演化系统灵敏度计算：一种实时降阶建模策略
Computing Sensitivities in Evolutionary Systems: A Real-Time Reduced Order Modeling Strategy
摘要：
我们提出了一种新的方法来计算灵敏度在进化系统中使用模型驱动的低秩近似。为此，我们制定了一个变分原理，旨在减少减少近似和灵敏度动态的时间导数之间的距离。一阶最优性条件的变分原理导致一个系统的封闭形式的发展方程的规范正交基和相应的灵敏度系数。这种方法允许通过在运行中提取不同灵敏度之间的相关性来以准确和易处理的方式计算相对于大量参数的灵敏度。该方法需要求解前向发展方程，避开了伴随灵敏度的前向/后向工作流所施加的限制。例如，所提出的方法，不像伴随方程，不施加任何I/O负载，并可用于实时灵敏度感兴趣的应用中。我们证明了三个测试情况下的实用程序的方法：（1）计算灵敏度相对于模型参数的Rossler系统（2）计算灵敏度相对于一个无限维强迫参数的混沌Kuramoto-Sivashinsky方程和（3）计算灵敏度相对于反应参数的物种传输在湍流反应流。
英文摘要：
We present a new methodology for computing sensitivities in evolutionary systems using a model-driven low-rank approximation. To this end, we formulate a variational principle that seeks to minimize the distance between the time derivative of the reduced approximation and sensitivity dynamics. The first-order optimality condition of the variational principle leads to a system of closed-form evolution equations for an orthonormal basis and corresponding sensitivity coefficients. This approach allows for the computation of sensitivities with respect to a large number of parameters in an accurate and tractable manner by extracting correlations between different sensitivities on the fly. The presented method requires solving forward evolution equations, sidestepping the restrictions imposed by forward/backward workflow of adjoint sensitivities. For example, the presented method, unlike the adjoint equation, does not impose any I/O load and can be used in applications in which real time sensitivities are of interest. We demonstrate the utility of the method for three test cases: (1) computing sensitivity with respect to model parameters in the Rossler system (2) computing sensitivity with respect to an infinite-dimensional forcing parameter in the chaotic Kuramoto-Sivashinsky equation and (3) computing sensitivity with respect to reaction parameters for species transport in a turbulent reacting flow.
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