Latent embeddings from our framework colored by physical state variables. Credit: Boyuan Chen/Columbia Engineering
A new Columbia University artificial intelligence program observes physical phenomena and reveals the relevant variables—a necessary precursor to any theory of physics. But the variables he found were unexpected.
Energy, mass, velocity. These three variables make up Einstein’s iconic equation E=MC2. But how did Albert Einstein know about these concepts in the first place? Before understanding the physics, you need to identify the relevant variables. Even Einstein could not have discovered relativity without the concepts of energy, mass and velocity. But can variables like these be detected automatically? This would greatly speed up scientific discoveries.
That’s the question Columbia Engineering researchers asked a new artificial intelligence program. The AI program is designed to observe physical phenomena through a video camera and then try to search for the minimal set of fundamental variables that fully describe the observed dynamics. The research was published in the journal Nature Computational Science on July 25.
The image shows a chaotic dynamic system with a rotating rod in motion. Our work aims to identify and extract the minimum number of state variables needed to describe such a system directly from large-scale video recordings. Credit: Yinuo Qin/Columbia Engineering
The scientists began by feeding the system raw video footage of physical phenomena for which they already knew the solution. For example, they played a video of a swinging double pendulum, which is known to have exactly four “state variables” – the angle and angular velocity of each of the two arms. After several hours of analysis, the AI came up with its answer: 4.7.
“We thought that answer was close enough,” said Hod Lipson, director of the Creative Machines Lab in the Department of Mechanical Engineering, where most of the work was done. “Especially since all the AI had access to was raw video footage, with no knowledge of physics or geometry. But we wanted to know what the variables actually were, not just their number.
The researchers then went on to visualize the actual variables the program identified. Extracting the variables themselves was difficult because the program could not describe them in any intuitive way that would be understandable to humans. After some research, it turned out that two of the variables selected by the program corresponded to the angles of the hands, but the other two remained a mystery.
“We tried to map the other variables to anything and everything we could think of: angular and linear velocities, kinetic and potential energy, and various combinations of known quantities,” explained Boyuan Chen PhD ’22, now an assistant professor at Duke University who led the work. “But nothing seemed to match perfectly.” The team was confident the AI had found a valid set of four variables because it was making good predictions, “but we still don’t understand the mathematical language it’s speaking,” he explained.
Boyuan Chen explains how a new artificial intelligence program observes physical phenomena and reveals the relevant variables—a necessary precursor to any theory of physics. Credit: Boyuan Chen/Columbia Engineering
After validating a number of other physical systems with known solutions, the scientists entered videos of systems for which they did not know the explicit answer. One of those videos featured an “air dancer” undulating in front of a local used car lot. After several hours of analysis, the program returned 8 variables. Likewise, a Lava Lamp video also produces 8 eight variables. When given a video of flames from a holiday fireplace, the program returned 24 variables.
A particularly interesting question was whether the set of variables was unique for each system, or whether a different set was produced each time the program was restarted. “I’ve always wondered, if we ever encountered an intelligent alien race, would they discover the same physical laws as us, or would they be able to describe the universe differently?” Lipson said. “Perhaps some phenomena seem enigmatically complex because we are trying to understand them using the wrong set of variables.”
In the experiments, the number of variables was the same each time the AI restarted, but the specific variables were different each time. So yes, there are indeed alternative ways of describing the universe, and it’s entirely possible that our choices aren’t perfect.
According to the researchers, this kind of AI could help scientists unravel complex phenomena for which theoretical understanding has not kept pace with the deluge of data — fields ranging from biology to cosmology. “While we used video data in this work, any kind of array of data sources could be used—radar arrays or DNA arrays, for example,” explained Dr. Kuang Huang ’22, who co-authored the paper.
The work is part of the Lipson Foundation Professor of Mathematics and Fu Qiang Du’s decades-long interest in creating algorithms that can distill data into scientific laws. Past software systems, such as Lipson and Michael Schmidt’s Eureqa software, could distill free-form physical laws from experimental data, but only if the variables were identified in advance. But what if the variables are still unknown?
Hod Lipson explains how the AI program was able to discover new physical variables. Credit: Hod Lipson/Columbia Engineering
Lipson, who is also the James and Sally Scapa Professor of Innovation, argues that scientists may misinterpret or misunderstand many phenomena simply because they don’t have a good set of variables to describe the phenomena. “For millennia people knew about objects moving fast or slow, but it wasn’t until the concept of speed and acceleration was formally quantified that Newton was able to discover his famous law of motion F=MA,” noted Lipson. The variables describing temperature and pressure had to be identified before the laws of thermodynamics could be formalized, and so on for every corner of the scientific world. Variables are the precursor to any theory. “What other laws are we missing simply because we don’t have the variables?” asked Du, who led the work.
The paper was also co-authored by Sunand Raghupathi and Ishaan Chandratreya, who helped collect the data for the experiments. As of July 1, 2022, Boyuan Chen is an assistant professor at Duke University. The work is part of a joint University of Washington, Columbia and Harvard NSF Dynamical Systems Institute aimed at accelerating scientific discovery using AI.
Reference: “Automated Discovery of Fundamental Variables Hidden in Experimental Data” by Boyuan Chen, Kuang Huang, Sunand Raghupathi, Ishaan Chandratreya, Qiang Du, and Hod Lipson, 25 July 2022, Nature Computational Science.DOI: 10.1038/s43588-022 -00281- 6
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