Symbolic regression via neural networks

Area of Science:

• Dynamical Systems
• Machine Learning
• Scientific Computing

Background:

• Identifying governing equations is crucial across science and engineering.
• Traditional deep learning lacks interpretability for dynamical systems.
• Existing symbolic methods often require domain expertise or struggle with overfitting.

Purpose of the Study:

• To develop a novel approach combining deep learning flexibility with symbolic solution utility.
• To create a deep neural network capable of generating symbolic expressions for governing equations.
• To demonstrate the accuracy of this new method across various classical dynamical systems.

Main Methods:

• A novel deep neural network architecture is proposed.
• The model is designed to output symbolic expressions representing governing equations.
• The approach integrates deep learning's data approximation capabilities with symbolic regression.

Main Results:

• The developed deep neural network accurately generates symbolic expressions for governing equations.
• The algorithm demonstrates high accuracy across a range of classical dynamical systems.
• The method offers insights beyond numerical prediction by providing interpretable symbolic solutions.

Conclusions:

• This novel deep learning approach successfully bridges the gap between accurate dynamical system prediction and interpretable symbolic modeling.
• The method enhances the utility of machine learning in scientific discovery by providing explicit governing equations.
• Future work can explore applications in complex systems where interpretability is paramount.