Breakthrough method links AI with mathematics and physics
A novel use of Physics-Informed Neural Networks has led to the discovery of new singularities in fluid dynamics, reshaping approaches to mathematical research.
Researchers have introduced a new AI-driven method that could help solve long-standing mathematical problems in fluid dynamics, physics, and engineering. The study examines unstable singularities, where equations fail and predict impossible results like infinite pressure or velocity.
Using Physics-Informed Neural Networks, the team discovered new unstable singularities across three fluid equations, including the Navier–Stokes system. Their findings reveal emerging patterns that could point to even more elusive solutions, advancing understanding of fluid motion.
The method combines deep mathematical knowledge with machine learning techniques, enabling precision at levels previously unattainable. For example, researchers reduced computational errors to a scale comparable with measuring the Earth’s diameter within just a few centimetres.
Such accuracy is essential for building reliable computer-assisted proofs in mathematics.
The study, carried out with mathematicians and geophysicists from leading universities, signals a shift in mathematical research. By embedding physics directly into neural networks, the approach transforms AI into a discovery tool that may reshape how complex equations are tackled in the years ahead.
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