Engineering robotics discover alternative physics

The first step to understanding physics is to identify the relevant variables. Columbia Engineers developed an AI program to address a longstanding problem: is it possible to identify state variables only from high-dimensional observational data. Using video footage of various physical dynamic systems, the algorithm discovers the intrinsic dimensions of the observed dynamics and identifies a candidate set of state variables — with no prior knowledge of the underlying physics.

Energy, Mass, Speed. These three variables make up Einstein’s iconic equation E=MC². But how did Einstein know about these concepts? The first step to understanding physics is to identify the relevant variables. Without the concepts of energy, mass, and velocity, even Einstein could not have discovered relativity. But can such a variable be found automatically? Doing so can greatly speed up scientific discovery.

This is the question that researchers at Columbia Engineering are asking on a new AI program. This program is designed to observe physical phenomena through a video camera, then try to find a minimal set of fundamental variables that fully describe the observed dynamics. The study was published on July 25 in Natural Computational Science.

The researchers started by feeding the raw video recording system of phenomena they already knew the answer to. For example, they included a video of a double pendulum swinging which is known to have four “state variables” — the angle and angular velocity of each of the two arms. After several hours of analysis, AI came up with the answer: 4.7.

“We think this answer is pretty close,” said Hod Lipson, director of the Creative Machinery Lab in the Department of Mechanical Engineering, where the work was primarily done. “Especially because all AIs have access to raw video footage, with no knowledge of physics or geometry. But we wanted to know what exactly those variables were, not just their numbers.”

The researchers then proceeded to visualize the actual variables identified by the program. Extracting the variable itself is not easy, because the program cannot describe it in any intuitive way that is understandable to humans. After some investigation, it turned out that the two variables the program chose were loosely related to the angle of the arm, but the other two remained a mystery. “We try to correlate other variables with anything and everything we can think of: angular and linear velocities, kinetic and potential energies, and various combinations of known quantities,” explains Boyuan Chen PhD ’22, now an assistant professor at Duke University, who lead the work. “But nothing seems to fit perfectly.” The team believes that the AI ​​has found four valid variables, because it makes good predictions, “but we don’t yet understand the mathematical language it uses,” he explained.

After validating a number of other physical systems with known solutions, the researchers included videos of systems for which they did not know an explicit answer. The first video features “air dancers” surging in front of a local used car park. After several hours of analysis, the program returns 8 variables. A video of the lava lamp also produces 8 eight variables. They then inserted a video clip of the fire from the holiday fireplace loop, and the program returned 24 variables.

A very interesting question is whether the set of variables is unique for each system, or whether a different set is generated each time the program is restarted. “I’ve always wondered, if we ever met a race of intelligent aliens, would they discover the same laws of physics as we do, or could they describe the universe in a different way?” Lipson said. “Maybe some phenomena seem mysteriously complicated because we’re trying to understand them using the wrong set of variables.” In the experiment, 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 of describing the universe and it’s quite possible that our choices were imperfect.

Researchers believe that this kind of AI can help scientists uncover complex phenomena whose theoretical understanding doesn’t align with the flood of data — areas from biology to cosmology. “While we used video data in this work, any kind of array data source could be used — radar arrays, or DNA arrays, for example,” explains Kuang Huang PhD ’22, who co-authored the paper.

This work is part of a decades-long interest by Professors of Mathematics from the Lipson Foundation and Fu Qiang Du in creating algorithms that can distill data into scientific laws. Past software systems, such as Eureqa Lipson and Michael Schmidt’s software, were able to filter free-form laws of physics from experimental data, but only if variables were identified first. But what if the variable is not known yet?

Lipson, who is also the James and Sally Scapa Professor of Innovation, argues that scientists may misinterpret or fail to understand many phenomena simply because they do not have a good set of variables to describe them. “For thousands of years, people knew about fast or slow moving objects, but only when the ideas of velocity and acceleration were formally quantified, was Newton able to discover his famous law of motion F=MA,” Lipson notes. Variables that describe temperature and pressure need to be identified before the laws of thermodynamics can be formalized, and so on for every corner of the scientific world. Variables are the precursor to any theory. “What other law are we missing just because we don’t have a variable?” asked Du, who co-led the work.

The paper was also co-authored by Sunand Raghupathi and Ishaan Chandratreya, who helped collect data for the experiment. Since July 1, 2022, Boyuan Chen has been an assistant professor at Duke University. This work is part of the University of Washington, Columbia, and the Harvard NSF AI Institute for dynamic systems, which aim to accelerate scientific discovery using AI.

Video: https://youtu.be/0yP5T4uuRuI

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