Robust Approximation of the Stochastic Koopman Operator
Robust Approximation of the Stochastic Koopman Operator
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DOI：
10.1137/21m1414425
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发表时间：
2020-10
期刊：
影响因子：
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通讯作者：
Mathias Wanner;Igor Mezi'c
中科院分区：
文献类型：
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作者：
Mathias Wanner;Igor Mezi'c
我们分析了动态模式分解 (DMD) 的随机库普曼算子近似的性能，适用于动态或可观测量受到噪声影响的随机动态系统。在某些遍历性假设下，我们表明，只要可观测量不包含任何噪声并且跨越随机库普曼算子的不变子空间，标准 DMD 算法就会收敛。对于带有噪声的可观测量，我们引入了一种新的、鲁棒的 DMD 算法，该算法可以近似随机 Koopman 算子，并演示如何使用在单个轨迹上测量的单个可观测量将该算法应用于基于 Krylov 子空间的方法。我们通过几个示例测试算法的性能。
We analyze the performance of Dynamic Mode Decomposition (DMD)-based approximations of the stochastic Koopman operator for random dynamical systems where either the dynamics or observables are affected by noise. Under certain ergodicity assumptions, we show that standard DMD algorithms converge provided the observables do not contain any noise and span an invariant subspace of the stochastic Koopman operator. For observables with noise, we introduce a new, robust DMD algorithm that can approximate the stochastic Koopman operator and demonstrate how this algorithm can be applied to Krylov subspace based methods using a single observable measured over a single trajectory. We test the performance of the algorithms over several examples.