What was already known
Earlier numerical work had found stable profiles and the first unstable CCF profile. Rigorous proofs for related stable blow-up profiles do not cover these new unstable families.
AI involvement
Physics-informed neural networks generated the retained profiles and scaling parameters. The researchers designed the equations, training and refinement process and analyzed the candidates.
The trained networks supplied new candidate profiles within a human-designed search and refinement method.
Importance
The numerical search adds candidate unstable profiles in several fluid models and improves their measured accuracy.
Limitations
Finite-grid tests do not prove that exact singular solutions exist. The 2D Boussinesq setting is related to 3D Euler with a boundary; this is not a Navier–Stokes result.
Technical verification
The authors tested finite-grid residuals and stability modes; exact existence was not rigorously certified.
Human understanding
The authors explain the self-similar equations, numerical search and stability analysis.
Correction and publication history
Numerical candidate profiles are distinct from proved fluid blow-up results and from the unvalidated fourth Boussinesq candidate.
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