Triple
T243868
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Langevin dynamics |
E4992
|
entity |
| Predicate | numericalSchemes |
P4447
|
FINISHED |
| Object |
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.
|
E31546
|
NE FINISHED |
How this triple was built (5 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Euler–Maruyama method | Statement: [Langevin dynamics, numericalSchemes, Euler–Maruyama method]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Euler–Maruyama method Context triple: [Langevin dynamics, numericalSchemes, Euler–Maruyama method]
-
A.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
B.
Itô calculus
Itô calculus is a branch of stochastic analysis that extends classical calculus to functions of stochastic processes, particularly Brownian motion, enabling rigorous treatment of stochastic differential equations.
-
C.
Gauss–Seidel method
The Gauss–Seidel method is an iterative numerical technique used to solve systems of linear equations, particularly in large, sparse problems arising in scientific and engineering computations.
-
D.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
E.
von Neumann stability analysis
Von Neumann stability analysis is a mathematical technique used in numerical analysis to determine the stability of finite difference schemes for solving partial differential equations by examining the growth of Fourier modes.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Euler–Maruyama method Triple: [Langevin dynamics, numericalSchemes, Euler–Maruyama method]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Euler–Maruyama method Target entity description: 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.
-
A.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
B.
Itô calculus
Itô calculus is a branch of stochastic analysis that extends classical calculus to functions of stochastic processes, particularly Brownian motion, enabling rigorous treatment of stochastic differential equations.
-
C.
Gauss–Seidel method
The Gauss–Seidel method is an iterative numerical technique used to solve systems of linear equations, particularly in large, sparse problems arising in scientific and engineering computations.
-
D.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
E.
von Neumann stability analysis
Von Neumann stability analysis is a mathematical technique used in numerical analysis to determine the stability of finite difference schemes for solving partial differential equations by examining the growth of Fourier modes.
- F. None of above. chosen
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: numericalSchemes Context triple: [Langevin dynamics, numericalSchemes, Euler–Maruyama method]
-
A.
solutionType
Indicates the specific category or kind of solution associated with an entity or problem.
-
B.
approximationType
chosen
Indicates the specific method or scheme used to approximate a value, function, or relationship in a given context.
-
C.
mathematicallyUses
Indicates that one entity employs or applies another entity within a mathematical context, such as in a formula, proof, computation, or theoretical framework.
-
D.
usesComputationMethod
Indicates that an entity performs its processing or decision-making by applying a specified computational method or algorithm.
-
E.
admitsSolution
Indicates that a problem, system, or situation allows for or possesses at least one valid solution.
- F. None of above.
Provenance (6 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69a257c3d0708190b0871c4269d273e6 |
completed | Feb. 28, 2026, 2:49 a.m. |
| NER | Named-entity recognition | batch_69a25dcd2b208190855d5d8d70a3acfc |
completed | Feb. 28, 2026, 3:15 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69a36cf2e84c81908d87847d498f96f4 |
completed | Feb. 28, 2026, 10:32 p.m. |
| NEDg | Description generation | batch_69a36d68858c81908cc2d2dc94b1a482 |
completed | Feb. 28, 2026, 10:34 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69a36dbb7dc88190a75f2c0bbb478ccc |
completed | Feb. 28, 2026, 10:35 p.m. |
| PD | Predicate disambiguation | batch_69a25b62839c8190824064fe5da6a92a |
completed | Feb. 28, 2026, 3:05 a.m. |
Created at: Feb. 28, 2026, 2:53 a.m.