Research map / Probabilistic and scientific modeling / Dynamical systems
Hamiltonian Neural Networks
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's title only (no summary yet). Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a learned Hamiltonian and its symplectic gradient instead of directly predicting the state derivative | HNN · Ideal mass-spring | Energy MSE: 170\pm20 -> \mathbf{.38\pm.1} | Helped |
| Use a learned Hamiltonian and its symplectic gradient instead of directly predicting the state derivative | HNN · Ideal pendulum | Energy MSE: 42\pm10 -> \mathbf{25\pm5} | Helped |
| Use a learned Hamiltonian and its symplectic gradient instead of directly predicting the state derivative | HNN · Real pendulum | Energy MSE: 390\pm7 -> \mathbf{14\pm5} | Helped |
| Use a learned Hamiltonian and its symplectic gradient instead of directly predicting the state derivative | HNN · Two-body problem | Energy MSE: 6.3e4\pm3e4 -> \mathbf{39\pm5} | Helped |
| Use a learned Hamiltonian and its symplectic gradient instead of directly predicting the state derivative | HNN · Pixel pendulum | Energy MSE: 9.3\pm1 -> \mathbf{.15\pm.01} | Helped |
| Use a learned Hamiltonian and its symplectic gradient instead of directly predicting the state derivative | HNN · Three-body problem | Energy MSE: \mathbf{1.1e4\pm8e3} -> 4.2\pm3 | Helped |
| Use HNN rather than the direct-derivative baseline | HNN · Ideal mass-spring | Test loss: 37\pm2 -> \mathbf{36\pm2} | No clear effect |
| Use HNN rather than the direct-derivative baseline | HNN · Real pendulum | Test loss: \mathbf{2.2\pm.3} -> 6.0\pm.6 | Hurt |
| Use HNN rather than the direct-derivative baseline | HNN · Two-body problem | Test loss: 30\pm.1 -> \mathbf{2.8\pm.1} | Helped |
| Use HNN rather than the direct-derivative baseline | HNN · Pixel pendulum | Test loss: \mathbf{17\pm.3} -> 18\pm.3 | No clear effect |
| Use HNN rather than the direct-derivative baseline | HNN · Three-body problem | Test loss: \mathbf{38\pm40} -> 49\pm48 | Hurt |
Closest papers by meaning
- Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach (ICML 2026 · similarity 0.90)
- Hamiltonian Neural PDE Solvers through Functional Approximation (NeurIPS 2025 · similarity 0.88)
- Towards Cross Domain Generalization of Hamiltonian Representation via Meta Learning (ICLR 2024 · similarity 0.87)
- Riemann Tensor Neural Networks: Learning Conservative Systems with Physics-Constrained Networks (ICML 2025 · similarity 0.86)
- Hamiltonian Score Matching and Generative Flows (NeurIPS 2024 · similarity 0.85)
- Physics-Informed Regularization for Domain-Agnostic Dynamical System Modeling (NeurIPS 2024 · similarity 0.85)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.