Portrait of Daniel Jonas Mielke

Hey there, my name is Daniel,

a CS master's student in AI & Data Science at HAW Hamburg.

Welcome! Here you'll find my blog posts on the topics that interest me most: simulating physical systems through neural networks as PDE approximators. My posts focus on the intersection of physics, mathematics, and machine learning by explaining the underlying concepts in a way that is accessible to everyone through intuition and visualizations of the given topics.

Physics Simulation Series

start at part 01

series · 13 parts · 5 chapters

From Neural ODEs to Navier–Stokes

Every part of this series builds on the one before it, nothing is used before it has been explained.

  1. Differential equations

    1. 01ODEs & Neural ODEsnext
    2. 02PDEs & Neural PDEs
  2. The wave equation

    1. 03Deriving the wave equation
    2. 04A neural wave solver
  3. Numerical stability

    1. 05Von Neumann analysis
    2. 06The CFL condition
  4. Neural operators

    1. 07Neural operators & DeepONet
    2. 08The Fourier transform
    3. 09Fourier Neural Operators
  5. The Navier–Stokes equations

    1. 10The material derivative
    2. 11Conservation of mass
    3. 12Forces on a fluid parcel
    4. 13Putting the equations together

the series is ongoing: new parts are added to the end of the path

Featured Posts

All 18 posts
The pressure field adjusting itself to satisfy the incompressibility constraintnavier–stokes 04/04
Educational

Putting the Navier–Stokes Equations Together: The Pressure Poisson Equation

Diagram of the Fourier Neural Operator architecture with lifting, Fourier layers and projectionphysics simulation 09/13
Educational

Fourier Neural Operators (FNOs)

A step by step guide through the architecture of Fourier Neural Operators, their applications, and how they efficiently process global information through the Fourier transform.

Stable and unstable numerical wave solutions on either side of the CFL limitphysics simulation 06/13
Educational

The CFL Condition of the Wave Equation

A deep dive into the Von Neumann stability analysis of the wave equation and its connection to the CFL condition.

Projects

## Education

  1. 2024 — today

    M.Sc. Computer Science · AI & Data Science

    HAW Hamburg

    • GPA 1.0
    • Neural ODEs/PDEs & operators, transformers, VAEs, diffusion & flow matching
  2. 02/2026 — 07/2026

    Postgraduate Exchange Semester Scholarship

    UNSW Sydney

    • Led a five-student NLP research project on LLM context faithfulness — High Distinction
  3. 2020 — 2024

    B.Sc. Media Computer Science

    University of Flensburg

    • Programming, databases, artificial neural networks

## Experience

  1. 2025 — today

    Working Student · AI & Data Science

    Statista

    • RAG systems, data automation pipelines, scraping & structuring
  2. 2021 — 2025

    Working Student · Fullstack Development

    Jung von Matt TECH, SOFTSTACK, Events United

    • 4+ years of fullstack engineering — projects for dfb.de, bmw.com and more

## Honors

  1. Deutschlandstipendium

    Scholarship for Gifted and High-Achieving Students