Discovering new solutions to century-old problems in fluid dynamics (deepmind.google)

Researchers from teams including Brown, NYU and Stanford announced a new AI-driven method that systematically discovers previously unknown families of unstable singularities (blow ups) in several foundational fluid equations. Using Physics-Informed Neural Networks (PINNs) enhanced with second-order optimizers and a high-precision training framework, the authors pushed residual minimization to near–machine precision and located unstable solutions across three equations (notably the Incompressible Porous Media and Boussinesq systems). They observed a striking pattern: the blow-up speed parameter λ plotted against the “order of instability” (the number of distinct deviation modes) falls along a line for two equations, suggesting many more unstable solutions with predictable λ values. Visualizations include vorticity fields and one-dimensional slices showing evolution toward higher instability. This work is significant because unstable singularities are believed to be central to open questions in fluid dynamics—most famously the Navier–Stokes Millennium Prize Problem—and yet are extremely delicate to find by conventional analysis. By embedding mathematical insight into PINN training and achieving unprecedented numerical accuracy (authors compare their largest corrected errors to predicting Earth’s diameter within centimeters), the project demonstrates a viable path for computer-assisted proofs and AI-augmented mathematical discovery. The approach extends PINNs beyond black-box PDE solvers into a tool for exploring the landscape of exotic, hard-to-detect solutions in physics and engineering.