DAMSL-210 Modeling in Physical Sciences

Type

Elective

Course Code

DAMSL-210

Teaching Semester

B Semester

ECTS Credits

Lab assignments, Course project, Final exam

Models and their derivation. Dimensional analysis. Examples.
Population (Logistic, Lotka-Volterra) and disease spreading (SIR) models. Numerical solution of the models.
Hamiltonian systems (discrete and continuous). Klein-Gordon equation.
The Schrödinger equation and the Gross-Pitaevskii model.
Diffusion equation, derivation, properties, diffusion in the presence of constant force.
Deterministic – Stochastic systems. Modeling of deterministic systems: Molecular dynamics simulations. Dynamics of stochastic systems: Langevin, Brownian dynamics.
Introduction to Monte Carlo methods. Monte Carlo algorithms of importance sampling.
Markovian chains. Metropolis – Hastings type algorithms. Examples.
Molecular simulations and multi-scale modeling of complex systems
Data-driven models and Machine Learning algorithms for complex systems
Hybrid physics-based data-driven models
Advanced Topics: Reaction diffusion systems

After the successful completion of the course the students will be able to:

Understand the structure of mathematical models for discrete and continuous systems, which appear in Physics, Material Science, Biology and Engineering sciences.
They will be able to construct mathematical models for similar problems
They will be able to use modern simulation methods, algorithms for data analysis and machine learning widely used for the solution of these models
Be in position to search for solutions to these models with analytical and computational tools
They will be able to interpreter and explain the characteristics of the obtained solution with the respect to the origins of the models and its correspondence to the physical problem