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.