Keke Wu

Keke Wu, Xiong-bin Yan, Shi Jin et al.

In this paper, we introduce two types of novel Asymptotic-Preserving Convolutional Deep Operator Networks (APCONs) designed to address the multiscale time-dependent linear transport problem. We observe that the vanilla physics-informed DeepONets with modified MLP may exhibit instability in maintaining the desired limiting macroscopic behavior. Therefore, this necessitates the utilization of an asymptotic-preserving loss function. Drawing inspiration from the heat kernel in the diffusion equation, we propose a new architecture called Convolutional Deep Operator Networks, which employ multiple local convolution operations instead of a global heat kernel, along with pooling and activation operations in each filter layer. Our APCON methods possess a parameter count that is independent of the grid size and are capable of capturing the diffusive behavior of the linear transport problem. Finally, we validate the effectiveness of our methods through several numerical examples.

Stephen Smart, Keke Wu, Danielle Albers Szafir

Visualizations often encode numeric data using sequential and diverging color ramps. Effective ramps use colors that are sufficiently discriminable, align well with the data, and are aesthetically pleasing. Designers rely on years of experience to create high-quality color ramps. However, it is challenging for novice visualization developers that lack this experience to craft effective ramps as most guidelines for constructing ramps are loosely defined qualitative heuristics that are often difficult to apply. Our goal is to enable visualization developers to readily create effective color encodings using a single seed color. We do this using an algorithmic approach that models designer practices by analyzing patterns in the structure of designer-crafted color ramps. We construct these models from a corpus of 222 expert-designed color ramps, and use the results to automatically generate ramps that mimic designer practices. We evaluate our approach through an empirical study comparing the outputs of our approach with designer-crafted color ramps. Our models produce ramps that support accurate and aesthetically pleasing visualizations at least as well as designer ramps and that outperform conventional mathematical approaches.