Artificial Intelligence Helps Researchers Uncover Hidden State Variables in Physics

Einstein's famous equation, E=MC², consists of three variables: energy, mass, and velocity. However, researchers at Columbia Engineering wanted to know if these variables could be discovered automatically. This query is posed to a new AI program created to observe physical phenomena using a video camera. The program would attempt to find the minimal set of fundamental variables that accurately explain the observed dynamics.

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Based on the research published in Nature Computational Science, the researchers started by feeding the system raw video footage of events for which they already knew the solution. One of the videos they fed is a swinging double pendulum with four state variables, such as the angle and angular velocity of each of the two arms. The AI produced 4.7 as the answer after a few hours of analysis.

The researchers thought that the answer was close enough. Especially given that all the AI had access to raw video footage without any knowledge of physics or geometry. "But we wanted to know what the variables were, not just their number." Hod Lipson, director of the Creative Machines Lab in the Department of Mechanical Engineering, said.

So the researchers visualized the actual variables found by the program. The variables themselves were difficult to extract because the algorithm does not describe them in any intuitive way that humans can understand. After further investigation, it was discovered that two of the variables chosen by the program correspond to the angles of the arms, but the other two remain a mystery.

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According to the study's leader, Boyuan Chen, Ph.D., they explored linking the other variables with anything and everything they could think of, such as kinetic and potential energy, angular and linear velocities, and various combinations of known values. Yet, he remarked that nothing seemed to match exactly.

But because the AI made solid predictions, the team was convinced that it had discovered a viable set of four variables. Although they could not understand the mathematical language, it speaks.

Then the researchers fed videos of systems for which they did not know the explicit answer after evaluating a number of other physical systems with known answers. The first video showed an air dancer swaying in front of a used car lot. The program returned eight variables after a few hours of analysis. On the other hand, the lava lamp video produced eight variables. Then they provided the algorithm of a video clip of flames from a festive fireplace loop, which returned 24 variables.

A particularly intriguing question was whether the collection of variables was unique to each system or if a different set was generated each time the application was restarted. The researchers believe that the type of AI can assist scientists in uncovering difficult phenomena where theoretical understanding is falling behind the deluge of data, such as in biology and cosmology. "While we employed video data in this work, any array data source may be used, for example, radar arrays or DNA arrays co-author Kuang Huang, Ph.D. said.