang Pauli Institute, University of Vienna, Austria
  • Graduate Teaching Assistant (GTA) in Analysis 1 and 2 for Physicists
    Oct 2015 - Jul 2018 , University of Vienna, Austria