symbolic regression
In plain wordsGetting a computer to discover a readable mathematical formula, such as a law of physics, that fits a set of measurements, instead of only fitting numbers into a formula chosen in advance.
The task of finding a mathematical expression — built from variables, constants and operators such as +, ×, sin and exp — that fits data, searching over the structure of the formula as well as its parameters. Unlike ordinary regression, which fits coefficients of a fixed model, symbolic regression seeks compact, interpretable equations that may extrapolate beyond the data. Classic solvers use genetic programminggenetic programming, n.: Using simulated evolution to write computer programs: random programs compete at a task, and the best are combined and mutated over many generations until one does the task well., evolving expression trees under pressure for both accuracy and simplicity (a trade-off front of error against complexity); others use sparse regression over a library of candidate terms (SINDy), exhaustive or tree search, neural networksneural network, n.: A kind of computer program that learns a task from examples by tuning thousands to billions of connections between simple number-crunching units, an arrangement loosely inspired by nerve cells in the brain. that propose expressions, or physics-inspired simplifications such as dimensional analysis and symmetry detection. The general problem is NP-hard. Applications include scientific discovery, interpretable modeling and distilling trained neural networks into equations.
Symbolic regression recovered the pendulum's equation of motion from 30 seconds of video-tracked data.
Origin
Popularized by John Koza's genetic programming (1992). Michael Schmidt and Hod Lipson's 2009 Science paper recovered physical laws from motion data (later commercialized as Eureqa); Silviu-Marian Udrescu and Max Tegmark's AI Feynman (2020) and Miles Cranmer's open-source PySR (described in a 2023 paper) are prominent later systems.
Related
- genetic programminggenetic programming, n.: Using simulated evolution to write computer programs: random programs compete at a task, and the best are combined and mutated over many generations until one does the task well.
- program synthesisprogram synthesis, n.: Getting a computer to write a program automatically from a description of what the program should do — a logical specification, a few input–output examples or a request in plain language.
- evolutionary computationevolutionary computation, n.: Problem-solving by simulated evolution, much as breeders improve crops: keep many candidate answers, let the better ones produce slightly altered offspring, drop the worse, and repeat for many rounds.
- explainable AIexplainable AI, n.: The field and set of methods that let people understand why an AI system produced a particular output — for example, which factors led it to reject a loan application.
- AI scientistAI scientist, n.: An AI system meant to do research largely on its own: reading the literature, coming up with ideas, running experiments and writing up the results.
Sources
- Schmidt, M. & Lipson, H. (2009). Distilling Free-Form Natural Laws from Experimental Data. Science 324(5923), 81–85.
- Udrescu, S.-M. & Tegmark, M. (2020). AI Feynman: A Physics-Inspired Method for Symbolic Regression. Science Advances 6(16), eaay2631.
Mentioned in
genetic programminggenetic programming, n.: Using simulated evolution to write computer programs: random programs compete at a task, and the best are combined and mutated over many generations until one does the task well.