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Uncertainty quantification

Uncertainty quantification (UQ) is the science of quantitative characterization and reduction of uncertainties in both computational and real world applications. It tries to determine how likely certa

Lotka–Volterra equations

The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in w

Linear partial information

Linear partial information (LPI) is a method of making decisions based on insufficient or fuzzy information. LPI was introduced in 1970 by Polish–Swiss mathematician Edward Kofler (1911–2007) to simpl

Space mapping

The space mapping methodology for modeling and design optimization of engineering systems was first discovered by John Bandler in 1993. It uses relevant existing knowledge to speed up model generation

Open energy system models

Open energy system models are energy system models that are open source. However, some of them may use third party proprietary software as part of their workflows to input, process, or output data. Pr

Complex system

A complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as

Mixed-mating model

The mixed-mating model is a mathematical model that describes the mating system of a plant population in terms of degree of self-fertilisation. It is a fairly simplistic model, employing several simpl

Applications of sensitivity analysis to environmental sciences

Sensitivity analysis studies the relationship between the output of a model and its input variables or assumptions. Historically, the need for a role of sensitivity analysis in modelling, and many app

Radiation law for human mobility

The radiation law is way of modeling human mobility (geographic mobility, human migration) and it gives better empirical predictions than the gravity model of migration which is widely used in this su

Simulink

Simulink is a MATLAB-based graphical programming environment for modeling, simulating and analyzing multidomain dynamical systems. Its primary interface is a graphical block diagramming tool and a cus

Cebeci–Smith model

The Cebeci–Smith model is a 0-equation eddy viscosity model used in computational fluid dynamics analysis of turbulent boundary layer flows. The model gives eddy viscosity, , as a function of the loca

Vector field reconstruction

Vector field reconstruction is a method of creating a vector field from experimental or computer generated data, usually with the goal of finding a differential equation model of the system. A differe

Computational model

A computational model uses computer programs to simulate and study complex systems using an algorithmic or mechanistic approach and is widely used in a diverse range of fields spanning from physics, c

PottersWheel

PottersWheel is a MATLAB toolbox for mathematical modeling of time-dependent dynamical systems that can be expressed as chemical reaction networks or ordinary differential equations (ODEs). It allows

Press–Schechter formalism

The Press–Schechter formalism is a mathematical model for predicting the number of objects (such as galaxies, galaxy clusters or dark matter halos) of a certain mass within a given volume of the Unive

Classical control theory

Classical control theory is a branch of control theory that deals with the behavior of dynamical systems with inputs, and how their behavior is modified by feedback, using the Laplace transform as a b

Flail space model

The flail space model (FSM) is a model of how a car passenger moves in a vehicle that collides with a roadside feature such as a guardrail or a crash cushion. Its principal purpose is to assess the po

Generalised logistic function

The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves. The function is

Statistical model

A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model rep

Empirical modelling

Empirical modelling refers to any kind of (computer) modelling based on empirical observations rather than on mathematically describable relationships of the system modelled.

Microscale and macroscale models

Microscale models form a broad class of computational models that simulate fine-scale details, in contrast with macroscale models, which amalgamate details into select categories. Microscale and macro

Applications of sensitivity analysis in epidemiology

Sensitivity analysis studies the relation between the uncertainty in a model-based the inference and the uncertainties in the model assumptions. Sensitivity analysis can play an important role in epid

Overfitting

In mathematical modeling, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit to additional data or predict

Calculus of voting

Calculus of voting refers to any mathematical model which predicts voting behaviour by an electorate, including such features as participation rate. A calculus of voting represents a hypothesized deci

Boolean delay equation

A Boolean Delay Equation (BDE) is an evolution rule for the state of dynamical variables whose values may be represented by a finite discrete numbers os states, such as 0 and 1. As a novel type of sem

Apparent infection rate

Apparent infection rate is an estimate of the rate of progress of a disease, based on proportional measures of the extent of infection at different times. Firstly, a proportional measure of the extent

PCLake

PCLake is a dynamic, mathematical model used to study eutrophication effects in shallow lakes and ponds. PCLake models explicitly the most important biotic groups and their interrelations, within the

WRF-SFIRE

WRF-SFIRE is a coupled atmosphere-wildfire model, which combines the Weather Research and Forecasting Model (WRF) with a fire-spread model, implemented by the level-set method. A version from 2010 was

Secondary electrospray ionization

Secondary electro-spray ionization (SESI) is an ambient ionization technique for the analysis of trace concentrations of vapors, where a nano-electrospray produces charging agents that collide with th

Breath gas analysis

Breath gas analysis is a method for gaining information on the clinical state of an individual by monitoring volatile organic compounds (VOCs) present in the exhaled breath. Exhaled breath is naturall

Extended Mathematical Programming

Algebraic modeling languages like AIMMS, AMPL, GAMS, MPL and others have been developed to facilitate the description of a problem in mathematical terms and to link the abstract formulation with data-

Phase-field models on graphs

Phase-field models on graphs are a discrete analogue to phase-field models, defined on a graph. They are used in image analysis (for feature identification) and for the segmentation of social networks

Vflo

Vflo is a commercially available, physics-based distributed hydrologic model generated by Vieux & Associates, Inc. Vflo uses radar rainfall data for hydrologic input to simulate distributed runoff. Vf

Compartmental neuron models

Compartmental modelling of dendrites deals with multi-compartment modelling of the dendrites, to make the understanding of the electrical behavior of complex dendrites easier. Basically, compartmental

VisSim

VisSim is a visual block diagram program for simulation of dynamical systems and model-based design of embedded systems, with its own visual language. It is developed by Visual Solutions of Westford,

Iterative rational Krylov algorithm

The iterative rational Krylov algorithm (IRKA), is an iterative algorithm, useful for model order reduction (MOR) of single-input single-output (SISO) linear time-invariant dynamical systems. At each

Boolean model of information retrieval

The (standard) Boolean model of information retrieval (BIR) is a classical information retrieval (IR) model and, at the same time, the first and most-adopted one. It is used by many IR systems to this

LINGO (mathematical modeling language)

LINGO is a mathematical modeling language designed for formulating and solving optimization problems, including linear, integer, and nonlinear programming problems.

State-space representation

In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or differe

MAgPIE

MAgPIE is a non-linear, recursive, dynamic-optimization, global land and water-use model with a cost-minimization objective function.MAgPIE was developed and is employed by the land-use group working

Wildfire modeling

In computational science, wildfire modeling is concerned with numerical simulation of wildland fires in order to understand and predict fire behavior. Wildfire modeling can ultimately aid wildland fir

Arditi–Ginzburg equations

The Arditi–Ginzburg equations describes ratio dependent predator–prey dynamics. Where N is the population of a prey species and P that of a predator, the population dynamics are described by the follo

Microscopic traffic flow model

Microscopic traffic flow models are a class of scientific models of vehicular traffic dynamics. In contrast, to macroscopic models, microscopic traffic flow models simulate single vehicle-driver units

Mathematical exposure modeling

Mathematical exposure modeling is an indirect method of determining exposure, particularly for human exposure to environmental contaminants. It is useful when direct measurement of pollutant concentra

Info-metrics

Info-metrics is an interdisciplinary approach to scientific modeling, inference and efficient information processing. It is the science of modeling, reasoning, and drawing inferences under conditions

Quantum clock model

The quantum clock model is a quantum lattice model. It is a generalisation of the transverse-field Ising model . It is defined on a lattice with states on each site. The Hamiltonian of this model is H

Minimum-distance estimation

Minimum-distance estimation (MDE) is a conceptual method for fitting a statistical model to data, usually the empirical distribution. Often-used estimators such as ordinary least squares can be though

Logan plot

A Logan plot (or Logan graphical analysis) is a graphical analysis technique based on the compartment model that uses linear regression to analyze pharmacokinetics of tracers involving reversible upta

Multi-compartment model

A multi-compartment model is a type of mathematical model used for describing the way materials or energies are transmitted among the compartments of a system. Sometimes, the physical system that we t

OptimJ

OptimJ is an extension for Java with language support for writing optimization models and abstractions for bulk data processing. The extensions and the proprietary product implementing the extensions

Sensitivity analysis

Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in it

Dielectric breakdown model

Dielectric breakdown model (DBM) is a macroscopic mathematical model combining the diffusion-limited aggregation model with electric field. It was developed by Niemeyer, Pietronero, and Weismann in 19

JuMP

JuMP is an algebraic modeling language and a collection of supporting packages for mathematical optimization embedded in the Julia programming language. JuMP is used by companies, government agencies,

Electoral Calculus

Electoral Calculus is a political forecasting web site which attempts to predict future United Kingdom general election results. It considers national factors but excludes local issues.

Multislice

The multislice algorithm is a method for the simulation of the elastic interaction of an electron beam with matter, including all multiple scattering effects. The method is reviewed in the book by Cow

Energy modeling

Energy modeling or energy system modeling is the process of building computer models of energy systems in order to analyze them. Such models often employ scenario analysis to investigate different ass

Pontifex (project)

PONTIFEX (Planning Of Non-specific Transportation by an Intelligent Fleet EXpert) was a mid-1980s project that introduced a novel approach to complex aircraft fleet scheduling, partially funded by the

Soil production function

Soil production function refers to the rate of bedrock weathering into soil as a function of soil thickness. A general model suggested that the rate of physical weathering of bedrock (de/dt) can be re

Linear system

In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator.Linear systems typically exhibit features and properties that are much simpler than the non

Grey box model

In mathematics, statistics, and computational modelling, a grey box model combines a partial theoretical structure with data to complete the model. The theoretical structure may vary from information

Applications of sensitivity analysis to model calibration

Sensitivity analysis has important applications in model calibration. One application of sensitivity analysis addresses the question of "What's important to model or system development?" One can seek

Color model

A color model is an abstract mathematical model describing the way colors can be represented as tuples of numbers, typically as three or four values or color components. When this model is associated

Deterministic simulation

In mathematical modeling, deterministic simulations contain no random variables and no degree of randomness, and consist mostly of equations, for example difference equations. These simulations have k

Global cascades model

Global cascades models are a class of models aiming to model large and rare cascades that are triggered by exogenous perturbations which are relatively small compared with the size of the system. The

Historical dynamics

Historical dynamics broadly includes the scientific modeling of history. This might also be termed computer modeling of history, historical simulation, or simulation of history - allowing for an exten

Maas–Hoffman model

The Maas–Hoffman model is a mathematical tool to characterize the relation between crop production and soil salinity. It describes the crop response by a broken line of which the first part is horizon

The Chemical Basis of Morphogenesis

"The Chemical Basis of Morphogenesis" is an article that the English mathematician Alan Turing wrote in 1952. It describes how patterns in nature, such as stripes and spirals, can arise naturally from

Baldwin–Lomax model

The Baldwin–Lomax model is a 0-equation turbulence model used in computational fluid dynamics analysis of turbulent boundary layer flows.

Particle-in-cell

In plasma physics, the particle-in-cell (PIC) method refers to a technique used to solve a certain class of partial differential equations. In this method, individual particles (or fluid elements) in

Forward problem of electrocardiology

The forward problem of electrocardiology is a computational and mathematical approach to study the electrical activity of the heart through the body surface. The principal aim of this study is to comp

History of network traffic models

Design of robust and reliable networks and network services relies on an understanding of the traffic characteristics of the network. Throughout history, different models of network traffic have been

Water Protection Zone

A Water Protection Zone is a statutory regulation imposed under Schedule 11 to the Water Resources Act 1991. The power was subsequently subsumed into The Water Resources Act (Amendment) (England and W

Variance-based sensitivity analysis

Variance-based sensitivity analysis (often referred to as the Sobol method or Sobol indices, after Ilya M. Sobol) is a form of global sensitivity analysis. Working within a probabilistic framework, it

Chemical reaction model

Chemical reaction models transform physical knowledge into a mathematical formulation that can be utilized in computational simulation of practical problems in chemical engineering. Computer simulatio

AIMMS

AIMMS (acronym for Advanced Interactive Multidimensional Modeling System) is a prescriptive analytics software company with offices in the Netherlands, United States, China and Singapore. It has two m

Head injury criterion

The head injury criterion (HIC) is a measure of the likelihood of head injury arising from an impact. The HIC can be used to assess safety related to vehicles, personal protective gear, and sport equi

Macroscopic traffic flow model

A Macroscopic traffic flow model is a mathematical traffic model that formulates the relationships among traffic flow characteristics like density, flow, mean speed of a traffic stream, etc.. Such mod

Resource selection function

Resource selection functions (RSFs) are a class of functions that are used in spatial ecology to assess which habitat characteristics are important to a specific population or species of animal, by as

Multiscale modeling

Multiscale modeling or multiscale mathematics is the field of solving problems which have important features at multiple scales of time and/or space. Important problems include multiscale modeling of

Propagation graph

Propagation graphs are a mathematical modelling method for radio propagation channels. A propagation graph is a signal flow graph in which vertices represent transmitters, receivers or scatterers. Edg

Analytica (software)

Analytica is a visual software developed by Lumina Decision Systems for creating, analyzing and communicating quantitative decision models. It combines hierarchical influence diagrams for visual creat

Equation-free modeling

Equation-free modeling is a method for multiscale computation and computer-aided analysis. It is designed for a class of complicated systems in which one observes evolution at a macroscopic, coarse sc

Open Energy Modelling Initiative

The Open Energy Modelling Initiative (openmod) is a grassroots community of energy system modellers from universities and research institutes across Europe and elsewhere. The initiative promotes the u

Reaction–diffusion system

Reaction–diffusion systems are mathematical models which correspond to several physical phenomena. The most common is the change in space and time of the concentration of one or more chemical substanc

Actuarial Society of South Africa HIV/AIDS models

The Actuarial Society of South Africa HIV/AIDS models, also known as ASSA AIDS models, are a series of mathematical models developed to assist the actuarial profession and the in assessing and address

Predictive intake modelling

Predictive intake modelling uses mathematical modelling strategies to estimate intake of food, personal care products, and their formulations.

Quantitative models of the action potential

In neurophysiology, several mathematical models of the action potential have been developed, which fall into two basic types. The first type seeks to model the experimental data quantitatively, i.e.,

Fractional-order system

In the fields of dynamical systems and control theory, a fractional-order system is a dynamical system that can be modeled by a fractional differential equation containing derivatives of non-integer o

Von Bertalanffy function

The von Bertalanffy growth function (VBGF), or von Bertalanffy curve, is a type of growth curve for a time series and is named after Ludwig von Bertalanffy. It is a special case of the generalised log

Patlak plot

A Patlak plot (sometimes called Gjedde–Patlak plot, Patlak–Rutland plot, or Patlak analysis) is a graphical analysis technique based on the compartment model that uses linear regression to identify an

AMPL

AMPL (A Mathematical Programming Language) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (i.e., large-scale optimization and s

Modelling biological systems

Modelling biological systems is a significant task of systems biology and mathematical biology. Computational systems biology aims to develop and use efficient algorithms, data structures, visualizati

Van Genuchten–Gupta model

The van Genuchten–Gupta model is an inverted S-curve applicable to crop yield and soil salinity relations.

Bueno-Orovio–Cherry–Fenton model

The Bueno-Orovio–Cherry–Fenton model, also simply called Bueno-Orovio model, is a minimal ionic model for human ventricular cells. It belongs to the category of phenomenological models, because of its

Quasispecies model

The quasispecies model is a description of the process of the Darwinian evolution of certain self-replicating entities within the framework of physical chemistry. A quasispecies is a large group or "c

Seshat (project)

The Seshat: Global History Databank (named after Seshat, the ancient Egyptian goddess of wisdom, knowledge, and writing) is an international scientific research project of the nonprofit Evolution Inst

Price's model

Price's model (named after the physicist Derek J. de Solla Price) is a mathematical model for the growth of citation networks. It was the first model which generalized the Simon model to be used for n

Theta model

The theta model, or Ermentrout–Kopell canonical model, is a biological neuron model originally developed to model neurons in the animal Aplysia, and later used in various fields of computational neuro

Autowave

Autowaves are self-supporting non-linear waves in active media (i.e. those that provide distributed energy sources). The term is generally used in processes where the waves carry relatively low energy

Cumulative accuracy profile

A cumulative accuracy profile (CAP) is a concept utilized in data science to visualize discrimination power. The CAP of a model represents the cumulative number of positive outcomes along the y-axis v

Effective selfing model

The effective selfing model is a mathematical model that describes the mating system of a plant population in terms of the degree of self-fertilisation present.

Superiority and inferiority ranking method

The superiority and inferiority ranking method (or SIR method) is a multi-criteria decision making model (MCDA) which can handle real data and provides six different preference structures for the syst

Landscape evolution model

A landscape evolution model is a physically-based numerical model that simulates changing terrain over the course of time. The change in, or evolution of, terrain, can be due to: glacial or fluvial er

Elementary effects method

The elementary effects (EE) method is the most used screening method in sensitivity analysis. EE is applied to identify non-influential inputs for a computationally costly mathematical model or for a

Bidomain model

The bidomain model is a mathematical model to define the electrical activity of the heart. It consists in a continuum (volume-average) approach in which the cardiac mictrostructure is defined in terms

Bounded growth

Bounded growth occurs when the growth rate of a mathematical function is constantly increasing at a decreasing rate. Asymptotically, bounded growth approaches a fixed value. This contrasts with expone

Excitable medium

An excitable medium is a nonlinear dynamical system which has the capacity to propagate a wave of some description, and which cannot support the passing of another wave until a certain amount of time

Backtesting

Backtesting is a term used in modeling to refer to testing a predictive model on historical data. Backtesting is a type of retrodiction, and a special type of cross-validation applied to previous time

Calculation of glass properties

The calculation of glass properties (glass modeling) is used to predict glass properties of interest or glass behavior under certain conditions (e.g., during production) without experimental investiga

Movable cellular automaton

The movable cellular automaton (MCA) method is a method in computational solid mechanics based on the discrete concept. It provides advantages both of classical cellular automaton and discrete element

Quadratic integrate and fire

The quadratic integrate and fire (QIF) model is a biological neuron model and a type of integrate-and-fire neuron which describes action potentials in neurons. In contrast to physiologically accurate

Viral dynamics

Viral dynamics is a field of applied mathematics concerned with describing the progression of viral infections within a host organism. It employs a family of mathematical models that describe changes

Surrogate model

A surrogate model is an engineering method used when an outcome of interest cannot be easily measured or computed, so a model of the outcome is used instead. Most engineering design problems require e

Proper generalized decomposition

The proper generalized decomposition (PGD) is an iterative numerical method for solving boundary value problems (BVPs), that is, partial differential equations constrained by a set of boundary conditi

Akaike information criterion

The Akaike information criterion (AIC) is an estimator of prediction error and thereby relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC es

Autowave reverberator

In the theory of autowave phenomena an autowave reverberator is an autowave vortex in a two-dimensional active medium. A reverberator appears a result of a rupture in the front of a plane autowave. Su

Malthusian equilibrium

A population is in Malthusian equilibrium when all of its production is used only for subsistence. Malthusian equilibrium is a locally stable and a dynamic equilibrium.

Turing pattern

The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis" which describes how patterns in nature, such as stripes and

SAMPL

SAMPL, which stands for "Stochastic AMPL", is an algebraic modeling language resulting by expanding the well-known language AMPL with extended syntax and keywords. It is designed specifically for repr

Phase-field model

A phase-field model is a mathematical model for solving interfacial problems. It has mainly been applied to solidification dynamics, but it has also been applied to other situations such as viscous fi

Model order reduction

Model order reduction (MOR) is a technique for reducing the computational complexity of mathematical models in numerical simulations. As such it is closely related to the concept of metamodeling, with

Automated efficiency model

An automated efficiency model (AEM) is a mathematical model that estimates a real estate property’s efficiency by using details specific to the property which are available publicly and/or housing cha

Malthusian growth model

A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function

Two-fluid model

Two-fluid model is a macroscopic traffic flow model to represent traffic in a town/city or metropolitan area, put forward in the 1970s by Ilya Prigogine and Robert Herman. There is also a two-fluid mo

Analysis

Analysis (PL: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathema

Exponential growth

Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the q

Applications of sensitivity analysis to multi-criteria decision making

A sensitivity analysis may reveal surprising insights in multi-criteria decision making (MCDM) studies aimed to select the best alternative among a number of competing alternatives. This is an importa

Mathematical model

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used

Variational multiscale method

The variational multiscale method (VMS) is a technique used for deriving models and numerical methods for multiscale phenomena. The VMS framework has been mainly applied to design stabilized finite el

Traffic model

A traffic model is a mathematical model of real-world traffic, usually, but not restricted to, road traffic. Traffic modeling draws heavily on theoretical foundations like network theory and certain t

Gradient-enhanced kriging

Gradient-enhanced kriging (GEK) is a surrogate modeling technique used in engineering. A surrogate model (alternatively known as a metamodel, response surface or emulator) is a prediction of the outpu

Linear seismic inversion

Inverse modeling is a mathematical technique where the objective is to determine the physical properties of the subsurface of an earth region that has produced a given seismogram. Cooke and Schneider

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