Show HN: Unstable Singularity Detector update 1.4.1

Hi HN, I'm the author of this project.

Unstable Singularity Detector is an open-source implementation of a Physics-Informed Neural Network (PINN) system that detects blow-up singularities in PDEs — like those found in fluid dynamics.

It’s inspired by the methodology in a recent DeepMind paper, but fully independently built from scratch. The system predicts instability thresholds (lambda values), trains PINNs in multiple stages, and reaches machine-level residuals (10⁻¹³) using a high-precision Gauss–Newton optimizer.

This new v1.4.1 release adds: - Multi-stage PINN orchestration with FSDP and Meta/K-FAC support - Rank-1 Hessian + EMA for memory-efficient Gauss–Newton optimization - Residual certificate generation (CI-ready) - CLI bridge to external CFD solver output (e.g., `.npz` files) - Docker/Gradio support for easier setup

No signups, no cloud dependencies — everything runs locally (CLI, Docker, or Gradio).

GitHub: https://github.com/Flamehaven/unstable-singularity-detector Paper inspiration: https://arxiv.org/abs/2509.14185

Would love feedback from folks working on scientific computing, PDE solvers, numerical methods, or ML-based verification. I’m around for questions.