TMA4320 – Introduction to Scientific Computing

Project Hand-ins (Spring 2024)

This repository contains the three project hand-ins for the course TMA4320 – Introduksjon til vitenskapelige beregninger at the Norwegian University of Science and Technology (NTNU).

The projects cover Monte Carlo methods, particle transport, and neural networks / transformers, and are implemented as Jupyter notebooks.

Authors

• Henrik S. Grønlund
• Magnus Ulmo Rønneseth
• Theodoros Xenakis

Spring 2024.

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Project Overview

The repository consists of three independent projects:

1. Monte Carlo Simulation of Polymer Folding

A Monte Carlo based study of polymer folding on a 2D lattice. The project introduces a numerical representation of polymers and applies stochastic sampling techniques to investigate polymer configurations and energy states.

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2. Transformer Model for Sequence Prediction

This project explores transformer-based neural networks for sequence prediction. A synthetic dataset is constructed, and a transformer model is trained to learn simple arithmetic relationships.

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3. Particle Transport with Ocean Currents

A numerical simulation of particle transport driven by ocean currents, motivated by real-world maritime and environmental applications. Particles are advected using velocity fields to study transport patterns.

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Code Structure

The repository contains the following notebooks:

• polymers_handin.ipynb – Monte Carlo simulations of polymer folding (Project 1)
• neuralnet_handin.ipynb – Transformer model for sequence prediction (Project 2)
• oceanparticles_handin.ipynb – Particle transport with ocean currents (Project 3)