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In this work, we introduce the ConvPDE-UQ framework for constructing light-weight numerical solvers for partial differential equations (PDEs) using convolutional neural networks. A theoretical justification for the neural network approximation to partial differential equation solvers on varied domains is established based on the existence and properties of Green's functions. These solvers are able to effectively reduce the computational demands of traditional numerical methods into a single forward-pass of a convolutional network. The network architecture is also designed to predict pointwise Gaussian posterior distributions, with weights trained to minimize the associated negative log-likelihood of the observed solutions. This setup facilitates simultaneous training and uncertainty quantification for the network's solutions, allowing the solver to provide pointwise uncertainties for its predictions. The associated training procedure avoids the computationally expensive Bayesian inference steps used by other state-of-the-art uncertainty models and allows training to be scaled to the large data sets required for learning on varied problem domains. The performance of the framework is demonstrated on three distinct classes of PDEs consisting of two linear elliptic problem setups and a nonlinear Poisson problem. After a single offline training procedure for each class, the proposed networks are capable of accurately predicting the solutions to linear and nonlinear elliptic problems with heterogeneous source terms defined on any specified two-dimensional domain using just a single forward-pass of a convolutional neural network. Additionally, an analysis of the predicted pointwise uncertainties is presented with experimental evidence establishing the validity of the network's uncertainty quantification schema. • Solutions to PDEs on general domains are accurately approximated by a single forward-pass of a convolutional neural network. • A theoretical justification for the neural network approximation is established based on the theory of Green's functions. • Neural networks are trained to produce accurate uncertainty estimates using a scalable framework suitable for large datasets. • The empirical statistics of the uncertainty estimates are observed to align precisely with the designed Gaussian error model. [ABSTRACT FROM AUTHOR]

Design protocol analysis is a technique to understand designers’ cognitive processes by analyzing sequences of observations on their behavior. These observations typically use audio, video, and transcript data in order to gain insights into the designer's behavior and the design process. The recent availability of sophisticated sensing technology has made such data highly multimodal, requiring more flexible protocol analysis tools. To address this need, we present VizScribe, a visual analytics framework that employs multiple coordinated multiple views that enable the viewing of such data from different perspectives. VizScribe allows designers to create, customize, and extend interactive visualizations for design protocol data such as video, transcripts, sketches, sensor data, and user logs. User studies where design researchers used VizScribe for protocol analysis indicated that the linked views and interactive navigation offered by VizScribe afforded the researchers multiple, useful ways to approach and interpret such multimodal data. [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]

We present Sketcholution, a method for automatically creating visual histories of hand-drawn sketches. Such visual histories are useful for a designer to reflect on a sketch, communicate ideas to others, and fork from or revert to an earlier point in the creative process. Our approach uses a bottom-up agglomerative clustering mechanism that groups adjacent frames based on their perceptual similarity while maintaining the causality of how a sketch was constructed. The resulting aggregation dendrogram can be cut at any level depending on available display space, and can be used to create a visual history consisting of either a comic strip of highlights or a single annotated summary frame. We conducted a user study comparing the speed and accuracy of participants recovering causality in a sketch history using comic strips, summary frames, and simple animations. Although animations with interaction may seem better than static graphics, our results show that both comic strip and summary frame significantly outperform animation. [ABSTRACT FROM AUTHOR]

• Material context matters to perceptions of collaboration quality. • Spatial context matters to creative fluency in collaborative design. • Synchronous interaction has important roles in collaboration quality. • Reciprocal interaction has important roles in creative fluency. Engineering design typically occurs as a collaborative process situated in specific context such as computer-supported environments, however there is limited research examining the dynamics of design collaboration in specific contexts. In this study, drawing from situative learning theory, we developed two analytic lenses to broaden theoretical insights into collaborative design practices in computer-supported environments: (a) the role of spatial and material context, and (b) the role of social interactions. We randomly assigned participants to four conditions varying the material context (paper vs. tablet sketching tools) and spatial environment (private room vs commons area) as they worked collaboratively to generate ideas for a toy design task. We used wearable sociometric badges to automatically and unobtrusively collect social interaction data. Using partial least squares regression, we generated two predictive models for collaboration quality and creative fluency. We found that context matters materially to perceptions of collaboration, where those using collaboration-support tools perceived higher quality collaboration. But context matters spatially to creativity, and those situated in private spaces are more fluent in generating ideas than those in commons areas. We also found that interaction dynamics differ: synchronous interaction is important to quality collaboration, but reciprocal interaction is important to creative fluency. These findings provide important insights into the processual factors in collaborative design in computer-supported environments, and the predictive role of context and conversation dynamics. We discuss the theoretical contributions to computer-supported collaborative design, the methodological contributions of wearable sensor tools, and the practical contributions to structuring computer-supported environments for engineering design practice. [ABSTRACT FROM AUTHOR]