Constrained Lagrangian Neural Networks with Learned Physical Constraints

This project is conducted as my Bachelor’s Thesis at Boğaziçi University, co-supervised by Asst. Prof. İnci Meliha Baytaş and Asst. Prof. Arkadaş Özakin, starting in September 2025.

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Project Overview

This research extends the framework of Lagrangian Neural Networks (LNNs) by introducing automated constraint learning, forming a Constrained Lagrangian Neural Network (CLNN) architecture.
The model jointly learns the Lagrangian and system constraints from trajectory data, enabling physically consistent modeling even when the governing equations are partially constrained or unknown.

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Research Goals

• Develop a hybrid loss that integrates constraint prediction with Lagrangian dynamics learning
• Enable automatic discovery of hidden constraints (e.g., conservation laws, holonomic constraints) from raw data
• Benchmark the proposed CLNN against standard LNNs and physics-informed baselines
• Demonstrate how AI can uncover interpretable physical structure directly from motion data

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Key Technologies

• Lagrangian Neural Networks (LNNs): Neural architectures enforcing physics through the Lagrangian formalism
• Constraint Learning: Auxiliary networks predicting implicit system constraints
• PyTorch: Deep learning framework for implementation and training
• Symbolic Regression: Extracting interpretable expressions from learned dynamics
• Python: Main environment for simulation, modeling, and analysis