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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 experiments and/or simulations to evaluate design objective and constraint functions as a function of design variables. For example, in order to find the optimal airfoil shape for an aircraft wing, an engineer simulates the airflow around the wing for different shape variables (length, curvature, material, ..). For many real-world problems, however, a single simulation can take many minutes, hours, or even days to complete. As a result, routine tasks such as design optimization, design space exploration, sensitivity analysis and ''what-if'' analysis become impossible since they require thousands or even millions of simulation evaluations. One way of alleviating this burden is by constructing approximation models, known as surrogate models, ''metamodels'' or ''emulators'', that mimic th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curve Fitting
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. A related topic is regression analysis, which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data. For linear-algebraic analysis o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal Transform
In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express this is Q^\mathrm Q = Q Q^\mathrm = I, where is the transpose of and is the identity matrix. This leads to the equivalent characterization: a matrix is orthogonal if its transpose is equal to its inverse: Q^\mathrm=Q^, where is the inverse of . An orthogonal matrix is necessarily invertible (with inverse ), unitary (), where is the Hermitian adjoint (conjugate transpose) of , and therefore normal () over the real numbers. The determinant of any orthogonal matrix is either +1 or −1. As a linear transformation, an orthogonal matrix preserves the inner product of vectors, and therefore acts as an isometry of Euclidean space, such as a rotation, reflection or rotoreflection. In other words, it is a unitary transformation. The set of orthogonal matrices, under multiplication, forms the group , known as the orthogonal gro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Experiment
A computer experiment or simulation experiment is an experiment used to study a computer simulation, also referred to as an in silico system. This area includes computational physics, computational chemistry, computational biology and other similar disciplines. Background Computer simulations are constructed to emulate a physical system. Because these are meant to replicate some aspect of a system in detail, they often do not yield an analytic solution. Therefore, methods such as discrete event simulation or finite element solvers are used. A computer model is used to make inferences about the system it replicates. For example, climate models are often used because experimentation on an earth sized object is impossible. Objectives Computer experiments have been employed with many purposes in mind. Some of those include: * Uncertainty quantification: Characterize the uncertainty present in a computer simulation arising from unknowns during the computer simulation's construc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fitness Approximation
Fitness approximationY. JinA comprehensive survey of fitness approximation in evolutionary computation ''Soft Computing'', 9:3–12, 2005 aims to approximate the objective or fitness functions in evolutionary optimization by building up machine learning models based on data collected from numerical simulations or physical experiments. The machine learning models for fitness approximation are also known as meta-models or surrogates, and evolutionary optimization based on approximated fitness evaluations are also known as surrogate-assisted evolutionary approximation.Surrogate-assisted evolutionary computation: Recent advances and future challenges Swarm and Evolutionary Computation, 1(2):61–70, 2011 Fitness approximation in evolutionary optimiz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surrogate Data
Surrogate data, sometimes known as analogous data, usually refers to time series data that is produced using well-defined (linear) models like ARMA processes that reproduce various statistical properties like the autocorrelation structure of a measured data set. The resulting surrogate data can then for example be used for testing for non-linear structure in the empirical data, see surrogate data testing. Surrogate or analogous data may refer to data used to supplement available data from which a mathematical model is built. Under this definition, it may be generated (i.e., synthetic data) or transformed from another source. Uses Surrogate data is used in environmental and laboratory settings, when study data from one source is used in estimation of characteristics of another source. For example, it has been used to model population trends in animal species. It can also be used to model biodiversity, as it would be difficult to gather actual data on all species in a given area. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surrogate Endpoint
In clinical trials, a surrogate endpoint (or surrogate marker) is a measure of effect of a specific treatment that may correlate with a ''real'' clinical endpoint but does not necessarily have a guaranteed relationship. The National Institutes of Health (USA) defines surrogate endpoint as "a biomarker intended to substitute for a clinical endpoint". Surrogate markers are used when the primary endpoint is undesired (e.g., death), or when the number of events is very small, thus making it impractical to conduct a clinical trial to gather a statistically significant number of endpoints. The FDA and other regulatory agencies will often accept evidence from clinical trials that show a direct clinical benefit to surrogate markers. Surrogate endpoints can be obtained from different modalities, such as, behavioural or cognitive scores, or biomarkers from Electroencephalography ( qEEG), MRI, PET, or biochemical biomarkers. A correlate does not make a surrogate. It is a common misconception ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 and design optimization of a system. The knowledge is updated with new validation information from the system when available. Concept The space mapping methodology employs a "quasi-global" formulation that intelligently links companion "coarse" (ideal or low-fidelity) and "fine" (practical or high-fidelity) models of different complexities. In engineering design, space mapping aligns a very fast coarse model with the expensive-to-compute fine model so as to avoid direct expensive optimization of the fine model. The alignment can be done either off-line (model enhancement) or on-the-fly with surrogate updates (e.g., aggressive space mapping). Methodology At the core of the process is a pair of models: one very accurate but too expensive to use directly with a conventional optimizati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OptiY
OptiY is a design environment software that provides modern optimization strategies and state of the art probabilistic algorithms for uncertainty, reliability, robustness, sensitivity analysis, data-mining and meta-modeling. Features OptiY is an open-source, multidisciplinary design environment, which provides direct and generic interfaces to many CAD/CAE-systems and house-intern codes. Furthermore, a complex COM-interface and a user-node with predefined template are available so that user can self-integrate extern programs for ease of use. The insertion of any system to an arbitrary process chain is very easy using the graphical workflow editor. Collaborating different simulation model classes is possible as networks, finite-element-method, multi-body-system, material test bench etc. Data mining Data mining is the process of extracting hidden patterns from data. Data mining identifies trends within data that go beyond simple data analysis. Through the use of sophisticated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 output of an expensive computer code. This prediction is based on a small number of evaluations of the expensive computer code. Introduction Adjoint solvers are now becoming available in a range of computational fluid dynamics (CFD) solvers, such as Fluent, OpenFOAM, SU2 and US3D. Originally developed for optimization, adjoint solvers are now finding more and more use in uncertainty quantification. Linear speedup An adjoint solver allows one to compute the gradient of the quantity of interest with respect to all design parameters at the cost of one additional solve. This, potentially, leads to a linear speedup: the computational cost of constructing an accurate surrogate decrease, and the resulting computational speedup s scales linearly with the number d of design parameters. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radial Basis Function
A radial basis function (RBF) is a real-valued function \varphi whose value depends only on the distance between the input and some fixed point, either the origin, so that \varphi(\mathbf) = \hat\varphi(\left\, \mathbf\right\, ), or some other fixed point \mathbf, called a ''center'', so that \varphi(\mathbf) = \hat\varphi(\left\, \mathbf-\mathbf\right\, ). Any function \varphi that satisfies the property \varphi(\mathbf) = \hat\varphi(\left\, \mathbf\right\, ) is a radial function. The distance is usually Euclidean distance, although other metrics are sometimes used. They are often used as a collection \_k which forms a basis for some function space of interest, hence the name. Sums of radial basis functions are typically used to approximate given functions. This approximation process can also be interpreted as a simple kind of neural network; this was the context in which they were originally applied to machine learning, in work by David Broomhead and David Lowe in 1988, which st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kriging
In statistics, originally in geostatistics, kriging or Kriging, also known as Gaussian process regression, is a method of interpolation based on Gaussian process governed by prior covariances. Under suitable assumptions of the prior, kriging gives the best linear unbiased prediction (BLUP) at unsampled locations. Interpolating methods based on other criteria such as smoothness (e.g., smoothing spline) may not yield the BLUP. The method is widely used in the domain of spatial analysis and computer experiments. The technique is also known as Wiener–Kolmogorov prediction, after Norbert Wiener and Andrey Kolmogorov. The theoretical basis for the method was developed by the French mathematician Georges Matheron in 1960, based on the master's thesis of Danie G. Krige, the pioneering plotter of distance-weighted average gold grades at the Witwatersrand reef complex in South Africa. Krige sought to estimate the most likely distribution of gold based on samples from a few boreholes. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Response Surface Methodology
In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. The method was introduced by George E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an optimal response. Box and Wilson suggest using a second-degree polynomial model to do this. They acknowledge that this model is only an approximation, but they use it because such a model is easy to estimate and apply, even when little is known about the process. Statistical approaches such as RSM can be employed to maximize the production of a special substance by optimization of operational factors. Of late, for formulation optimization, the RSM, using proper design of experiments (DoE), has become extensively used. In contrast to conventional methods, the interaction among process variables can be determined by statistical techniques. Basic approach of response surface ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
