Latent embeddings of our framework colored by physical state variables. Credit: Boyuan Chen/Columbia Engineering
a new[{” attribute=””>Columbia University AI program observed physical phenomena and uncovered relevant variables—a necessary precursor to any physics theory. But the variables it discovered 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 physics you need to identify relevant variables. Not even Einstein could discover relativity without the concepts of energy, mass, and velocity. But can variables like these be discovered automatically? Doing so would greatly accelerate scientific discovery.
This is the question that Columbia Engineering researchers posed to a new artificial intelligence program. The AI program was 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 study was published in the journal Nature Computational Science on July 25.
The image shows a chaotic rocking lever dynamic system in motion. Our work aims to identify and extract the minimum number of state variables necessary to describe such a system directly from high-dimensional video images. 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 fed a video of a swinging double pendulum that 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 issued its 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 really were, not just their number.”
The researchers then proceeded to visualize the actual variables identified by the program. Extracting the variables themselves was difficult because the program cannot describe them in an intuitive way that is understandable to humans. After some investigation, it turned out that two of the variables the program chose vaguely corresponded to the angles of the arms, but the other two remain a mystery.
We correlatively tested other things the balance of the quantities and quantities of angular and quantitative quantities, and various combinations, Chen PhD ’22, an assistant at Duke University, who led the work. “But nothing seemed to fit perfectly.” The team was confident that the AI had found a valid set of four variables, since 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 AI program observed physical phenomena and discovered 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 these videos showed an “air dancer” undulating in front of a local used car lot. After several hours of analysis, the program returned 8 variables. Likewise, a video of a Lava lamp also produced 8 eight variables. When they provided a video clip of flames from a Christmas fireplace loop, 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 that we did, or could they describe the universe in a different way?” Lipson said. “Perhaps some phenomena seem puzzlingly 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 was restarted, but the specific variables were different each time. So yes, there are alternative ways to describe the universe, and our choices may not be perfect.
According to the researchers, 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[{” attribute=””>DNA arrays, for example,” explained Kuang Huang PhD ’22, who coauthored 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. Past software systems, such as Lipson and Michael Schmidt’s Eureqa software, could distill freeform physical laws from experimental data, but only if the variables were identified in advance. But what if the variables are yet 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 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. It was necessary to identify the variables that describe temperature and pressure 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. Since July 1, 2022, Boyuan Chen has been an assistant professor at Duke University. The work is part of a set[{” attribute=””>University of Washington, Columbia, and Harvard NSF AI institute for dynamical systems, aimed to accelerate 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
