Lagrangian System

Lagrangian systems, describing the dynamics of systems through energy considerations rather than forces, are a focus of intense research across diverse scientific fields. Current efforts concentrate on developing and applying Lagrangian-based models within machine learning, particularly using neural networks (e.g., Lagrangian Neural Networks, Physics Informed Neural Networks) and advanced optimization techniques (e.g., Lagrangian duality, augmented Lagrangian methods) to solve complex problems in areas such as fluid dynamics, robotics, and optimization. This research is significant because it enables more efficient and accurate simulations, improved control strategies for complex systems, and the development of novel algorithms for solving challenging optimization problems.