MaRDI Task Area 2 - Scientific Computing @ University of Münster. MathAlgoDB - Algorithm Knowledge Graph - Ontology (Version 0.1). MaRDI (Mathematical Research Data Initiative), 2022. https://mardi4nfdi.de/mathalgodb/0.1
Aurela Shehu (https://orcid.org/0000-0002-1994-0612), Weierstrass Institute Berlin for Applied Analysis and Stochastics (https://ror.org/00h1x4t21, https://isni.org/isni/000000010066936X)
Björn Schembera (https://orcid.org/0000-0003-2860-6621), Universität Stuttgart (https://ror.org/04vnq7t77, https://isni.org/isni/0000000419369713)
Burkhard Schmidt (https://orcid.org/0000-0002-9658-499X), Weierstrass Institute Berlin for Applied Analysis and Stochastics (https://ror.org/00h1x4t21, https://isni.org/isni/000000010066936X)
Christian Himpe (https://orcid.org/0000-0003-2194-6754)
Christine Biedinger (https://orcid.org/0009-0002-5082-8386), Fraunhofer Institute for Industrial Mathematics ITWM (https://ror.org/019hjw009)
Frank Wübbeling (https://orcid.org/0000-0002-2375-2008)
Hendrik Kleikamp (https://orcid.org/0000-0003-1264-5941)
Jochen Fiedler (https://orcid.org/0000-0002-9176-780X), Fraunhofer Institute for Industrial Mathematics ITWM (https://ror.org/019hjw009)
Marco Reidelbach (https://orcid.org/0000-0002-1919-1834), Zuse Institute Berlin (https://ror.org/02eva5865, https://isni.org/isni/000000011010926X)
Thomas Koprucki (https://orcid.org/0000-0001-6235-9412), Weierstrass Institute Berlin for Applied Analysis and Stochastics (https://ror.org/00h1x4t21, https://isni.org/isni/000000010066936X)
This vocabulary and grammar defines which types of objects are admissible to the MathAlgoDB - the algorithm knowledge graph - and by which properties they can relate. All in all five classes, "problem", "algorithm", "benchmark", "software", "publication", are defined, as well as a minimal but intuitively intelligible number of properties. As opposed to the more liberal WikiData, MathAlgoDB relies on the strict adherence to the ontology to provide a reliable machine-readable database of (numerical) algorithm knowledge.
This is the MathModDB Ontology for documenting mathematical models.
The main building blocks of the graph are algorithms. Here you can take a look at all algorithms documented in the graph.
For testing, evaluating and comparing numerical algorithms, so called benchmark problems are often useful.
When interested in algorithms solving a certain problem at hand, we here provide an overview of all problems defined in the graph.
An engineering challenge that includes a mathematical part
To find theoretical or numerical results on the performance of algorithms, take a look at the related publications in this list.
Union of all MathAlgoDB-Classes that *may* have a unique identifier.
This table contains software packages that implement some of the algorithms from the graph.
A specific computational tasks associated with a mathematical model. Typically, various tasks differ from each other by the choice of given quantities (input), unknown quantities (output), parameters or constants as well as boundary conditions, inital conditions and/or final conditions.
Berechnungsaufgabe
Computational Task
Typically, a mathematical formulation is based on equations (general construct indicating equality of quantities) or on inequalities (non-equal relations between quantities), or a logic quantifier
Mathematical Formulation
Mathematische Formulierung
A mathematical model for describing a part of the reality by means of abstraction and simplifying assumptions. The aim of modeling is to make a particular part or feature of the world easier to simulate, interpret and/or optimize based on existing knowledge.
Mathematical Model
Mathematisches Modell
A scientific publication
Publication
Publikation
A quantity is a property of a system that can be measured or obtained from calculation/simulation. Can be a scalar, a vector, a matrix or a higher-order tensor. The overarching, abstract quantity in the QuantityKind class should be referenced if possible/applicable.
Quantity
Quantität
The kind of quantity, e.g. the abstract, generalized concept of a quantity. Typically, it could be chosen from an established, controlled vocabulary of quantityKinds, such as QUDT, IEC, .... Note that the kind of a quantity cannot be generalized by another (kind of a) quantity.
Basisquantität
Quantity Kind
A field of research (or academic discipline), e.g. Arts & Humanities, Life Sciences & Biomedicine, Physical & Natural Sciences or Engineering.
Forschungsgebiet
Research Field
A research problem (or research question) to be investigated, typically from a scientific or engineering application, i.e. a specific issue or gap in existing knowledge that you aim to address in your research.
Forschungsthema
Research Problem
A specific task associated with a mathematical model. The subclasses of this superclass should reflect their differences, e.g. a computational task or a task of doing a mathematical analysis (the latter is not yet implemented).
Aufgabe
Task
applied by
applied by task
applies
applies model
approximated by
approximated by formulation
approximated by model
approximated by quantity
approximated by task
approximates
approximates formulation
approximates model
approximates quantity
approximates task
Assumptions in a mathematical model|task|formulation are the conditions that must be met for the mathematical model|task|formulation to be valid.
contained as assumption in
contained as boundary condition in
This property serves to indicate that a certain quantity is considered as a constant in a computational task.
contained as constant in
contained as constraint condition in
contained as final condition in
use this property to denote that a formulation is contained in a (single or coupled) model or formulation or task, e.g., a Darcy formulation is contained in a Darcy-Stokes model or formulation or a related task
contained as formulation in
contained as initial condition in
Note that (base) quantities may be assigned as input or output or parameter in the context of a (specific!) mathematical task but not in the context of a (general!) model or equation.
contained as input in
This property serves to indicate that a certain quantity is to be minimized or maximized in a mathematical optimization task.
contained as objective in
contained as output in
contained as parameter in
contained in
contained in field
use this property to denote that a quantity is contained in a formulation e.g. masses are contained in a Newton Equation
contained in formulation
use this property to denote that a single model is included in a coupled model, e.g. a Darcy model and a Stokes model are included in a Darcy Stokes model
contained in model
This indicates that a computational sub-task is contained in a higher task.
contained in task
contains
contains assumption
In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions.[1] A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions.
contains boundary condition
contains constant
contains constraint condition
Conditions needed to model the interaction of two or more systems that are interacting with each other
Similar to initial conditions. Sometimes used in the context of optimal control.
contains final condition
use this property to denote that a (single or coupled) model or formulation includes a mathematical formulation, e.g. a Darcy Stokes model/formulation includes a Darcy formulation and a Stokes formulation
contains formulation
In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted t = 0).
contains initial condition
Indicates that a (base) quantity is considered as input in the context of a (specific!) computational task.
contains input
use this property to denote that a coupled model includes single models, e.g. a Darcy Stokes model includes a Darcy model and a Stokes model
contains model
This property serves to indicate that a certain quantity is to be minimized or maximized in a computational optimization task. An objective function, a target function, a loss function or cost function (minimization), a utility function or fitness function (maximization), or, in certain fields, an energy function or energy functional.
contains objective
Indicates that a (base) quantity is considered as output in the context of a (specific!) computational task.
contains output
Auxiliary variable or arbitrary constant that characterizes a system or specifies a mathematical function among a family of functions. This property serves to indicate that a certain quantity is considered as a parameter in a computational task.
contains parameter
contains problem
use this property to denote that a mathematical formulation contains a quantity, e.g., a Newton Equation contains masses
contains quantity
This indicates that a computational task contains a subtask.
contains task
defined by
defines
Equations, inequalities, expressions, logic quantifiers, ... in Latex or MathML, e.g. $F = ma$, $v \llt c$, $\forall n \in N$, ...
defining formulation
Discrete models are the discrete analogues of continuous models. In discrete modelling, processes are described by discrete data, i.e., data that could potentially take on only a countable set of values, such as the integers, and which are not infinitely divisible. Thus, discrete modeling yields a computer representable and computable versions of continuous mathematical models,
discretized by
Discretizing is the process of obtaining discrete formulations that are the analogues of continuous formulations. Thus, discretization yields a computer representable and computable versions. Here, they serve as a connecting node to the AlgoData ontology (TA2 of MaRDI) which mainly deals with software, algorithms and benchmarks.
discretized by formulation
Discretizing is the process of obtaining discrete models that are the analogues of continuous models. Thus, discretization yields a computer representable and computable versions. Here, they serve as a connecting node to the AlgoData ontology (TA2 of MaRDI) which mainly deals with software, algorithms and benchmarks.
discretized by model
discretized by task
Discretizing is the process of obtaining discrete models/formulations that are the analogues of continuous models/formulations. Thus, discretization yields a computer representable and computable versions.
discretizes
Discretizing is the process of obtaining discrete formulations that are the analogues of continuous formulations. Thus, discretization yields a computer representable and computable versions.
discretizes formulation
Discretizing is the process of obtaining discrete models that are the analogues of continuous models, thus making them computer representable and hopefully(!) computer solvable. Note, however, that certain models are already discretized from the outset.
discretizes model
discretizes task
A property to express that an entity (problem, model, ...) is documented in a specific Publication
documented in
A property that expresses a Publication is documenting some entity (problem, model, ...)
documents
Formulation Property
generalized by
generalized by field
generalized by formulation
generalized by model
generalized by problem
generalized by task
generalizes
generalizes field
generalizes formulation
generalizes model
generalizes problem
generalizes quantity
generalizes task
Symbol / Term of formulation and corresponding quantity in comma-separated list, e.g. ($\mathbf{F}$,qudt:Force) and/or ($m$,dbpedia:Mass) and/or ($\mathbf{a}$,wikidata:Q11376)
A property that states that some entity (problem, model, ...) was invented in a specific Publication
invented in
A property that states that a Publication invented some entity (problem, model, ...)
invents
Boolean. True if convex, false if not convex
is convex
Boolean. True, if the model is deterministic; false, if the model is probabilistic (stochastic)
is dimensionless
Boolean. True, if dynamic; false, if static
Boolean. True, if linear; false, if non-linear
Boolean. True, if continuous in space; false, if discrete in space
is space-continuous
Boolean. True, if dynamic; false, if stiff
Boolean. True, if continuous in time; false, if discrete in time
linearized by
A property that states that a formulation is linearized (exact or approximate) by another formulation.
linearized by formulation
A property that states that a model is linearized (exact or approximate) by another model.
linearized by model
A property that states that a quantity is linearized (exact or approximate) by another quantity.
linearized by quantity
A property that states that a task is linearized (exact or approximate) by another task.
linearized by task
Linearization of a formulation, model, quantity or task.
linearizes
A property that states that a formulation linearizes (exact or approximate) another formulation.
linearizes formulation
A property that states that a model linearizes (exact or approximate) another model.
linearizes model
A property that states that a quantity linearizes (exact or approximate) another quantity.
linearizes quantity
A property that states that a task linearizes (exact or approximate) another task.
linearizes task
Mathematical modeling describes a part of the reality, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features.
modeled by
models
A property that states that a quantity nondimensionalizes (partially or complete) another quantity.
nondimensionalizes quantity
nondimensionalized by
A property that states that a formulation is nondimensionalized (partially or complete) by another formulation.
nondimensionalized by formulation
A property that states that a quantity is nondimensionalized (partially or complete) by another quantity.
nondimensionalized by quantity
Partial or full removal of physical dimensions from a quantity or a formulation.
nondimensionalizes
A property that states that a formulation nondimensionalizes (partially or complete) another formulation.
nondimensionalizes formulation
use this property only if the two things are similar but the one is not the generalization of the other one
similar to
similar to field
similar to formulation
similar to model
similar to problem
similar to quantity
similar to task
This property states that an entity (problem, model, ...) is studied in a specific Publication
studied in
This property states that a Publication studies an entity (problem, model, ...)
studies
This property states that an entity (problem, model, application, ...) is surveyed in a specific Publication. Surveys are e.g. a review article, a handbook, an encyclopedia, monographs, a documentation, technical report ... .
surveyed in
This property states that a Publication surveys some entity (problem, model, application...). Surveys are e.g. a review article, a handbook, an encyclopedia, monographs, a documentation, technical report ... .
surveys
A property that states that an entity (problem, model, ...) is used in a Publication
used in
A property that states that a Publication uses a specific entity (problem, model, ...)
uses