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This paper presents the Dual Neural Network (DuNN) method, a physics-driven numerical method designed to solve elliptic partial differential equations and systems using deep neural network functions and a dual formulation. The underlying elliptic problem is formulated as an optimization of the complementary energy functional in terms of the dual variable, where the Dirichlet boundary condition is weakly enforced in the formulation. To accurately evaluate the complementary energy functional, we employ a novel discrete divergence operator. This discrete operator preserves the underlying physics and naturally enforces the Neumann boundary condition without penalization. For problems without reaction term, we propose an outer-inner iterative procedure that gradually enforces the equilibrium equation through a pseudo-time approach. 

Abstract Prototyping use cases for augmented reality (AR) applications can be beneficial to elicit the functional requirements of the features early-on, to drive the subsequent development in a goal-oriented manner. Doing so would require designers to identify the goal-oriented interactions and map the associations between those interactions in a spatio-temporal context. Pertaining to the multiple scenarios that may result from the mapping, and the embodied nature of the interaction components, recent AR prototyping methods lack the support to adequately capture and communicate the intent of designers and stakeholders during this process. We present ImpersonatAR, a mobile-device-based prototyping tool that utilizes embodied demonstrations in the augmented environment to support prototyping and evaluation of multi-scenario AR use cases. The approach uses: (1) capturing events or steps in the form of embodied demonstrations using avatars and 3D animations, (2) organizing events and steps to compose multi-scenario experience, and finally (3) allowing stakeholders to explore the scenarios through interactive role-play with the prototypes. We conducted a user study with ten participants to prototype use cases using ImpersonatAR from two different AR application features. Results validated that ImpersonatAR promotes exploration and evaluation of diverse design possibilities of multi-scenario AR use cases through embodied representations of the different scenarios. 

Abstract Domain users (DUs) with a knowledge base in specialized fields are frequently excluded from authoring virtual reality (VR)-based applications in corresponding fields. This is largely due to the requirement of VR programming expertise needed to author these applications. To address this concern, we developed VRFromX, a system workflow design to make the virtual content creation process accessible to DUs irrespective of their programming skills and experience. VRFromX provides an in situ process of content creation in VR that (a) allows users to select regions of interest in scanned point clouds or sketch in mid-air using a brush tool to retrieve virtual models and (b) then attach behavioral properties to those objects. Using a welding use case, we performed a usability evaluation of VRFromX with 20 DUs from which 12 were novices in VR programming. Study results indicated positive user ratings for the system features with no significant differences across users with or without VR programming expertise. Based on the qualitative feedback, we also implemented two other use cases to demonstrate potential applications. We envision that the solution can facilitate the adoption of the immersive technology to create meaningful virtual environments.