Reduced-order model-based convergence acceleration of reverse mode discrete adjoint solvers
Reduced-order model-based convergence acceleration of reverse mode discrete adjoint solvers
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DOI：
10.1016/j.ast.2019.105334
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发表时间：
2019-10
影响因子：
5.6
通讯作者：
Andrew L. Kaminsky;K. Ekici
中科院分区：
文献类型：
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作者：
Andrew L. Kaminsky;K. Ekici
这项工作提出了一种新的技术，以减少计算灵敏度的计算成本使用离散伴随求解器开发的反向模式自动微分。利用原始时间步长伴随方法，建立了离散伴随灵敏度方程的不动点迭代法。然后通过建立降阶模型(ROM)来加速定点灵敏度解，该模型映射灵敏度解与其相应残差之间的关系。然后，该模型被用来近似收敛的解，对应于零残差。虽然近似解可能不会产生完全收敛的解，但它通常提供了一种改进的解，可以用来重新初始化定点求解器，这是本工作的新方面之一。在重新初始化解之后，可以重新应用只读存储器加速技术，直到达到所需的收敛标准。建议的只读存储器的一个主要特点是，它是在单一灵敏度解决方案期间动态形成的。此外，它的实现只需要对现有的定点迭代求解器进行很小的修改。结合水平风力机叶片型线的优化设计，对ROM型线投影技术进行了评估，成本降低了57%~80%。
This work presents a new technique to reduce the computational cost of sensitivities calculated using a discrete adjoint solver developed via reverse mode automatic differentiation. A fixed-point iterative method is built for the discrete adjoint sensitivity equations by employing the primal time-stepping adjoint approach. The fixed-point sensitivity solution is then accelerated by building a reduced-order model (ROM) that maps the relationship between the sensitivity solution and its corresponding residual. This model is then used to approximate the converged solution, corresponding to a zero residual. While the approximation might not produce the fully converged solution, it typically provides an improved solution that the fixed-point solver can be re-initialized with, which is one of the novel aspects of the present work. After re-initializing the solution, the ROM acceleration technique can be reapplied until the desired convergence criterion is reached. A key feature of the proposed ROM is that it is formed on the fly during a single sensitivity solution. Additionally, its implementation requires only minor modifications to an existing fixed-point iterative solver. The ROM projection technique is evaluated by considering design optimization of horizontal wind turbine blade profiles and cost reductions of 57 to 80% were achieved.