AI Solves a Century-Old Navier-Stokes Problem
AI Solves Navier-Stokes: A Scientific Leap (Banner).
Introduction to Navier-Stokes
The Navier-Stokes equations are the real textbook of fluid dynamics. They tell us how things like air, water, and gas (i.e. fluids) move and collide. These formulas have everything—how fast, how much pressure, what temperature, and how heavy the object is. The crazy swirl of air around the wings of a plane, or the huge waves and weather that form at sea—these are the Navier-Stokes equations behind it all.
But for more than a hundred years, the smartest people have not been able to find a clear and precise solution to these equations. Often, these equations tell us about strange things called singularities—that is, there are some places where the pressure or speed suddenly reaches the sky. But then again, these things corrupt all the formulas, making them difficult to trust. That's why this problem was considered the biggest puzzle in mathematics. Since this problem was so big and difficult, it was included in the seven Millennium Prize Problems. Whoever finds a general solution to it will receive a million dollars. If we understand these formulas completely, many fields will be shaken up—for example, in making airplanes, in calculating the weather, in the science of the depths of the sea and space. We will get extremely powerful control over the work of fluids.
What AI Did
DeepMind utilized Physics-Informed Neural Networks (PINNs) to solve complex fluid dynamics problems.
The Deep Minds recently tried a new approach to this century-old dispute. Leaving aside the old-fashioned stubborn mathematical solutions or the sleight of hand of supercomputers, they brought AI into the middle. Specifically, they used physics-informed neural networks (PINNs)—AI that has the laws of physics already built into it. Normal machine learning models, right? They learn by looking at a bunch of data. But PINNs were designed to understand the fundamental relationships of physics on their own. They did this by constantly checking their answers against the laws of physics and minimizing the variance. This time, the AI was “trained” directly on the Navier-Stokes equations, repeatedly asking them to check what the physics said.
In the midst of all this, the AI went all out and came up with entirely new types of singularities—solutions that humans had never seen before. The surprise wasn’t just this discovery, but what happened next was also amazing. Math professors from the world's top universities came to verify the answers themselves, saying that the AI's solutions were robust, correct, and mathematically accurate.
Key Discoveries
The biggest discovery made by the DeepMind team is that they found entirely **new solutions** for such a big and difficult equation as **Navier-Stokes**. These were solutions that the world's greatest mathematicians had failed to find for the past century. These solutions are difficult to observe easily; they are very **delicate** and **unstable**. By finding them, the AI has opened the way to understanding the hidden holes or **Singularities** that can create unexpected and large distortions in the flow of water or air (Fluid motion). Scientists believe that these new solutions will tell us how large **storm waves** and **agitation (Turbulence)** are created and how they disappear. This was a major mystery that affects everything from the movement of spaceships to the processes in the depths of the ocean.
Practical Implications
These discoveries are far more important than just calculations. They will have a huge impact on the real world of engineering, environmental science, and astrophysics. In meteorology, having models that better understand fluid motion will allow us to better predict the weather and prepare for disasters. We will be able to predict storms, floods, and hurricanes with greater accuracy. In the field of aircraft design, understanding how this turbulence is created and operates will lead to safer, more fuel-efficient aircraft that burn less gasoline and emit less smoke.
In space science, these findings will explain how gases around stars, planets, and black holes behave. By understanding how these cosmic fluids flow under high pressure and heat, scientists can fine-tune their simulations of how planets form, how galaxies move, and other space phenomena. There’s also good news for industries—especially in pipelines, ship design, and power systems—where fluid motion determines safety, efficiency, and budget.
A New Era for Science
The collaboration between human researchers and AI marks a new chapter in scientific discovery.
Perhaps the greatest gift of DeepMind’s research is this: AI is no longer just a calculating machine, but is becoming a regular research partner. This work makes it abundantly clear that AI can do more than just sift through old data; it can also create brand-new, sophisticated mathematical knowledge—something we once thought only humans could do. Now that we combine our sixth sense (conscience) with the superfast accuracy of AI, researchers can penetrate areas of mathematics and physics that were previously impossible to reach. AI can pick out hidden things from a vast ocean of millions of possible solutions that elude our eyes, and then tell us where we should focus our next research efforts. This collaboration is a whole new chapter in computer-aided discovery. Here, human brains and machine intelligence are working together to solve problems that have defied centuries of effort. It opens the door to great new work everywhere—from theoretical physics and meteorology to engineering and cosmology.
A century-old mystery of fluid dynamics—once thought impossible—has now been cracked open by artificial intelligence. Using these physics-informed neural networks, DeepMind’s AI has done what generations of mathematicians have failed to do: find completely new, proven solutions to one of the most complex systems in science. This isn’t just a technological triumph; it’s a major intellectual leap in how we acquire knowledge. As AI advances, its power to unlock the secrets hidden in the laws of nature could change everything—whether it’s the way we predict the weather or explore the stars.
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What was once impossible is, in fact, now possible—and it heralds a new era of scientific discovery powered by human ideas and AI working together.
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