DR may be supervised by taking advantage of class information.

Weaknesses: I have the following critical concerns about this paper: 1. The used datasets are too simple. More complex datasets such as SculptFaces in NeRV paper are required to evaluate the performance of the proposed algorithm. As detailed above, ClassNeRV could be seen as a variation of NeRV through penalizing within-class missed neighbors and between-class false neighbors with class information. Therefore, in my opinion, it is not a significant contribution. According to Sec 3.2, they derived the ClassNeRV Stress Function from NeRV Stress Function by splitting Eq. 2 into within-class and between-class relations.

Stress-strain curves, or more generally, stress functions, are an extremely important characterization of a material's mechanical properties. However, stress functions are often difficult to derive and are narrowly tailored to a specific material. Further, large deformations, high strain-rates, temperature sensitivity, and effect of material parameters compound modeling challenges. We propose a generalized deep neural network approach to model stress as a state function with quantile regression to capture uncertainty. We extend these models to uniaxial impact mechanics using stochastic differential equations to demonstrate a use case and provide a framework for implementing this uncertainty-aware stress function. We provide experiments benchmarking our approach against leading constitutive, machine learning, and transfer learning approaches to stress and impact mechanics modeling on publicly available and newly presented data sets. We also provide a framework to optimize material parameters given multiple competing impact scenarios.

In recent years, the rapid advancement of deep learning has significantly impacted various fields, particularly in solving partial differential equations (PDEs) in the realm of solid mechanics, benefiting greatly from the remarkable approximation capabilities of neural networks. In solving PDEs, Physics-Informed Neural Networks (PINNs) and the Deep Energy Method (DEM) have garnered substantial attention. The principle of minimum potential energy and complementary energy are two important variational principles in solid mechanics. However, the well-known Deep Energy Method (DEM) is based on the principle of minimum potential energy, but there lacks the important form of minimum complementary energy. To bridge this gap, we propose the deep complementary energy method (DCEM) based on the principle of minimum complementary energy. The output function of DCEM is the stress function, which inherently satisfies the equilibrium equation. We present numerical results using the Prandtl and Airy stress functions, and compare DCEM with existing PINNs and DEM algorithms when modeling representative mechanical problems. The results demonstrate that DCEM outperforms DEM in terms of stress accuracy and efficiency and has an advantage in dealing with complex displacement boundary conditions, which is supported by theoretical analyses and numerical simulations. We extend DCEM to DCEM-Plus (DCEM-P), adding terms that satisfy partial differential equations. Furthermore, we propose a deep complementary energy operator method (DCEM-O) by combining operator learning with physical equations. Initially, we train DCEM-O using high-fidelity numerical results and then incorporate complementary energy. DCEM-P and DCEM-O further enhance the accuracy and efficiency of DCEM.

Stress minimization is among the best studied force-directed graph layout methods because it reliably yields high-quality layouts. It thus comes as a surprise that a novel approach based on stochastic gradient descent (Zheng, Pawar and Goodman, TVCG 2019) is claimed to improve on state-of-the-art approaches based on majorization. We present experimental evidence that the new approach does not actually yield better layouts, but that it is still to be preferred because it is simpler and robust against poor initialization.

The complexity and tight integration of electromechanical systems often makes them "brittle" and hard to modify in response to changing requirements. We aim to remedy this by capturing expert knowledge as functional blueprints, an idea inspired by regulatory processes that occur in natural morphogenesis. We then apply this knowledge in an intelligent design variation tool. When a user modifies a design, our tool uses functional blueprints to modify other components in response, thereby maintaining integration and reducing the need for costly search or constraint solving. In this paper, we refine the functional blueprint concept and discuss practical issues in applying it to electromechanical systems. We then validate our approach with a case study applying our prototype tool to create variants of a miniDroid robot and by empirical evaluation of convergence dynamics of networks of functional blueprints.