Research Output per year

## Personal profile

### Quote

“Conjecturally, in the depths of the human brain runs an immensely powerful, simple, efficient and task- and signal-independent learning algorithm. It is my ultimate aim to use mathematics to uncover and develop such algorithms.”

### Research profile

Jim Portegies is an Assistant Professor in the Applied Analysis group of the Centre for Analysis, Scientific computing and Applications (CASA) at Eindhoven University of Technology (TU/e). Jim Portegies works in the mathematical fields of analysis, measure theory and geometry, and applies techniques from these fields to problems in machine-learning and artificial intelligence. He has applied techniques from spectral geometry to prove guarantees on performance of nonlinear dimensionality reduction algorithms. Currently, he is investigating how to design algorithms that mimic how humans and animals learn.

Despite the large number of recent advances in artificial intelligence, humans still outperform machines in many tasks. The central question of how to design machines that learn like humans is still wide open. The answer may lie in universal learning algorithms. Such algorithms are simple, efficient and can be applied to a broad variety of signals and tasks and are conjectured to exist in the depths of the human brain.

### Academic background

Jim Portegies obtained his MSc in Industrial and Applied Mathematics and Applied Physics from the TU/e in 2009. He spent the 2007-2008 academic year as an exchange student at the University of Bonn, Germany. He received his PhD in Mathematics from the Courant Institute of Mathematical Sciences in New York. In the Fall of 2013, he spent a semester at NYU Shanghai, in Shanghai, China. After completing his PhD in 2014, he spent two years a postdoc at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany until he returned to the TU/e as an assistant professor in Mathematics in 2016. Jim is a member of the TU/e Young Academy of Engineering.

## Fingerprint Dive into the research topics where Jim W. Portegies is active. These topic labels come from the works of this person. Together they form a unique fingerprint.

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## Research Output 2008 2019

## Hamiltonian fast marching: a numerical solver for anisotropic and non-holonomic eikonal PDEs

Mirebeau, J. M. & Portegies, J., 1 Jan 2019, In : Image Processing On Line. 9, p. 47-93 47 p.Research output: Contribution to journal › Article › Academic › peer-review

## Total variation and mean curvature PDEs on the space of positions and orientations

Duits, R., St-Onge, E., Portegies, J. & Smets, B., 5 Jun 2019,*Scale Space and Variational Methods in Computer Vision - 7th International Conference, SSVM 2019, Proceedings.*Lellmann, J., Modersitzki, J. & Burger, M. (eds.). Berlin: Springer, p. 211-223 13 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 11603 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

## Asymptotic dependency structure of multiple signals: Asymptotic equipartition property for diagrams of probability spaces

Matveev, R. & Portegies, J. W., Dec 2018, In : Information Geometry. 1, 2, p. 237-285Research output: Contribution to journal › Article › Academic › peer-review

## Continuity of nonlinear eigenvalues in CD (K, ∞) spaces with respect to measured Gromov–Hausdorff convergence

Ambrosio, L., Honda, S. & Portegies, J. W., 1 Apr 2018, In : Calculus of Variations and Partial Differential Equations. 57, 2, 34.Research output: Contribution to journal › Article › Academic › peer-review

## Ergo learning

Portegies, J. W., Sep 2018, In : Nieuw Archief voor Wiskunde. 5th Series, Volume 19, 3, p. 199-205Research output: Contribution to journal › Article › Academic

## Courses

## Student theses

## A comparison of the Krasnoselskii spectrum and the homotopy significant spectrum

Author: Fokma, S. (., 6 Jul 2018Supervisor: Portegies, J. (Supervisor 1)

Student thesis: Bachelor

## Active learning in VAE latent space

Author: Tonnaer, L., 25 Sep 2017Supervisor: Menkovski, V. (Supervisor 1), Portegies, J. W. (Supervisor 2) & Holenderski, M. (Supervisor 2)

Student thesis: Master

## Computer programs for analysis

Author: Beurskens, T. P., 1 Jul 2019Supervisor: Portegies, J. W. (Supervisor 1)

Student thesis: Bachelor

## Convergence of several reinforcement learning algorithms

Author: Mohamed, A., 29 Oct 2018Supervisor: Portegies, J. W. (Supervisor 1)

Student thesis: Bachelor

## Differential equations driven by rough signals

Author: Verstraelen, L. H., 31 Aug 2018Supervisor: Prokert, G. (Supervisor 1) & Portegies, J. (Supervisor 2)

Student thesis: Bachelor