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Discovering physical laws with parallel symbolic enumeration.

Kai Ruan1, Yilong Xu1, Ze-Feng Gao1

  • 1Gaoling School of Artificial Intelligence, Renmin University of China, Beijing, China.

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Summary

Parallel Symbolic Enumeration (PSE) efficiently discovers interpretable mathematical models from data. This new method significantly improves accuracy and speed for complex symbolic regression tasks.

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Area of Science:

  • Data Science
  • Computational Science
  • Scientific Discovery

Background:

  • Symbolic regression is vital for extracting concise, interpretable mathematical expressions from data.
  • A major challenge is efficiently searching infinite spaces for parsimonious, generalizable formulas.
  • Current algorithms struggle with accuracy and efficiency for complex problems, slowing scientific exploration.

Purpose of the Study:

  • To introduce Parallel Symbolic Enumeration (PSE) for efficient, data-driven discovery of mathematical expressions.
  • To address the limitations of existing symbolic regression algorithms in accuracy and speed.
  • To enhance the application of symbolic learning in interdisciplinary scientific domains.

Main Methods:

  • Developed Parallel Symbolic Enumeration (PSE), a novel algorithm for symbolic regression.
  • Designed PSE to efficiently distill generic mathematical expressions from limited datasets.
  • Focused on improving scalability and performance for complex data-driven discovery tasks.

Main Results:

  • PSE demonstrated superior accuracy and computational speed compared to state-of-the-art methods.
  • Achieved up to 99% improvement in recovery accuracy and an order of magnitude reduction in runtime.
  • Validated performance across over 200 synthetic and experimental problem sets.

Conclusions:

  • PSE advances accurate and efficient data-driven discovery of symbolic, interpretable models.
  • The method shows significant improvements in recovering underlying physical laws and other scientific principles.
  • PSE enhances the scalability and applicability of symbolic learning for scientific research.