MATHICSE Technical Report: Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval
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.
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Kazashi, Y., & Nobile, F. (2020). MATHICSE Technical Report: Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval [Working Paper]. MATHICSE. https://doi.org/10.5075/epfl-MATHICSE-274320
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2020-02-06
MATHICSE
NON-REVIEWED
EPFL
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