Class Symbolic Regression: Gotta Fit 'Em All (2312.01816v2)

Abstract: We introduce 'Class Symbolic Regression' (Class SR) a first framework for automatically finding a single analytical functional form that accurately fits multiple datasets - each realization being governed by its own (possibly) unique set of fitting parameters. This hierarchical framework leverages the common constraint that all the members of a single class of physical phenomena follow a common governing law. Our approach extends the capabilities of our earlier Physical Symbolic Optimization ($\Phi$-SO) framework for Symbolic Regression, which integrates dimensional analysis constraints and deep reinforcement learning for unsupervised symbolic analytical function discovery from data. Additionally, we introduce the first Class SR benchmark, comprising a series of synthetic physical challenges specifically designed to evaluate such algorithms. We demonstrate the efficacy of our novel approach by applying it to these benchmark challenges and showcase its practical utility for astrophysics by successfully extracting an analytic galaxy potential from a set of simulated orbits approximating stellar streams.

• The paper introduces a framework that discovers universal analytical forms across multiple datasets using an extension of the Φ-SO methodology.
• It separates shared class parameters from unique dataset-specific parameters to accurately capture underlying physics while mitigating overfitting.
• Testing on synthetic and astrophysical data demonstrates its potential to reliably extract laws from noisy or biased observations.

A recent framework introduced in the field of symbolic regression (SR) promises to revolutionize the way we analyze clusters of data by identifying universal laws that simultaneously fit multiple datasets. Termed "Class Symbolic Regression," this advanced method builds upon the previously developed Physical Symbolic Optimization (Φ-SO) framework, which uses deep reinforcement learning to discover analytical functions from data, extending it to accommodate scenarios with numerous datasets governed by their own unique parameters.

The new Class SR approach is particularly impactful in areas like astrophysics, where multiple observations of a single phenomenon are traditionally available. Normally, the challenge in traditional SR is that fitting individual datasets might lead to solutions heavily influenced by dataset-specific peculiarities such as noise or biases. Class SR, however, is designed to tease out the universal analytical forms that apply across a class of phenomena, therefore representing the underlying physics more reliably.

To illustrate its efficacy, the framework was tested with a panel of synthetic datasets as well as in a practical application involving astrophysical data. In a complex exercise, the framework accurately determined the analytic potential of a simulated galaxy by examining data from orbits that approximate stellar streams, a feat that showcases its potential utility in interpreting astronomical information.

The Class SR framework handles both class-parameters, which are shared across an entire set of observations, and dataset-specific parameters, allowing it to model unique aspects of each set of data without conflating them. This dual-layered approach means that rather than seeing dataset-specific parameters as extra input variables (which might mislead one to think Class SR is akin to regular SR with unbalanced data), these parameters represent the nuanced differences to be determined and hence are more meaningful.

One of the key benefits of the Class SR framework is its ability to mitigate the risks of overfitting, which often plague SR applications. By analyzing multiple datasets and searching for a shared underlying structure, Class SR reduces the likelihood of mistaking random fluctuations or particulars of a dataset for significant trends or laws.

In conclusion, the Class Symbolic Regression framework provides a powerful new tool for scientists and researchers across various fields who wish to extract deeper insights from complex datasets linked by a common phenomenon. As this tool integrates into the analytics process, it holds the potential to accelerate our understanding and usher in new discoveries across multiple scientific disciplines.