Research map / Probabilistic and scientific modeling / Dynamical systems
Hyperverlet: A Symplectic Hypersolver for Hamiltonian Systems
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 |
|---|---|---|---|
| add a SympNet corrector to velocity Verlet | Hyperverlet · Spring-mass, h=0.025–0.2 | MSE: 7.7e−5 ± 1.2e−4 -> 1.2e−5 ± 3.8e−5; 1.2e−3 ± 1.8e−3 -> 2.2e−5 ± 4.9e−5; 1.9e−2 ± 2.9e−2 -> 4.7e−5 ± 1.6e−4; 2.5e−1 ± 3.6 | Helped |
| add a SympNet corrector to velocity Verlet | Hyperverlet · Pendulum, h=0.04–0.08 | MSE: 5.8e−1 ± 5.7e−1 -> 6.3e−2 ± 1.5e−1; 2.2e+0 ± 2.1e+0 -> 1.4e−1 ± 2.6e−1; 4.8e+0 ± 5.1e+0 -> 3.5e−1 ± 5.2e−1 | Helped |
| add a SympNet corrector to velocity Verlet | Hyperverlet · Pendulum, h=0.02 | MSE: 4.1e−2 ± 4.4e−2 -> 4.7e−2 ± 9.2e−2 | Hurt |
| add time-invariant-property parameterization to the symplectic transformations (ablation) | SympNet corrector · Pendulum, h=0.08 | MSE | Helped |
| replace sigmoid with tanh in a parameterized SympNet (ablation) | Parameterized SympNet · Pendulum, h=0.08 | MSE: 42% decrease in mean MSE | Helped |
| replace sigmoid with tanh while keeping SympNet weights static (ablation) | SympNet · Pendulum, h=0.08 | MSE | No clear effect |
| remove parameterization from the symplectic transformations (ablation) | Full Hyperverlet · Pendulum, h=0.08 | MSE | Hurt |
| replace the symplectic corrector with a non-symplectic neural corrector (ablation) | Hyperverlet · Pendulum, h=0.08 | MSE | Hurt |
Closest papers by meaning
- Sparse Symplectically Integrated Neural Networks (NeurIPS 2020 · similarity 0.90)
- Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control (ICLR 2020 · similarity 0.89)
- Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach (ICML 2026 · similarity 0.89)
- Hamiltonian Neural PDE Solvers through Functional Approximation (NeurIPS 2025 · similarity 0.86)
- SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases (ICLR 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.