We present Atlas, a procedural grammar for constructing data visualizations. Unlike most visualization grammars which use declarative specifications to describe visualization components, Atlas exposes the generative process of a visualization through a set of concatenated high-level production rules. Each of these rules describes how an input graphical object is created, transformed, or joined with abstract data to derive an output object. The visualization state can thus be inspected throughout the generative process. We demonstrate Atlas’ expressivity through a catalog of visualization designs, and discuss the trade-offs in its design by comparing it to state-of-the-art grammars.

In this paper we present a novel analysis of variance Gaussian process (ANOVA-GP) emulator for models governed by partial differential equations (PDEs) with high-dimensional random inputs. The Gaussian process (GP) is a widely used surrogate modeling strategy, but it can become invalid when the inputs are high-dimensional. In this new ANOVA-GP strategy, high-dimensional inputs are decomposed into unions of local low-dimensional inputs, and principal component analysis (PCA) is applied to provide dimension reduction for each ANOVA term. We then systematically build local GP models for PCA coefficients based on ANOVA decomposition to provide an emulator for the overall high-dimensional problem. We present a general mathematical framework of ANOVA-GP, validate its accuracy and demonstrate its efficiency with numerical experiments.