Machine learning in crowd modelling and simulation - MLCMS

Winter semester 2021-2022

Solutions of the exercises from the master-praktikum course at the department of informatics, Technische Universität München - TUM for group C

Exercise 1: Modelling of human crowds

Implementing a modelling software based in the Cellular automaton model

Implemented using Python and Pythons GUI library Tkinter

Exercise 2: Using and analysing simulation software

Getting to know an open source simulation software Vadere, developed at the Department of Computer Science and Mathematics at the Munich University of Applied Sciences.

Exercise 3: Dynamical systems and bifurcation theory

Examining the properties of dynamical systems and bifurcation theory along with the notion of chaos dynamics.

Exercise 4: Representation of data

Simplify n-dimensional data sets to a lower dimensional data set with minimum loss of information. Methods used in the exercise: Principal component analysis, Diffusion Maps and Variational autoencoder.

Exercise 5: Extracting dynamical systems from data

Using linear and nonlinear function approximation methods in order to approximate vector fields via data. Using Takens theorem describing a lower bound on how many time-embedded states needed in order to sufficiently describe a state space.

Final project: Learning dynamical systems from data, artificial neural network

Learning dynamical systems via neural networks, implemented using known numerical methods for solving ODEs: Eulers method and Runge-Kutta.