论文标题
在最大间隔上随机半线性进化方程的动态低等级近似值的存在
Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval
论文作者
论文摘要
对于随机半线性进化方程的动力学低等级（DLR）近似，提出了一个存在结果。 DLR解通过确定性和随机基础函数的乘积的线性组合在每次瞬间近似真正的解决方案，这两者都会随时间发展。我们证明的关键是找到适合原始问题的等效表述。所谓的双重直通正交配方很方便。基于此公式，DLR近似是在合适的线性空间中重塑了抽象的Cauchy问题，为此，在最大间隔中建立了解决方案的存在和唯一性。
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.
