Publication

MATHICSE Technical Report: Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval

2020
Working Papers

Abstract

An existence result is presented for the dynamical low rank (DLR) approximation for random semi-linear evolutionary equations. The DLR solution approximates the true solution at each time instant by a linear combination of products of deterministic and stochastic basis functions, both of which evolve over time. A key to our proof is to find a suitable equivalent formulation of the original problem. The so-called Dual Dynamically Orthogonal formulation turns out to be convenient. Based on this formulation, the DLR approximation is recast to an abstract Cauchy problem in a suitable linear space, for which existence and uniqueness of the solution in the maximal interval are established.

Official source

https://infoscience.epfl.ch/entities/publication/662a1efd-6334-4845-9b58-e957230fc331

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2020
Working Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/662a1efd-6334-4845-9b58-e957230fc331

About this result

Related concepts (32)

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In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants). The concept of linear combinations is central to linear algebra and related fields of mathematics. Most of this article deals with linear combinations in the context of a vector space over a field, with some generalizations given at the end of the article.

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MATHICSE Technical Report: Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval

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