Parsimonious neural networks learn interpretable physical laws.

Area of Science:

• Physical Sciences
• Materials Science
• Computational Physics

Background:

• Machine learning (ML) is increasingly integrated into physical sciences, with advancements in embedding domain knowledge.
• Discovering interpretable physical laws directly from data using ML remains an underexplored area.
• Existing methods often prioritize predictive accuracy over model simplicity and interpretability.

Purpose of the Study:

• To introduce Parsimonious Neural Networks (PNNs) for discovering interpretable physical laws from data.
• To demonstrate the capability of PNNs in balancing model accuracy with parsimony.
• To apply PNNs to classical mechanics and material melting point prediction.

Main Methods:

• Developed Parsimonious Neural Networks (PNNs) combining neural networks with evolutionary optimization.
• Applied PNNs to derive models for classical mechanics, focusing on time integrators.
• Utilized PNNs to predict material melting temperatures from fundamental properties.

Main Results:

• PNNs successfully rediscovered Newton's second law as an interpretable time integrator in classical mechanics, highlighting time-reversibility and energy conservation.
• Parsimony was crucial for extracting underlying physical symmetries from the data.
• For melting temperature prediction, PNNs identified the Lindemann law and discovered novel, more accurate relationships.

Conclusions:

• PNNs offer a powerful approach for discovering interpretable physical laws from data.
• The method effectively balances predictive accuracy with model parsimony.
• PNNs demonstrate versatility across different domains in the physical sciences, yielding both known and new scientific insights.