Robotics discover alternative physics

Energy, mass, speed. These three variables make up the iconic Einstein equation E=MC^two. But how did Einstein know about these concepts in the first place? A previous step to understanding physics is the identification of relevant variables. Without the concept of energy, mass, and speed, not even Einstein could discover relativity. But can those variables be discovered automatically? If he does so, he could greatly speed up scientific discovery.

This is the question Columbia Engineering researchers posed to a new AI program. The program was designed to observe physical phenomenon through a video camera, then try to find the minimum set of fundamental variables that fully describe the observed dynamics. The study was published on July 25 in Nature Computer Science.

The researchers began by feeding the system raw video footage of phenomena for which they already knew the answer. For example, they fed a video of a swinging double pendulum that is known to have exactly four “state variables”: the angle and angular velocity from each of the two arms. After a few hours of analysis, the AI ​​produced the answer: 4.7.

“We thought this answer was close enough,” said Hod Lipson, director of the Creative Machines Laboratory in the Department of Mechanical Engineering, where the work was primarily done. “Especially since the AI ​​only had access to raw video footage, without any knowledge of physics or geometry. But we wanted to know what the variables actually were, not just their number.”

The researchers then proceeded to visualize the actual variables identified by the program. Extracting the variables themselves was not easy, as the program cannot intuitively describe them in a way that is understandable to humans. After some testing, it seemed that two of the variables the program chose vaguely corresponded to the angles of the arms, but the other two remain a mystery.

“We tried to correlate the other variables with everything we could think of: angular and linear velocities, kinetics and potential energyand various combinations of known quantities,” explained Boyuan Chen Ph.D., now an assistant professor at Duke University, who led the work. “But nothing seemed to match perfectly.” The team was confident that the AI ​​had found a set of four variables, since he was making good predictions, “but we still don’t understand the mathematical language he’s speaking,” he explained.

After validating a number of other physical systems with known solutions, the researchers fed in videos of systems for which they didn’t know the explicit answer. Early videos featured an “air dancer” undulating in front of a local used car lot. After a few hours of analysis, the program returned eight variables. A video of a lava lamp also produced eight variables. They then fed a video clip of flames from a Christmas fireplace loop, and the program returned 24 variables.

A particularly interesting question was whether the set of variables was unique to each system or whether a different set was produced each time the program was restarted.

“I always wondered, if we ever met an intelligent alien race, would they have discovered the same physical laws as us, or might they describe the universe in a different way?” Lipson said. “Perhaps some phenomena seem puzzlingly complex because we’re trying to understand them using the wrong set of variables. In the experiments, the number of variables was the same each time the AI ​​was restarted, but the specific variables were different each time. So yes, there are alternative ways to describe the universe and our choices may very well not be perfect.”

The researchers believe that this type of AI can help scientists discover complex phenomena for which theoretical understanding is not keeping pace with the flood of data, areas ranging from biology to cosmology. “While we used video data in this work, any type of array data source could be used: radar arrays or DNA arrays, for example,” explained Kuang Huang, Ph.D., a co-author on the paper.

The work is part of Lipson and Fu Foundation Professor of Mathematics Qiang Du’s decades-long interest in creating algorithms that can distill data into scientific laws. Earlier 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?

Lipson, who is also the James and Sally Scapa Professor of Innovation, argues that scientists may be misunderstanding or failing to understand many phenomena simply because they don’t have a good set of variables to describe the phenomena.

“For millennia, people knew about objects moving quickly or slowly, but it was only when the notion of velocity and acceleration was formally quantified that Newton was able to discover his famous law of motion F=MA,” Lipson noted. The variables describing temperature and pressure needed to be identified before the laws of thermodynamics could be formalized, and so on for all corners of the scientific world. Variables are a precursor to any theory.

“What other laws are we missing simply because we don’t have the variables?” asked Du, who co-led the work.

The paper was also co-authored by Sunand Raghupathi and Ishaan Chandratreya, who helped collect the data for the experiments.