Agent-based parametric semiology
Enhancing parametricism and semiology, architectural terms coined by
Patrik Schumacher, with agent-based simulations and preditions.

The main output is a statistical interpretation of pedestrian movement patterns in indoor office spaces. Website

The main output is a statistical interpretation of pedestrian movement patterns in indoor office spaces. Website

Minimal surfaces
A non-iterative solver for minimal (soap-film) surfaces .... these are
solutions to nonlinear PDEs but here is a solution that quickly and non-iteratively
generates a
Rhino CAD minimal surface approximation.
Github

Karamba 3d
A parametric structural engineering tool by Clemens Preisinger et al. I am
helping to rewrite the mesher.
Website

Understanding the variance of machine learning error algorithm's error
estimates
has been my main interest in pure statistics. In particular, a goal of
this work is to set up a rigorous framework for error rates in machine learning.
Paper

Test set size in simulation studies on supervised learning
A tool which computes the optimal test set size in simulation studies on
supervised machine learning
Github

Minimization and estimation of the variance of prediction errors for
cross-validation designs
Machine learning theory. We present a general framework for computing
quickly the theortically guaranteed best estimator of the machine learning
generalizytion
error
and its variance.
Paper

R-package confintvar
The variance estimator of a sample tells you how much the data vary ....
but how much does that variance estimator vary around the true variance? This R-package
for
computation of exact confidence intervals of the variance estimator, without normality
assumption on the underlyingdistribution, tells you.
CRAN

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.
Project
Proposal

Geometry and shell structures
Rhino3d grasshopper plugin that designs membranes in real-time and computes
approximate solutions to the classical Poisson problem of PDE theory, using a complex
analysis-based
algorithm instead of a direct matrix method.

A spatial process interpretation of pedestrian indoor tracks
learn simulated and observed pedestrian flows as spatial processes, and
extrapolating them in real-time to new geometries.

Predicting pedestrian density flow - Real-time occupation modelling in
Rhino

A spatial visualisation of pedestrian tracks and density

Real-time prediction of tracks

Non-stationary heat diffusion

Computational fluid dynamics - port of classical code by Stam, Taxen, Nealen to
modern fftw3

A simple

shape recognitionof a 2D office layout by the straight skeleton

Wrapping mmgtool for Rhino3d