Introduction to Spatiotemporal Modeling and Simulation

This course teaches modeling techniques for spatially resolved systems. You will learn to account for the geometry of a system and for transport in space. After repetition of the basics from mathematics and physics, you will model processes such as diffusion and flow, and simulate them in the computer.

dimensionality analysis, causality diagrams, vector fields, particle methods, governing equations for diffusion and flow, hybrid particle-mesh methods for computer simulations, student project: simulation of a biological system.

Topic Prerequisites

Working knowledge of computer programming in any language (e.g. Matlab, Python, Java), basic knowledge of classical physics, and solid undergraduate knowledge in calculus and vector analysis.

Format

2 SWS lecture, 2 SWS exercise, self-study

Programs / Modules

M.Sc. Computational Modeling and Simulation: Module CMS-CLS-MOS

Registration to the course

For students of the Master program Computational Modeling and Simulation: via CampusNet SELMA

For ERASMUS and exchange students: via the Computer Science examination office

Teachers

Lecture: Dr. Nandu Gopan, Prof. Ivo F. Sbalzarini
Exercises: Serhii Yaskovets

Learning goals

Analysis of the dynamic behavior of biological or physical systems with spatial structure
Formulation of a model of the system behavior
Computer simulation of the model using numerical methods

Special remarks

We focus on biological systems. The taught methods and concepts are, however, applicable in a much broader sense.

Lecture language: ENGLISH

Script

Full lecture notes can be found here: Script (PDF).

Project

The student project will aim at implementing the Quorum Sensing model proposed by J. Müller et al. as described in this publicly available preprint. The final version of the paper is available from Springer Link with university access.

Time/Place

Summer Term 2024

Lecture: Tuesdays, 14:50-16:20h, APB E/010/U. LECTURES START ON APRIL 9,2024.
Exercises: Tuesdays, 16:40-18:10h, APB E/010/U. NO TUTORIAL IN THE FIRST WEEK. EXERCISES START ON APRIL 16, 2024.
LECTURES AND EXERCISES WILL BE IN PRESENCE FOR THE WHOLE SEMESTER, BUT SUPPORTED WITH ONLINE VIDEO RECORDINGS

Link to the videos in OPAL: https://bildungsportal.sachsen.de/opal/auth/RepositoryEntry/33993129986

Exam 2024

TBA

Grade scale:

All exams are graded in absolute terms w.r.t. the following pre-defined grade scale that remains constant over the years:

The top grade of 1.0 is reached with 80% of the maximum possible points
Half of that, i.e., 40% of the maximum possible points, amount to a grade of 4.0.
Below 40%, or no-show, is a fail.

Between the top grade and the passing threshold, the grading scale is linear. In the end, grades are rounded to the nearest allowed grade according to the exam regulations: 1.0, 1.3, 1.7, 2.0, 2.3, 2.7, 3.0, 3.3, 3.7, 4.0, 5.0. The grades 0.7, 4.3, and 4.7 are not allowed. Any grade above 4.1 is rounded to 5.0 (see exam regulations). The maximum number of points that can be reached in the exam is given by the number of minutes the exam lasts (i.e., a 120 minute exam yields maximum 120 points). Points are distributed amongst the exam questions to reflect the number of minutes a good student would need to solve the problem. This provides some guidance for your time management in the exam. In order to reduce the risk of correction mistakes, all exams are checked by at least two independent, qualified assessors (typically professors or teaches with officially conferred examination rights). The exam review session (see below) is for you to come look at your exam paper and report correction mistakes you found.

Registration to the exam

For students of the Master program Computational Modeling and Simulation: via CampusNet SELMA
For students of other degree programs: via your respective examination office
For ERASMUS and exchange students: via the Computer Science examination office

Lecture syllabus/Handouts

Lecture 1 - Administration and Introduction
Lecture 2 - Dimensional Analysis
Lecture 3 - Modeling Dynamics: Reservoirs and Flows
Lecture 4 - Recap on Vector Calculus
Lecture 5 - Conservation Laws and Control Volume Methods
Lecture 6 - Particle Methods
Lecture 7 - Diffusion
Lecture 8 - Reaction-Diffusion
Lecture 9 - Advection-Diffusion
Lecture 10 - Flow
Lecture 11 - PDEs
Lecture 12 - Discussion on Data Driven Simulations
Lecture 13 - Discussion on Data Driven Simulations