Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval
2020
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.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
21
References
4
Citations
NaN
KQI