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The aim of this paper is to solve an important inverse source problem which arises from the well-known inverse scattering problem. We propose to truncate the Fourier series of the solution to the governing equation with respect to a special basis of L2. By this, we obtain a system of linear elliptic equations. Solutions to this system are the Fourier coefficients of the solution to the governing equation. After computing these Fourier coefficients, we can directly find the desired source function. Numerical examples are presented. 

Engineered systems are designed to serve societal needs, from bridges providing mobility to communication systems enabling the transfer of information. It is essential that engineers recognize the social impact of their work to ensure they provide equitable benefits across communities when implementing such systems. In times of crisis, such as after natural disasters, these ethical considerations and awareness of community needs are especially important. Ethical development must begin when engineers are still students so that they can be trained to consider ethical issues before they begin working. Ethical development can be observed using James Rest’s Four-Component Model of Morality: moral sensitivity, moral judgement, moral motivation, and moral behavior. Previous work has focused largely on the second stage, moral judgement, which describes the ability to determine which action is morally right when confronted with an ethical issue. Here, however, we focus on the first stage, moral sensitivity, emphasizing one’s ability to recognize a moral issue. Studies show that while moral sensitivity does not always lead to moral behavior; moral sensitivity can help explain variances in moral behavior. Researchers argue that pinpointing students’ gaps in moral sensitivity can help educators identify gaps in engineering ethics curriculum. Towards this goal, we interviewed undergraduate engineering students to evaluate their moral sensitivity, using a current event, the 2021 Hurricane Ida in Southern Louisiana, as background. This natural disaster provided a useful context to evaluate moral sensitivity due to the complex effects of such a crisis on engineered, natural, and social systems. The story is framed using Lind’s Indicators of Ethical Sensitivity, providing the story characteristics, stakeholders, and consequences. We asked interviewees to provide the final indicator—ethical issues. Using a qualitative content analysis, we found that interviewees connected several ethical issues with the primary consequence of socioeconomic inequities. Identified ethical issues included topics of climate change, infrastructure, disaster planning, and corporate/government accountability. Implications of this study include recommendations for future moral sensitivity research and applications to improve classroom learning. 

Recent research shows that the dynamics of an infinitely wide neural network (NN) trained by gradient descent can be characterized by Neural Tangent Kernel (NTK) [27]. Under the squared loss, the infinite-width NN trained by gradient descent with an infinitely small learning rate is equivalent to kernel regression with NTK [4]. However, the equivalence is only known for ridge regression currently [6], while the equivalence between NN and other kernel machines (KMs), e.g. support vector machine (SVM), remains unknown. Therefore, in this work, we propose to establish the equivalence between NN and SVM, and specifically, the infinitely wide NN trained by soft margin loss and the standard soft margin SVM with NTK trained by subgradient descent. Our main theoretical results include establishing the equivalence between NN and a broad family of L2 regularized KMs with finite width bounds, which cannot be handled by prior work, and showing that every finite-width NN trained by such regularized loss functions is approximately a KM. Furthermore, we demonstrate our theory can enable three practical applications, including (i) non-vacuous generalization bound of NN via the corresponding KM; (ii) nontrivial robustness certificate for the infinite-width NN (while existing robustness verification methods would provide vacuous bounds); (iii) intrinsically more robust infinite-width NNs than those from previous kernel regression.