Discovery of unstable singularities

In this talk I will explain how to construct numerically several new unstable singularities to certain equations in fluids (CCF, IPM, Boussinesq) using machine learning methods. Our approach combines curated machine learning architectures and training schemes with a high-precision Gauss-Newton optimizer, achieving accuracies that significantly surpass previous work across all discovered solutions, reaching near double-float machine precision, attaining a level of accuracy constrained only by the round-off errors of the GPU hardware, potentially leading to rigorous mathematical validation via computer-assisted proofs.