Machine Learning Turns PDE Singularity Search Into Computer-Assisted Proof
Caltech applied math PhD candidate Yixuan Wang argues that high-precision computation can make singularity questions in nonlinear PDEs tractable only when it is tied to stability analysis and rigorous verification. In a Microsoft Research seminar on Navier-Stokes blowup and weak-solution nonuniqueness, Wang presents machine-learning tools such as PINNs, neural operators, and Kolmogorov–Arnold Networks as ways to discover candidate singular structures, not as substitutes for proof. His broader case is that numerics, analytical a posteriori estimates, and interval-certified computation must work together if singularities in systems such as Navier-Stokes are to be identified and verified.
Microsoft Research·May 26, 2026·13 min read
