Many visualization designs feature phenomena referred to as ``visual multiplexing'', where multiple pieces of information associated with the same data point are conveyed simultaneously. Although visualization designers are able to bring such phenomena, often unconsciously, into their designs, the design space of visual multiplexing is huge, and it is uncommon to explore visual multiplexing systematically as design patterns. In this paper, we propose a design method for exploring a smaller design space constrained by an application. As an illustrative case study, we focus on machine learning (ML) workflows for developing ML models that approximate partial differential equations (PDEs). In these workflows, ML researchers need to analyze the inter-relationships among multiple 2D scalar fields frequently. Since superimposing one heatmap on top of another is not an effective design, we formulate three design steps to explore the design space of visual multiplexing in the context of multiple 2D scalar fields. Our design method also includes a pre-design step for domain grounding and theoretical analysis, and involves domain experts in both co-design and evaluation activities. The design process enables us to identify relatively optimal default multiplexing designs as well as the need for small variations that domain experts can control through a user interface.

翻译：许多可视化设计呈现出被称为“视觉复用”的现象，即与同一数据点相关的多条信息被同时传达。尽管可视化设计者有时会不自觉地在其设计中引入此类现象，但视觉复用的设计空间极为广阔，且人们很少将其作为设计模式进行系统性探索。本文提出一种设计方法，旨在探索由具体应用约束的较小型设计空间。作为说明性案例研究，我们聚焦于开发近似偏微分方程（PDEs）的机器学习（ML）工作流。在此类工作流中，ML研究者需频繁分析多个二维标量场之间的相互关系。由于将热力图直接叠加并非有效设计，我们制定了三个设计步骤，以探索面向多个二维标量场的视觉复用设计空间。该方法还包含一个用于领域基础与理论分析的预设计步骤，并涉及领域专家在协同设计与评估活动中的参与。该设计流程使我们能够识别相对最优的默认复用设计，以及可通过用户界面由领域专家控制的细微变体需求。