Mass, energy, and speed. Einstein's equation is made up of these variables. Einstein knew about these concepts in the beginning. Identifying relevant variables is a part of understanding physics. Einstein wasn't able to discover relativity without the concept of mass and energy. Is it possible to discover such variables automatically? It could speed up scientific discovery.
Researchers at Columbia Engineering asked a new question. After observing physical phenomena through a video camera, the program tried to find the minimal set of fundamental variables that describe the observed dynamics. The study was published in a scientific journal.
The researchers fed the system raw video footage of phenomena that they already knew what to do. They fed a video of a swinging double pendulum, which has four state variables, the angle and angular velocity of each arm. The answer was given after a few hours of analysis.
The director of the Creative Machines Lab in the department of mechanical engineering thought the answer was close enough. There was no knowledge of physics or geometry in the raw video footage. We wanted to know what the variables were.
The variables that the program identified were visualized by the researchers. The program can't describe the variables in a way that would be understandable to humans, so it's hard to extract them. Two of the variables the program chose seemed to correspond to the angles of the arms, but the other two remained a mystery.
The work was led by Boyuan Chen who is now an assistant professor at Duke University. It didn't seem to match perfectly. He explained that the team was confident that the artificial intelligence had found a valid set of four variables, but they didn't know the mathematical language it was speaking.
The researchers fed the videos of the systems they did not know the answer to. The first videos had an air dancer in front of a car lot. The program returned eight variables after a short time of analysis. Eight variables were created by a video of a lava lamp. The program returned 24 variables after they fed a video clip of flames from a fireplace.
There was a question of whether the set of variable was unique for every system or if a different set was produced each time the program was started.
If we ever met an intelligent alien race, would they have discovered the same physics laws as we have, or a different way of describing the universe? We are trying to understand phenomena using the wrong variables. The number of variables was the same for each restart but the specific variables were different. There are alternatives to describe the universe and it is possible that our choices aren't perfect.
The researchers think that this type of artificial intelligence can help scientists uncover complex phenomena for which theoretical understanding is not keeping up with the amount of data. "While we used video data in this work, any kind of array data source could be used," said Kuang Huang, who co-authored the paper.
The work is part of the research done by the Professor of Mathematics at the Fu Foundation. If the variables were identified in advance, past software systems like Lipson and Eureqa could distill freeform physical laws. What if the variables aren't known?
According to Lipson, scientists may be misinterpreting phenomena because they don't have a good set of variables to describe them.
"For thousands of years, people knew about objects moving quickly or slowly, but it was only when the idea of speed and acceleration was quantified that the famous law of motion was discovered," he said. Variables describing temperature and pressure need to be identified before the laws of thermodynamics can be codified. Any theory can be traced back to the variables.
"What other laws are we missing because we don't have the variables?" asked Du.
The data for the experiments was collected by Sunand and Ishaan Chandratreya.
More information: Boyuan Chen et al, Automated discovery of fundamental variables hidden in experimental data, Nature Computational Science (2022). DOI: 10.1038/s43588-022-00281-6 Journal information: Nature Computational Science
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