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A partial differential equation (PDE) constrained design optimization problem usually optimizes a characteristic of a dynamical system around an equilibrium point. However, a commonly omitted constraint is the linear stability constraint at the equilibrium point, which undermines the optimized solution’s applicability. To enforce the linear stability constraint in practical gradient-based optimization, the derivatives must be computed accurately, and their computational cost must scale favorably with the number of design variables. In this paper, we propose an algorithm based on the coupled adjoint method and the algorithmic differentiation method that can compute the derivative of such constraint accurately and efficiently. We verify the proposed method using several simple low-dimensional dynamical systems. The relative difference between the adjoint method and the finite differences is between [Formula: see text] to [Formula: see text]. The proposed method is demonstrated through several optimizations, including a nonlinear aeroelastic optimization. The proposed algorithm has the potential to be applied to more complex problems involving large-scale nonlinear PDEs, such as aircraft flutter and buffet suppression. 

Abstract A central question in the science of science concerns how to develop a quantitative understanding of the evolution and impact of individual careers. Over the course of history, a relatively small fraction of individuals have made disproportionate, profound, and lasting impacts on science and society. Despite a long-standing interest in the careers of scientific elites across diverse disciplines, it remains difficult to collect large-scale career histories that could serve as training sets for systematic empirical and theoretical studies. Here, by combining unstructured data collected from CVs, university websites, and Wikipedia, together with the publication and citation database from Microsoft Academic Graph (MAG), we reconstructed publication histories of nearly all Nobel prize winners from the past century, through both manual curation and algorithmic disambiguation procedures. Data validation shows that the collected dataset presents among the most comprehensive collection of publication records for Nobel laureates currently available. As our quantitative understanding of science deepens, this dataset is expected to have increasing value. It will not only allow us to quantitatively probe novel patterns of productivity, collaboration, and impact governing successful scientific careers, it may also help us unearth the fundamental principles underlying creativity and the genesis of scientific breakthroughs.