Data-driven closures for stochastic dynamical systems
Data-driven closures for stochastic dynamical systems
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DOI：
10.1016/j.jcp.2018.06.038
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发表时间：
2018-04
期刊：
影响因子：
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通讯作者：
Catherine Brennan;D. Venturi
中科院分区：
文献类型：
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作者：
Catherine Brennan;D. Venturi
我们开发了一种新的数据驱动的闭包近似方法来计算高维随机动力系统中感兴趣的量的统计特性。所提出的框架依赖于从样本路径或实验数据估计系统相关的条件期望，然后使用这些估计来计算精确概率密度函数（PDF）方程的数据驱动的解决方案。我们还解决了一个重要的问题，是否有足够的有用的数据被注入到精确的PDF方程的计算精确的数值解的目的。数值例子和讨论的原型非线性动力系统和模型的系统生物学从随机初始状态。
We develop a new data-driven closure approximation method to compute the statistical properties of quantities of interest in high-dimensional stochastic dynamical systems. The proposed framework relies on estimating system-dependent conditional expectations from sample paths or experimental data, and then using such estimates to compute data-driven solutions to exact probability density function (PDF) equations. We also address the important question of whether enough useful data is being injected into the exact PDF equation for the purpose of computing an accurate numerical solution. Numerical examples are presented and discussed for prototype nonlinear dynamical systems and models of systems biology evolving from random initial states.