leapfrog integrator
E898982
A leapfrog integrator is a symplectic numerical method for solving Hamiltonian dynamics that conserves energy well over long simulations, making it especially useful in physics and Hamiltonian Monte Carlo.
All labels observed (1)
| Label | Occurrences |
|---|---|
| leapfrog integrator canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11002318 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: leapfrog integrator Context triple: [Hamiltonian Monte Carlo, typicallyUses, leapfrog integrator]
-
A.
Euler’s method for numerical integration
Euler’s method for numerical integration is a simple first-order numerical procedure used to approximate solutions to ordinary differential equations by stepping forward in small increments.
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B.
Heun’s method
Heun’s method is a second-order Runge–Kutta numerical integration technique that improves on Euler’s method by using a predictor-corrector approach to achieve greater accuracy.
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C.
Runge–Kutta methods
Runge–Kutta methods are a family of iterative techniques for numerically solving ordinary differential equations with higher accuracy than simple one-step schemes.
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D.
Euler–Maruyama method
The Euler–Maruyama method is a basic time-stepping scheme for numerically approximating solutions to stochastic differential equations, widely used in simulations of systems with noise such as Langevin dynamics.
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E.
classical fourth-order Runge–Kutta method
The classical fourth-order Runge–Kutta method is a widely used, higher-accuracy numerical technique for solving ordinary differential equations by combining multiple intermediate slope evaluations within each integration step.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: leapfrog integrator Target entity description: A leapfrog integrator is a symplectic numerical method for solving Hamiltonian dynamics that conserves energy well over long simulations, making it especially useful in physics and Hamiltonian Monte Carlo.
-
A.
Euler’s method for numerical integration
Euler’s method for numerical integration is a simple first-order numerical procedure used to approximate solutions to ordinary differential equations by stepping forward in small increments.
-
B.
Heun’s method
Heun’s method is a second-order Runge–Kutta numerical integration technique that improves on Euler’s method by using a predictor-corrector approach to achieve greater accuracy.
-
C.
Runge–Kutta methods
Runge–Kutta methods are a family of iterative techniques for numerically solving ordinary differential equations with higher accuracy than simple one-step schemes.
-
D.
Euler–Maruyama method
The Euler–Maruyama method is a basic time-stepping scheme for numerically approximating solutions to stochastic differential equations, widely used in simulations of systems with noise such as Langevin dynamics.
-
E.
classical fourth-order Runge–Kutta method
The classical fourth-order Runge–Kutta method is a widely used, higher-accuracy numerical technique for solving ordinary differential equations by combining multiple intermediate slope evaluations within each integration step.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
geometric numerical integrator
ⓘ
numerical integration method ⓘ symplectic integrator ⓘ |
| advantageOver | non‑symplectic integrators for long‑time Hamiltonian simulation ⓘ |
| appliedTo | separable Hamiltonians ⓘ |
| approximates | Hamiltonian flow ⓘ |
| assumes | Hamiltonian separable into kinetic and potential energy ⓘ |
| comparedTo | Runge–Kutta methods NERFINISHED ⓘ |
| enables | high acceptance rates in Hamiltonian Monte Carlo ⓘ |
| hasAlternativeName |
Störmer–Verlet integrator
NERFINISHED
ⓘ
leapfrog method NERFINISHED ⓘ |
| hasOrder | 2 ⓘ |
| hasProperty |
conditionally stable
ⓘ
explicit method ⓘ good long‑term energy conservation ⓘ second‑order accurate ⓘ symplectic ⓘ time‑reversible ⓘ volume‑preserving in phase space ⓘ |
| hasStepStructure |
full‑step position update
ⓘ
half‑step momentum update ⓘ half‑step momentum update at end of step ⓘ |
| isSpecialCaseOf |
partitioned Runge–Kutta method
ⓘ
second‑order symplectic Runge–Kutta–Nyström method ⓘ |
| minimizes | long‑term energy drift ⓘ |
| numericalErrorType | bounded energy error over long times ⓘ |
| preserves |
phase‑space volume
ⓘ
symplectic structure ⓘ |
| relatedTo |
Störmer–Verlet method
NERFINISHED
ⓘ
Verlet integration NERFINISHED ⓘ position Verlet integrator NERFINISHED ⓘ velocity Verlet integrator NERFINISHED ⓘ |
| requires | choice of time step ⓘ |
| tradeoff | smaller time step improves accuracy but increases cost ⓘ |
| typicalUseContext |
Bayesian computation
ⓘ
Markov chain Monte Carlo NERFINISHED ⓘ classical mechanics ⓘ computational physics ⓘ |
| usedFor |
Hamiltonian Monte Carlo
NERFINISHED
ⓘ
Hybrid Monte Carlo NERFINISHED ⓘ N‑body simulations in astrophysics ⓘ long‑time integration of Hamiltonian systems ⓘ molecular dynamics simulations ⓘ solving Hamiltonian dynamics ⓘ |
| usedIn |
galactic dynamics simulations
ⓘ
lattice quantum chromodynamics simulations ⓘ planetary orbit integration ⓘ rigid‑body dynamics ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: leapfrog integrator Description of subject: A leapfrog integrator is a symplectic numerical method for solving Hamiltonian dynamics that conserves energy well over long simulations, making it especially useful in physics and Hamiltonian Monte Carlo.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.