Polynomial chaos (PC), also called polynomial chaos expansion (PCE) and Wiener chaos expansion, is a method for representing a random variable in terms...

uncertainty quantification a surrogate model, e.g. a Gaussian process or a Polynomial Chaos Expansion, is learnt from computer experiments, this surrogate exhibits...

weight data points to sequentially reduce error. Polynomial chaos expansions, which use orthogonal polynomials to approximate the response surface. Smoothing...

the emulator uncertainty to the total uncertainty (see also Bayesian Polynomial Chaos). Bayesian kriging can also be mixed with co-kriging. The unknown value...

spectral/hp-element methods for fluids in complex geometries, general polynomial chaos for uncertainty quantification, and the Sturm-Liouville theory for...

concept in mathematical topology Precalculus, a level in math education Polynomial chaos, a concept in stochastic mathematics Principal component Posterior...

Gaussian processes, auto-regressive Gaussian processes, or Bayesian polynomial chaos expansions. The approach used depends on the domain and properties...

surface Kardar–Parisi–Zhang equation Kushner equation Malliavin calculus Polynomial chaos Wick product Zakai equation Prévôt, Claudia; Röckner, Michael (2007)...

Airport, in Indiana, US Gel permeation chromatography Generalized polynomial chaos General Polygon Clipper, a graphics library Giant papillary conjunctivitis...

work on integral equations and Fourier transforms. Wiener studied polynomial chaos, a key piece of which is the Hermite-Laguerre expansion. This was developed...

Stochastic Collocation Monte Carlo sampler (SCMC sampler) within a polynomial chaos expansion framework. This allows us to generate any number of Monte...

_{0}^{T}h(\lambda ,t)h(s,\lambda )\,d\lambda } Principal component analysis Polynomial chaos Reproducing kernel Hilbert space Mercer's theorem Sapatnekar, Sachin...

Expeditions, a British expedition organising company Wiener Chaos Expansion, another name for Polynomial chaos This disambiguation page lists articles associated...

equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words...

complex quadratic polynomial is a quadratic polynomial whose coefficients and variable are complex numbers. Quadratic polynomials have the following...

(2017). "Uncertainty quantification in prognostics: A data driven polynomial chaos approach". 2017 IEEE International Conference on Prognostics and Health...

Poly-Weibull distribution Polychoric correlation Polynomial and rational function modeling Polynomial chaos Polynomial regression Polytree (Bayesian networks)...

solutions, similarly as polynomial algebras are used for the study of algebraic varieties, which are solution sets of systems of polynomial equations. Weyl algebras...

arithmetic. This is accomplished by using a polynomial of high degree, and/or narrowing the domain over which the polynomial has to approximate the function. Narrowing...

parameters c {\displaystyle c} for which the Julia set of the corresponding polynomial forms a connected set. In the same way, the boundary of the Mandelbrot...

realized using the Pomeau–Manneville map. The Pomeau–Manneville map is a polynomial mapping (equivalently, recurrence relation), often referred to as an archetypal...

including bifurcations, chaos, harmonics, and subharmonics which cannot be produced or analyzed using linear methods. Polynomial signal processing is a...

and outer billiards Bouncing ball dynamics Circle map Complex quadratic polynomial Double pendulum Dyadic transformation Dynamical system simulation Hénon...

then it has at least one real root (this is true for all odd-degree polynomial functions). All of the roots of the cubic equation can be found by the...

quadratic difference equation: Equivalently it is a recurrence relation and a polynomial mapping of degree 2. It is often referred to as an archetypal example...

values again: In the case of the Mandelbrot set for complex quadratic polynomial f ( z ) = z 2 + c {\displaystyle f(z)=z^{2}+c} the Feigenbaum constant...

theory. A knot polynomial is a knot invariant that is a polynomial. Well-known examples include the Jones polynomial, the Alexander polynomial, and the Kauffman...

number variable). Examples of quadratic growth include: Any quadratic polynomial. Certain integer sequences such as the triangular numbers. The n {\displaystyle...

and/or algebraic points under repeated application of a polynomial or rational function. Chaos theory describes the behavior of certain dynamical systems...

Two-dimensional Crossing and Product Polynomial Systems, Springer (2025). Albert C. J. Luo, Two-dimensional Self and Product Polynomial Systems, Springer (2025)....