Summary of Learning Generalized Hamiltonians Using Fully Symplectic Mappings, by Harsh Choudhary et al.
Learning Generalized Hamiltonians using fully Symplectic Mappings
by Harsh Choudhary, Chandan Gupta, Vyacheslav kungrutsev, Melvin Leok, Georgios Korpas
First submitted to arxiv on: 17 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper presents an approach to learning the Hamiltonian of physical systems using Neural Networks (NNs). Specifically, it focuses on Physics-Informed Neural Networks (PINNs) and Hamiltonian Neural Networks (HNNs), which incorporate structural inductive bias by conserving physical properties. This allows for improved sample complexity and out-of-distribution accuracy compared to standard NNs. The authors demonstrate the importance of learning the Hamiltonian as a function of its canonical variables, such as position and velocity, for system identification and long-term prediction. They also propose an extension to symplectic integrators for generalized non-separable Hamiltonians, bypassing computationally intensive backpropagation through an ODE solver. The method is shown to be robust to noise and provides a good approximation of the system Hamiltonian. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper talks about using special kinds of neural networks (NNs) to learn about physical systems. These NNs are designed to follow the same rules as the physical world, like conserving energy. This helps them make better predictions and be more accurate when things don’t go exactly as expected. The main idea is to use these NNs to figure out how a physical system works by learning its “Hamiltonian”, which is like a blueprint for the system’s behavior. |
Keywords
» Artificial intelligence » Backpropagation
