The Holy Grail of Computational Science: How Fluid Neural Networks Push the Limits of Mathematics

The Holy Grail of Computational Science: How Fluid Neural Networks Push the Limits of Mathematics

Throwing pebbles into a flowing stream of water may not change the flow pattern significantly. But throwing the pebble elsewhere can make a big difference. Who can make predictions?

Answer:Neural NetworksCan.California Institute of Technology, Pasadena, USA(California Institute of Technology, Caltech)of computer scientists and mathematicians, by showing that neural networks can teach themselves howSolve a broad class of fluid flow problems faster and more accurately than any previous computer programfor artificial intelligence(AI)opened up a new stage.

Professor of Computational and Mathematical Sciences, Scientific Artificial Intelligence at Caltech(AI4Science)Co-leader Animashree Anandkumar said: “When our group got together two years ago, we discussed which fields of science were ripe for AI to disrupt. We thought that if we could identify a robust framework for solving partial differentials equation, then we can have a broad impact.”

Their first goal isTwo-dimensional Navier-Stokes equations(Navier-Stokes equation),This equation describes the motion of an infinitely thin layer of water(figure 1).their neural network(They call it a “Fourier Neural Operator”)when solving such problemsits performance(400 times faster and 30% more accurate)Significantly better than any previous differential equation solver.

The water flows in flakes above the fountain. The neural network predicts this two-dimensional fluid flow faster and more accurately than computer programs that solve differential equations using standard methods, reports the Caltech Scientific Artificial Intelligence team. They go on to conduct experiments in three-dimensional fluid flow that could have broad implications for advancing science through improved modeling of natural phenomena such as nuclear fusion. Image source: Pixabay (public domain)

Partial Differential Equations(PDE)It is a class of equations that arise naturally from Newton’s laws of motion. To this end, partial differential equations are the foundation of science, and any significant progress in solving these equations has widespread implications. Anandkumar said: “We are in discussions with many teams in various industries, as well as in academia and national laboratories. We are already conducting experiments in three-dimensional fluid flow.”

Anandkumar says a good use case isFusion Modeling Equations. She added: “Another application case is material design, especially plastic and elastic material design. The team member, Kaushik Bhattacharya, professor of mechanics and materials science, has extensive experience in this field.”

During World War II, computers came into being in part because of the use of differential equations to predict the motion of artillery shells. Since then, computers have been used to solve differential equations with a certain degree of accuracy and success. But previous approaches, whether involving traditional computer programming or artificial intelligence, have always dealt with only one equation at a time. For example, a computer can figure out how a pebble thrown in one spot affects the flow of water. The computer can then learn how pebbles thrown elsewhere change the flow of water.But the computer doesn’t go any further to understand how a pebble thrown anywhere changes the flow of water. That’s the grand goal behind the Fourier Neural Operator at Caltech.

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Published on 08/28/2022