高保真度模拟的一致性增强随机优化
Gradient-enhanced stochastic optimization of high-fidelity simulations
摘要：
复杂非定常流的优化和控制仍然是一个重要的挑战，这是由于执行功能评估（即，完整的计算流体动力学（CFD）模拟）的成本很高。减少所需函数求值的数量将有助于降低整个优化过程的计算成本。在本文中，我们考虑了基于随机导数自由代理模型的动态坐标搜索使用响应曲面（DYCORS）算法，并提出了几个增强：第一，梯度信息添加到代理模型，以提高其精度和提高算法的收敛速度。其次，径向基函数的内部参数用于生成代理模型进行优化，通过最小化的情况下的原始算法的留一法的错误，并通过使用梯度增强版本的情况下的梯度信息。我们将由此产生的优化算法应用于通过线性叶栅的总压损失最小化，并将不同雷诺数下的随机算法与基于梯度的优化算法所得结果进行比较。结果表明，随机优化优于基于梯度的优化，即使在非常低的$Re$数，和所提出的梯度增强版本提高了原算法的收敛速度。该算法的梯度增强版本的开源实现是可用的。
英文摘要：
Optimization and control of complex unsteady flows remains an important challenge due to the large cost of performing a function evaluation, i.e. a full computational fluid dynamics (CFD) simulation. Reducing the number of required function evaluations would help to decrease the computational cost of the overall optimization procedure. In this article, we consider the stochastic derivative-free surrogate-model based Dynamic COordinate search using Response Surfaces (DYCORS) algorithm and propose several enhancements: First, the gradient information is added to the surrogate model to improve its accuracy and enhance the convergence rate of the algorithm. Second, the internal parameters of the radial basis function employed to generate the surrogate model are optimized by minimizing the leave-one-out error in the case of the original algorithm and by using the gradient information in the case of the gradient-enhanced version. We apply the resulting optimization algorithm to the minimization of the total pressure loss through a linear cascade of blades, and we compare the results obtained with the stochastic algorithms at different Reynolds numbers with a gradient-based optimization algorithm. The results show that stochastic optimization outperforms gradient-based optimization even at very low $Re$ numbers, and that the proposed gradient-enhanced version improves the convergence rate of the original algorithm. An open-source implementation of the gradient-enhanced version of the algorithm is available.
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