A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.



A visual exploration of Gaussian Processes and Infinite Neural Networks

44 minute read


Gaussian Processes (GPs) generalize Gaussian distributions to random variables that are functions (stochastic processes). As such, they are a powerful tool for regression and Bayesian inference. In the past years, they have received increased attention due to the interest in machine learning. An intriguing connection between GPs and neural network exists when the width of layers in feed-forward neural networks tends towards infinity. For a specific choice of the prior distributions that governs the network parameters, the resulting network will be a GP.

An Introduction to Numerical Optimization with Python (Part 1)

13 minute read


This is the first post in a series of posts that I am planning to write on the topic of machine learning. This article introduces fundamental algorithms in numerical optimization. For now, this is the Gradient Descent and Netwon algorithm. I might extend it with momentum based methods and conjugate gradient methods in the future. All of the posts are essentially Jupyter notebooks that I will publish in this repository.




Large-Scale Tsunami Simulations using the Discontinuous Galerkin Method


Discontinuous Galerkin methods have desirable properties, which make them suitable for the com- putation of wave problems. Being parallelizable and hp-adaptive makes them attractive for the simulation of large-scale tsunami propagation. In order to retrieve such a scheme, we formulate the shallow water equations on the spherical shell and apply the discontinuous Galerkin discretiza- tion to construct a numerical method which is able to handle the effects of curvature and Coriolis forces naturally. Common challenges in solving the shallow water equations numerically are well- balancedness and wetting/drying. To overcome this, we utilize a method based on a timestep restriction, which guarantees the positivity of the numerical solution. Moreover, we show that our discretization yields a well-balanced numerical scheme. In this talk we will present our method as well as the numerical results, that we have obtained with our implementation.

Global-scale tsunami simulations using the discontinuous Galerkin method


We present a novel method for the simulation of large scale tsunami events using a high-order discontinuous Galerkin discretization of the spherical shallow water equations. This requires a well-balanced discretization, which cannot rely on exact quadrature, due to the curved mesh. We achieve this by splitting the well-balanced condition into individual problems for the flux and volume terms. As it turns out, this approach has significant advantages: It allows the construction of non-conforming, well-balanced flux discretizations. Thus we can perform non-conforming mesh refinement, all while preserving the well-balanced property of the scheme. More importantly, we are able to develop a new method for handling wet/dry transitions. In contrast to other wetting/drying methods, this method is well-balanced and able to handle wetting/drying at any order - all without the introduction of further model assumptions such as artificial viscosity, porosity or cancellation of gravity. We demonstrate our new method for both the one-dimensional and spherical shallow water equa- tions. In the latter case, we perform a simulation of the 2011 Tohoku tsunami and validate our results with real-world buoy data.

How we teach computers about the world and what we can learn from them.


While physics aims to describe nature in terms of mathematics, numerical mathematics aims to represent nature on a computer. This talk will show how we develop a computational model with the example of large-scale tsunami simulations. Finally, we will see how we can use these models to gain a better understanding of our world. Numerical mathematics brings together physics, computer science, engineering and of course, mathematics.


Teaching experience 2

Workshop, University 1, Department, 2015

This is a description of a teaching experience. You can use markdown like any other post.

Probability and Statistics

Undergraduate course, EPFL, Math department, 2019

Principal assistant for the course “Probabilité et Statistique”, teaching engineering students the fundamentals of probability theory and statistics.