Show HN: Unstable Singularity Detector (github.com)

Unstable Singularity Detector is an independent, open-source re‑implementation of methods from the DeepMind paper "Discovering new solutions to century-old problems in fluid dynamics" (arXiv:2509.14185v1). The repo implements physics‑informed neural networks (PINNs) and the algorithmic pipeline for discovering unstable blow‑up solutions: empirical lambda‑prediction formulas (Fig.2e) with <1% error, an automatic funnel‑inference secant method for λ discovery, a multi‑stage training framework (coarse Adam → Fourier refinement → Gauss‑Newton), and a high‑precision Gauss‑Newton optimizer that uses a rank‑1 Hessian approximation and EMA smoothing. The project includes FP64/FP128 support, comprehensive unit tests (99/101 passing), CI reproducibility checks, Docker/Gradio demos, and detailed reproduction guides. Significance: this code exposes the core numerical and optimization primitives used to chase singular solutions with PINNs, making high‑precision techniques (residuals ≲10⁻¹³) and lambda discovery workflows accessible to the community. Key technical notes and caveats: lambda formulas match the paper very closely (IPM unstable λ ~0.4721297, ~0.005% diff), funnel inference typically converges in ~10–20 secant iterations, and the enhanced Gauss‑Newton attains machine‑level residuals on test problems. Limitations remain—no full 3D Navier–Stokes solver, no end‑to‑end detection of actual blow‑up solutions or computer‑assisted proofs, and validation is against published empirical formulas (not DeepMind’s private numerics). The repo is a useful, reproducible research platform but requires further peer review and PDE‑solver extensions for scientific claims.