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The prolonged training time of the neural network (NN) has sparked considerable debate regarding their application in the field of optimization. The purpose of this paper is to explore the beneficial assistance of NN-based alternative models in inductance design, with a particular focus on multi-objective optimization and uncertainty analysis processes.

Under Gaussian-distributed manufacturing errors, this study predicts error intervals for Pareto points and select robust solutions with minimal error margins. Furthermore, this study establishes correlations between manufacturing errors and inductance value discrepancies, offering a practical means of determining permissible manufacturing errors tailored to varying accuracy requirements.

The NN-assisted methods are demonstrated to offer a substantial time advantage in multi-objective optimization compared to conventional approaches, particularly in scenarios where the trained NN is repeatedly used. Also, NN models allow for extensive data-driven uncertainty quantification, which is challenging for traditional methods.

Three objectives including saturation current are considered in the multi-optimization, and the time advantages of the NN are thoroughly discussed by comparing scenarios involving single optimization, multiple optimizations, bi-objective optimization and tri-objective optimization. This study proposes direct error interval prediction on the Pareto front, using extensive data to predict the response of the Pareto front to random errors following a Gaussian distribution. This approach circumvents the compromises inherent in constrained robust optimization for inductance design and allows for a direct assessment of robustness that can be applied to account for manufacturing errors with complex distributions.

Independent directors are important corporate decision participants and makers. Based on the Chinese cultural background, this paper interprets the listing order of independent directors as independent directors’ status, exploring their influence on the corporate research and development (R&D) behavior.

This paper studies A-share listed firms in China from 2008 to 2018 as the sample. The main method is ordinary least square (OLS) regression. We also use other methods to deal with endogenous problems, such as the firm fixed effect method, change model method, two-stage instrumental variable method, and Heckman two-stage method.

(1) Higher independent directors’ status attribute to more effective exertion of supervision and consultation function, and positively enhance the corporate R&D investment. The increase of the independent director’ status by one standard deviation will increase the R&D investment by 4.6%. (2) The above effect is more influential in firms with stronger traditional culture atmosphere, higher information opacity and higher performance volatility. (3) High-status independent directors promote R&D investment by improving the scientificity of R&D evaluation and reducing information asymmetry. (4) The enhancing effect of independent director’ status on R&D investment is positively associated with the firm’s patent output and market value.

This paper contributes to understanding the relationship between the independent directors’ status and their duty execution from an embedded cultural background perspective. The findings of the study enlighten the improvement of corporate governance efficiency and the healthy development of the capital market.