Adaptive sparse interpolation for accelerating nonlinear stochastic reduced-order modeling with time-dependent bases

Reduced Order Modeling of Some Nonlinear Stochastic Partial Differential Equations

Determining accurate statistical information about outputs from ensembles of realizations is not generally possible whenever the input-output map involves the (computational) solution of systems of nonlinear partial differential equations (PDEs). This is due to the high cost of effecting each realization. Recently, in applications such as control and optimization that also require multiple solu...

Reduced Order Modeling of Nonlinear Control Systems

Sparse Polynomial Interpolation in Nonstandard Bases

In this paper, we consider the problem of interpolating univariate polynomials over a eld of characteristic zero that are sparse in (a) the Pochhammer basis or, (b) the Chebyshev basis. The polynomials are assumed to be given by black boxes, i.e., one can obtain the value of a polynomial at any point by querying its black box. We describe eecient new algorithms for these problems. Our algorithm...

Parametric Reduced Order Models Using Adaptive Sampling and Interpolation

Over the past decade, a number of approaches have been put forth to improve the accuracy of projection-based reduced order models over parameter ranges. These can be classified as either i.) building a global basis that is suitable for a large parameter set by applying sampling strategies, ii.) identifying parameter dependent coefficient functions in the reduced order model, or iii.) changing t...

Sparse polynomial interpolation in Chebyshev bases

We study the problem of reconstructing a sparse polynomial in a basis of Chebyshev polynomials (Chebyshev basis in short) from given samples on a Chebyshev grid of [−1, 1]. A polynomial is called M -sparse in a Chebyshev basis, if it can be represented by a linear combination of M Chebyshev polynomials. For a polynomial with known and unknown Chebyshev sparsity, respectively, we present efficie...