Erlangen AI Hub Seminar: Numerically verified proofs aided by machine learning, Daniel Platt

Many methods are available to approximately solve all sorts of equations: ODEs, PDEs, polynomial systems, algebraic equations. Through recent advances it has become possible to turn these approximate solutions into rigorous existence proofs in some cases. I will explain how numerically verified proofs work and present several examples of them: (1) to get started, the classical problem of root enclosures for polynomials in one variable; (2) the main example is the Nirenberg problem, where in arXiv:2602.12368 a PDE was solved using a PINN, and in arXiv:2603.29544 I proved that there exists a genuine solution to the PDE; (3) another small application that’s to be decided, possibly related to topological data analysis.

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