For centuries, the complex mathematics explaining the movement of liquids and gases, from air running through the wings of planes to turbulent oceans, have baffled the world’s most incredible minds. These principles are governed by the well-known difficult partial differential equation (or PDE), known as the Naviestokes equation, which continues to be one of the seven unresolved “millennium award problems” in mathematics.
Researchers at DeepMind, Google’s AI lab, are now demonstrating a new approach that brings fresh insights.
By training a type of AI known as graph neural networks in complex fluid flow simulations, the system was able to discover “surprising new solutions” to the problems of these century. According to the DeepMind team, this achievement comes when machine learning models were first used when they were used.”
This is not just a matter of academic curiosity. Experts say a deeper understanding of fluid dynamics can have a deeper global meaning and impact everything from aerodynamics and weather predictions to naval engineering and astrophysics.
The ability to model and forecast more accurately can lead to more fuel-efficient aircraft and automobile designs, the development of more accurate climate and weather models, and new innovations in numerous scientific and industrial fields.
At the heart of the task is a phenomenon known as a “singularity” or “explosion”, which can result in infinite amounts of velocity and pressure. Although they may seem abstract at first glance, these scenarios help scientists understand the fundamental limitations of equations. Deepmind AI is adept at identifying patterns of data that have led to the discovery of new families of these mathematical explosions, Google said.
The discovery of AI has been described as “more than just scientific curiosity,” and has since been “proven mathematically correct.” In the case of truth, it represents an important step towards how artificial intelligence can be applied to basic science. Rather than simply calculating numbers faster than a supercomputer, AI has acted as a creative partner, identifying subtle patterns that lead human mathematicians to verifiable discoveries.
The process involved training AI to find connections and behavior in fluid simulations that human observers might miss. According to Yongji Wang, the first author of the study and a postdoctoral researcher at NYU, “By embedding mathematical insights and achieving extreme accuracy, we transformed PINNs (physics-based neural networks) into discovery tools that find elusive singularity.
This collaborative approach, in which AI offers insights and directions that are rigorously proven by human experts, is hailed as a potential new paradigm of scientific research. This suggests a future where AI systems will work with scientists to tackle long-standing challenges in mathematics, physics and engineering so far out of reach.
The perfect solution to the Navier-Stokes equation remains a monumental challenge, but this breakthrough shows that artificial intelligence may be an important tool to ultimately crack it.
