Lagrangian Neural Networks and Symbolic Regression
Technologies:
This project was conducted as undergraduate research (PHYS492) at Boğaziçi University under the supervision of Asst. Prof. Arkadaş Özakın from February 2024 to June 2024.
Project Overview
This project implemented Lagrangian Neural Networks (LNNs) in PyTorch, combining physics principles with deep learning. I developed a tool using symbolic regression (PySR) to infer the mathematical form of Lagrangian from trajectory data.
The work explored theoretical concepts including Noether’s theorem and symplectic integrators, creating a bridge between classical mechanics and modern machine learning techniques.
The work is presented in a seminar titled “Using Lagrangian Neural Networks to Learn Physics,” which can be viewed on YouTube.
Video of the Seminar: “Using Lagrangian Neural Networks to Learn Physics”
Key Components
- Lagrangian Neural Networks: Implementation of physics-informed neural networks that can learn the Lagrangian function from observational data
- Symbolic Regression: Integration with PySR to discover mathematical expressions that represent the learned Lagrangian
- Theoretical Foundation: Exploration of concepts including Noether’s theorem and symplectic integrators
- Data-Driven Physics: Development of methods to extract theoretical laws from experimental observations
Research Significance
This work demonstrated the potential of machine learning to discover fundamental physical laws from data, contributing to the emerging field of AI for scientific discovery. The combination of neural networks with symbolic regression provided interpretable models that could reveal the underlying mathematical structure of physical systems.