论文标题
计算进化系统中的敏感性：实时减少订单建模策略
Computing Sensitivities in Evolutionary Systems: A Real-Time Reduced Order Modeling Strategy
论文作者
论文摘要
我们提出了一种使用模型驱动的低级近似值计算进化系统敏感性的新方法。为此，我们制定了一种差异原理，该原理旨在最大程度地减少降低近似和灵敏度动力学的时间导数之间的距离。变异原理的一阶最佳条件导致封闭形式进化方程的系统，以正顺序和相应的灵敏度系数。这种方法允许通过在即时提取不同敏感性之间的相关性来以准确且可进行的方式计算大量参数的敏感性。提出的方法需要求解向前的进化方程，并避免伴随灵敏度的前进/向后工作流施加的限制。例如，与伴随方程式不同的方法不会施加任何I/O负载，并且可以用于实时敏感性感兴趣的应用中。我们证明了该方法在三种测试案例中的实用性：（1）计算对罗斯勒系统中模型参数的敏感性（2）计算相对于混乱的kuramoto-sivashinskine方程中的无限二维强迫参数的敏感性，并且（3）计算敏感性涉及对物种构成构图的反应反应的敏感性。
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.
