Goal-based sensitivity maps using time windows and ensemble perturbations
Goal-based sensitivity maps using time windows and ensemble perturbations
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发表时间：
2018-04
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通讯作者：
C. Heaney;P. Salinas;F. Fang;C. Pain;Ionel M. Navon
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作者：
C. Heaney;P. Salinas;F. Fang;C. Pain;Ionel M. Navon
我们提出了一种使用集成形成敏感度图（或敏感度）的方法。该方法是使用伴随函数的替代方法，伴随函数的制定非常具有挑战性，而且求解起来计算成本也很高。该方法的主要新颖之处在于：1）使用目标，对扰动进行加权以帮助解决最重要的敏感性，2）使用时间窗口，这使得可以针对每个窗口独立优化扰动，3）随时间重新正交化解决方案，这有助于在计算敏感性图时优化每个扰动。正如本文所示，这些新颖的方法大大减少了形成灵敏度图所需的集合数量。由于所提出的方法仅依赖于从正演模型获得的系综，因此它可以直接应用于由多物理场耦合、遗留代码或模型链等产生的任意复杂度的正演模型。它还可以应用于计算灵敏度，以优化传感器放置、优化设计或控制、基于目标的网格自适应性、目标评估（例如自然环境中的危害评估和缓解）、确定当前数据和数据同化的价值。我们通过将该方法应用于平流问题以及非线性异质多相多孔介质问题来分析和证明该方法的效率，结果表明，在所有情况下，获得准确灵敏度图所需的系综数量相对较低，约为 10 秒。
We present an approach for forming sensitivity maps (or sensitivites) using ensembles. The method is an alternative to using an adjoint, which can be very challenging to formulate and also computationally expensive to solve. The main novelties of the presented approach are: 1) the use of goals, weighting the perturbation to help resolve the most important sensitivities, 2) the use of time windows, which enable the perturbations to be optimised independently for each window and 3) re-orthogonalisation of the solution through time, which helps optimise each perturbation when calculating sensitivity maps. These novel methods greatly reduce the number of ensembles required to form the sensitivity maps as demonstrated in this paper. As the presented method relies solely on ensembles obtained from the forward model, it can therefore be applied directly to forward models of arbitrary complexity arising from, for example, multi-physics coupling, legacy codes or model chains. It can also be applied to compute sensitivities for optimisation of sensor placement, optimisation for design or control, goal-based mesh adaptivity, assessment of goals (e.g. hazard assessment and mitigation in the natural environment), determining the worth of current data and data assimilation. We analyse and demonstrate the efficiency of the approach by applying the method to advection problems and also a non-linear heterogeneous multi-phase porous media problem, showing, in all cases, that the number of ensembles required to obtain accurate sensitivity maps is relatively low, in the order of 10s.