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In this paper, we study the deep Ritz method for solving the linear elasticity equation from a numerical analysis perspective. A modified Ritz formulation using the H 1 / 2 (Γ D) norm is introduced and analyzed for linear elasticity equation in order to deal with the (essential) Dirichlet boundary condition. We show that the resulting deep Ritz method provides the best approximation among the set of deep neural network (DNN) functions with respect to the "energy" norm. Furthermore, we demonstrate that the total error of the deep Ritz simulation is bounded by the sum of the network approximation error and the numerical integration error, disregarding the algebraic error. To effectively control the numerical integration error, we propose an adaptive quadrature-based numerical integration technique with a residual-based local error indicator. This approach enables efficient approximation of the modified energy functional. Through numerical experiments involving smooth and singular problems, as well as problems with stress concentration, we validate the effectiveness and efficiency of the proposed deep Ritz method with adaptive quadrature. [ABSTRACT FROM AUTHOR]

Most three-dimensional (3D) computer-aided design (CAD) models of mechanical parts, created during the design stage, have high shape complexity. The shape complexity required of CAD models reduces according to the field of application. Therefore, it is necessary to simplify the shapes of 3D CAD models, depending on their applications. Traditional simplification methods recognize simplification target shape based on a pre-defined algorithm. Such algorithm-based methods have difficulty processing unusual partial shapes not considered in the CAD model. This paper proposes a method that uses a network based on a generative adversarial network (GAN) to simplify the 3D CAD models of mechanical parts. The proposed network recognizes and removes simplification target shapes included in the 3D CAD models of mechanical parts. A 3D CAD model dataset was constructed to train the 3D CAD model simplification network. 3D CAD models are represented in voxel form in the dataset. Next, the constructed training dataset was used to train the proposed network. Finally, a 3D voxel simplification experiment was performed to evaluate the performance of the trained network. The experiment results showed that the network had an average error rate of 3.38% for the total area of the mechanical part and an average error rate of 14.61% for the simplification target area. • We present a learning-based method for simplifying mechanical 3D CAD models. • The proposed method utilizes an adversarial learning approach. • The generator generates a simplified CAD model from the original model. • The discriminator classifies the data created by the generator as either false or true. • Our method achieved a simplification performance of around 15% error rate. [ABSTRACT FROM AUTHOR]

Interaction in mid-air can be fatiguing. A model-based method to quantify cumulative subjective fatigue for such interaction was recently introduced in HCI research. This model separates muscle units into three states: active (M A) fatigued (M F) or rested (M R) and defines transition rules between states. This method demonstrated promising accuracy in predicting subjective fatigue accumulated in mid-air pointing tasks. In this paper, we introduce an improved model that additionally captures the variations of the maximum arm strength based on arm postures and adds linearly-varying model parameters based on current muscle strength. To validate the applicability and capabilities of the new model, we tested its performance in various mid-air interaction conditions, including mid-air pointing/docking tasks, with shorter and longer rest and task periods, and a long-term evaluation with individual participants. We present results from multiple cross-validations and comparisons against the previous model and identify that our new model predicts fatigue more accurately. Our modeling approach showed a 42.5% reduction in fatigue estimation error when the longitudinal experiment data is used for an individual participant's fatigue. Finally, we discuss the applicability and capabilities of our new approach. • Posture-based maximum strength representation is compatible with the TCM fatigue modeling method. • Subjective fatigue and muscle fatigue can be connected without contact-based measurement. • A reliable cumulative fatigue model is introduced based on brain effort (BE). • Designers can run our model in Kinect-based systems with a user's joint torque and Borg ratings. • A 42.5% reduction in fatigue estimation error for individualized modeling. [ABSTRACT FROM AUTHOR]