Deep Learning Poised to ‘Blow Up’ Famed Fluid Equations | Quanta Magazine

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near.

**Hasnain says:**

“Unlike traditional neural networks, which get trained on lots of data in order to make predictions, a “physics-informed neural network,” or PINN, must satisfy a set of underlying physical constraints as well. These might include laws of motion, energy conservation, thermodynamics — whatever scientists might need to encode for the particular problem they’re trying to solve.

Injecting physics into the neural network serves several purposes. For one, it allows the network to answer questions when very little data is available. It also enables the PINN to infer unknown parameters in the original equations. In a lot of physical problems, “we know roughly how the equations should look like, but we don’t know what the coefficients of [certain] terms should be,” said Yongji Wang, a postdoctoral researcher in Lai’s lab and one of the new paper’s co-authors. That was the case for the parameter that Lai and Cowen-Breen were trying to determine.”