Qiang Du, a professor of mathematics at Lipson and Fu Foundation, has been interested in developing algorithms that can transform data into scientific rules for many years. Only if the variables were known in advance could earlier software systems, like Lipson and Michael Schmidt’s Eureqa software, extract freeform physical principles from experimental data. But what if none of the variables are not yet known?
Lipson, who is also the James and Sally Scapa Professor of Innovation, contends that a lack of an adequate collection of variables to define many occurrences may be causing scientists to misinterpret or underappreciate them.
“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 could discover his famous law of motion F=MA,” Lipson explained. Variables describing temperature and pressure needed to be identified before laws of thermodynamics could be formalized, and so on for every corner of the scientific world.
These variables, critically, 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.
You can view the entire study for yourself in the journal Nature Computational Science.
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 joint University of Washington, Columbia, and Harvard NSF AI institute for dynamical systems aimed to accelerate scientific discovery using AI.
Abstract:
“All physical laws are described as mathematical relationships between state variables. These variables give a complete and non-redundant description of the relevant system. However, despite the prevalence of computing power and artificial intelligence, the process of identifying the hidden state variables themselves has resisted automation. Most data-driven methods for modelling physical phenomena still rely on the assumption that the relevant state variables are already known. A longstanding question is whether it is possible to identify state variables from only high-dimensional observational data. Here we propose a principle for determining how many state variables an observed system is likely to have, and what these variables might be. We demonstrate the effectiveness of this approach using video recordings of a variety of physical dynamical systems, ranging from elastic double pendulums to fire flames. Without any prior knowledge of the underlying physics, our algorithm discovers the intrinsic dimension of the observed dynamics and identifies candidate sets of state variables.”
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