Current projects

Here, I’ll be trying to tell a few words for each one out of my current research interests and activities apart from the pedestrian ones.

A spatial process interpretation of pedestrian indoor tracks

spatial density process visualisation in 2.5 dimensions: tracks and spatial usage from Mathias Fuchs on Vimeo.

Predicting pedestrian density flow

With spatstat, mongo, & Rhino. We learn simulated and observed pedestrian flows as spatial processes, and extrapolate them in real-time to new geometries, as a Rhino plugin that obtains its data live from a web-based mongo database. Stay tuned. This is a demonstration of the basic functionality as a Rhino plugin:

Real-time occupation modelling in Rhino from Mathias Fuchs on Vimeo.

Geometry and shell structures

I wrote a little grasshopper pluging that designs membranes in real-time. In particular, it computes an approximate solution to the classical Poisson problem of PDE theory, using a slightly different algorithm than the usual suspects such as either a direct matrix method, or . In other words, it returns an infinitely smooth surface from an (almost) arbitrary closed input curve in real time,. You can find the source code here. Please drop me a line for the compiled DLL.

Understanding the variance of machine learning error algorithm’s error estimates

… has been my main interest in pure statistics. In particular, one of my dreams is to generalise the computations we did in this paper to more general linear regressions.

Inferential statistics of stress states in rigid body continuum mechanics

Series of four finite element calculations of a 2d rectangular element under shear stress, subject to random perturbations in each iteration, with first and second principal stress lines in blue and orange (deformations not to scale). In this project, we develop a framework for statistical analysis of stress fluctuations as in this series. In each subfigure, the point at the centre is associated with a particular two-by-two Cauchy stress tensor. A component-wise averaging procedure, resulting in the two-by-two mean Cauchy stress is not an adequate averaging procedure because it disrespects the magnitudes of its eigenvalues, the principal stresses. However, we propose a methodology for averaging and comparing large numbers of perturbed stress samples, circumventing this problem. We thereby allow the researcher to compute measures for the degree of certainty of difference in means between two sets of samples. An important application is quality control of finite element simulations. .