navier–stokes 04/05Daniel Jonas Mielke
deep learning for physical simulation
M.Sc. Computer Science · AI & Data Science · HAW Hamburg
I write textbook-style posts on simulating physical systems with neural networks. Each idea in my posts is built up from intuition and interactive visualizations, and each post comes with practice cards to internalize the concepts.
$ cat posts/
// readRead the posts
Interactive, step-by-step explanations, from neural ODEs to the Navier–Stokes equations.
- posts
- 19
- series parts
- 14
- chapters
- 5
$ practice
// learnPractise what you read
Practise your learnings with spaced repetition before you forget it. No sign up required.
- cards
- 207
- posts covered
- 14
- concepts
- 97
Physics Simulation Series
start at part 01series · 14 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.
Differential equations
The wave equation
Numerical stability
Neural operators
The Navier–Stokes equations
the series is ongoing: new parts are added to the end of the path
every part so far has practice cards: practise the series →
Featured Posts
All 19 postsnavier–stokes 04/05
physics simulation 09/14Educational
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.
physics simulation 06/14Educational
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
Context-Parametric Inversion
NLP research project at UNSW: does fine-tuning LLaMA 3.1 8B on QASPER make a RAG pipeline for NLP papers ignore its retrieved context? A controlled faithfulness study across 14 fine-tuning checkpoints.
LLMLoRARAGNLPTessera
Built at the Mistral AI Worldwide Hackathon in Sydney: a voice-first health companion that runs daily check-ins by voice or phone, tracks symptoms with Mistral and writes doctor-ready PDF reports.
Mistral AIElevenLabspgvectorNext.jsExpressDual MIDI Transformer
A MIDI Event based transformer architecture, utilizing two separate transformers operating on the global MIDI events and local event parameters.
TransformerDecoderMIDIPyTorchMusic Generation Review
A literature review of AI music generation: audio tokenisation with VQ-VAEs and neural codecs, autoregressive transformers, diffusion approaches, and models such as YuE, MusicGen and Jukebox.
VQ-VAETransformerDiffusionAudioMoodWave
A real-time streaming pipeline correlating German news sentiment (GDELT) with Spotify Top 200 musical features, using Kafka and Spark Streaming for dual-stream aggregation.
KafkaSparkPySparkNext.jsSupabase
## Education
2024 — today
M.Sc. Computer Science · AI & Data Science
HAW Hamburg
- GPA 1.0
- Neural ODEs/PDEs & operators, transformers, VAEs, diffusion & flow matching
02/2026 — 07/2026
Postgraduate Exchange Semester Scholarship
UNSW Sydney
- Led a five-student NLP research project on LLM context faithfulness — High Distinction
2020 — 2024
B.Sc. Media Computer Science
University of Flensburg
- Programming, databases, artificial neural networks
## Experience
2025 — today
Working Student · AI & Data Science
Statista
- RAG systems, data automation pipelines, scraping & structuring
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
Deutschlandstipendium
Scholarship for Gifted and High-Achieving Students