- Earlier this year, DeepMind published groundbreaking work on detecting unstable

singularities in fluid dynamics—one of the deepest open problems in mathematical

physics (arXiv:2509.14185).

- The challenge? No public code. - Extreme numerical precision requirements. - Complex multi-stage training. This makes independent verification nearly impossible. - So I built an open-source re-implementation to bridge that gap.

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### What It Does

Detects finite-time blow-ups in PDEs using Physics-Informed Neural Networks:

- Lambda prediction formulas (<1% error vs. published methodology) - Automated parameter discovery via funnel inference - High-precision Gauss-Newton optimization (residuals to 10⁻¹³) - Multi-stage training with configurable precision targets

Think: Making century-old fluid dynamics problems tractable with modern ML.

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### Who This Is For

- Researchers studying singularities in PDEs - Practitioners working with PINNs - Anyone frustrated by non-reproducible ML papers - Students learning scientific machine learning

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### Built For Reproducibility

- 119 comprehensive tests (all passing) - GPU-accelerated with PyTorch + CUDA - Automated validation CI/CD - Professional documentation + limitations clearly stated - Not just "research code"—designed to actually work in other people's hands.

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### Current Implementation Status

- Lambda prediction formulas (formula-based validation) - Funnel inference (secant method) - Enhanced Gauss-Newton optimizer (test problem verified) - PINN solver framework - Multi-stage training (framework complete, full validation pending) - Full 3D Navier-Stokes solver (future work) - Transparency matters: This shows exactly what works today vs. what's roadmap.

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### Links

GitHub: https://github.com/Flamehaven/unstable-singularity-detector

Paper: https://arxiv.org/abs/2509.14185

Documentation: README includes limitations, validation methodology, troubleshooting

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### Important Disclaimer

This is an independent re-implementation inspired by DeepMind's published

methodology. It is NOT affiliated with, endorsed by, or in collaboration

with DeepMind. Results are validated against published formulas, not

direct comparison with DeepMind's unpublished experimental data.

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If you've ever wished "I wish I could just run their code," this is for you.

Contributions, issues, and feedback welcome. Let's make frontier research

more accessible together.