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Abstract Creativity is increasingly recognized as a core competency for the 21st century, making its development a priority in education, research, and industry. To effectively cultivate creativity, researchers and educators need reliable and accessible assessment tools. Recent software developments have significantly enhanced the administration and scoring of creativity measures; however, existing software often requires expertise in experiment design and computer programming, limiting its accessibility to many educators and researchers. In the current work, we introduce CAP—the Creativity Assessment Platform—a free web application for building creativity assessments, collecting data, and automatically scoring responses (cap.ist.psu.edu). CAP allows users to create custom creativity assessments in ten languages using a simple, point-and-click interface, selecting from tasks such as the Short Story Task, Drawing Task, and Scientific Creative Thinking Test. Users can automatically score task responses using machine learning models trained to match human creativity ratings—with multilingual capabilities, including the new Cross-Lingual Alternate Uses Scoring (CLAUS), a large language model achieving strong prediction of human creativity ratings in ten languages. CAP also provides a centralized dashboard to monitor data collection, score assessments, and automatically generate text for a Methods section based on the study’s tasks, metrics, and instructions—with a single click—promoting transparency and reproducibility in creativity assessment. Designed for ease of use, CAP aims to democratize creativity measurement for researchers, educators, and everyone in between. 

Many design problems involve reasoning about points in high-dimensional space. A common strategy is to first embed these high-dimensional points into a low-dimensional latent space. We propose that a good embedding should be isometric—i.e., preserving the geodesic distance between points on the data manifold in the latent space. However, enforcing isometry is non-trivial for common neural embedding models such as autoencoders. Moreover, while theoretically appealing, it is unclear to what extent is enforcing isometry necessary for a given design analysis. This paper answers these questions by constructing an isometric embedding via an isometric autoencoder, which we employ to analyze an inverse airfoil design problem. Specifically, the paper describes how to train an isometric autoencoder and demonstrates its usefulness compared to non-isometric autoencoders on the UIUC airfoil dataset. Our ablation study illustrates that enforcing isometry is necessary for accurately discovering clusters through the latent space. We also show how isometric autoencoders can uncover pathologies in typical gradient-based shape optimization solvers through an analysis on the SU2-optimized airfoil dataset, wherein we find an over-reliance of the gradient solver on the angle of attack. Overall, this paper motivates the use of isometry constraints in neural embedding models, particularly in cases where researchers or designers intend to use distance-based analysis measures to analyze designs within the latent space. While this work focuses on airfoil design as an illustrative example, it applies to any domain where analyzing isometric design or data embeddings would be useful. 

A practical and well-studied method for computing the novelty of a design is to construct an ordinal embedding via a collection of pairwise comparisons between items (called triplets), and use distances within that embedding to compute which designs are farthest from the center. Unfortunately, ordinal embedding methods can require a large number of triplets before their primary error measure — the triplet violation error — converges. But if our goal is accurate novelty estimation, is it really necessary to fully minimize all triplet violations? Can we extract useful information regarding the novelty of all or some items using fewer triplets than classical convergence rates might imply? This paper addresses this question by studying the relationship between triplet violation error and novelty score error when using ordinal embeddings. Specifically, we compare how errors in embeddings produced by Generalized Non-Metric Dimensional Scaling (GNMDS) converge under different sampling methods, for different numbers of embedded items, sizes of latent spaces, and for the top K most novel designs. We find that estimating the novelty of a set of items via ordinal embedding can require significantly fewer human-provided triplets than is needed to converge the triplet error, and that this effect is modulated by the type of triplet sampling method (random versus uncertainty sampling). We also find that uncertainty sampling causes unique converge behavior in estimating most novel items compared to non-novel items. Our results imply that in certain situations one can use ordinal embedding techniques to estimate novelty error in fewer samples than is typically expected. Moreover, the convergence behavior of top K novel items motivates new potential triplet sampling methods that go beyond typical triplet reduction measures. 

Many data analysis and design problems involve reasoning about points in high-dimensional space. A common strategy is to embed points from this high-dimensional space into a low-dimensional one. As we will show in this paper, a critical property of good embeddings is that they preserve isometry — i.e., preserving the geodesic distance between points on the original data manifold within their embedded locations in the latent space. However, enforcing isometry is non-trivial for common Neural embedding models, such as autoencoders and generative models. Moreover, while theoretically appealing, it is not clear to what extent enforcing isometry is really necessary for a given design or analysis task. This paper answers these questions by constructing an isometric embedding via an isometric autoencoder, which we employ to analyze an inverse airfoil design problem. Specifically, the paper describes how to train an isometric autoencoder and demonstrates its usefulness compared to non-isometric autoencoders on both simple pedagogical examples and for airfoil embeddings using the UIUC airfoil dataset. Our ablation study illustrates that enforcing isometry is necessary to accurately discover latent space clusters — a common analysis method researchers typically perform on low-dimensional embeddings. We also show how isometric autoencoders can uncover pathologies in typical gradient-based Shape Optimization solvers through an analysis on the SU2-optimized airfoil dataset, wherein we find an over-reliance of the gradient solver on angle of attack. Overall, this paper motivates the use of isometry constraints in Neural embedding models, particularly in cases where researchers or designer intend to use distance-based analysis measures (such as clustering, k-Nearest Neighbors methods, etc.) to analyze designs within the latent space. While this work focuses on airfoil design as an illustrative example, it applies to any domain where analyzing isometric design or data embeddings would be useful. 

Design optimization, and particularly adjoint-based multi-physics shape and topology optimization, is time-consuming and often requires expensive iterations to converge to desired designs. In response, researchers have developed Machine Learning (ML) approaches — often referred to as Inverse Design methods — to either replace or accelerate tools like Topology optimization (TO). However, these methods have their own hidden, non-trivial costs including that of data generation, training, and refinement of ML-produced designs. This begs the question: when is it actually worth learning Inverse Design, compared to just optimizing designs without ML assistance? This paper quantitatively addresses this question by comparing the costs and benefits of three different Inverse Design ML model families on a Topology Optimization (TO) task, compared to just running the optimizer by itself. We explore the relationship between the size of training data and the predictive power of each ML model, as well as the computational and training costs of the models and the extent to which they accelerate or hinder TO convergence. The results demonstrate that simpler models, such as K-Nearest Neighbors and Random Forests, are more effective for TO warmstarting with limited training data, while more complex models, such as Deconvolutional Neural Networks, are preferable with more data. We also emphasize the need to balance the benefits of using larger training sets with the costs of data generation when selecting the appropriate ID model. Finally, the paper addresses some challenges that arise when using ML predictions to warmstart optimization, and provides some suggestions for budget and resource management. 

Abstract Design researchers have struggled to produce quantitative predictions for exactly why and when diversity might help or hinder design search efforts. This paper addresses that problem by studying one ubiquitously used search strategy—Bayesian optimization (BO)—on a 2D test problem with modifiable convexity and difficulty. Specifically, we test how providing diverse versus non-diverse initial samples to BO affects its performance during search and introduce a fast ranked-determinantal point process method for computing diverse sets, which we need to detect sets of highly diverse or non-diverse initial samples. We initially found, to our surprise, that diversity did not appear to affect BO, neither helping nor hurting the optimizer’s convergence. However, follow-on experiments illuminated a key trade-off. Non-diverse initial samples hastened posterior convergence for the underlying model hyper-parameters—a model building advantage. In contrast, diverse initial samples accelerated exploring the function itself—a space exploration advantage. Both advantages help BO, but in different ways, and the initial sample diversity directly modulates how BO trades those advantages. Indeed, we show that fixing the BO hyper-parameters removes the model building advantage, causing diverse initial samples to always outperform models trained with non-diverse samples. These findings shed light on why, at least for BO-type optimizers, the use of diversity has mixed effects and cautions against the ubiquitous use of space-filling initializations in BO. To the extent that humans use explore-exploit search strategies similar to BO, our results provide a testable conjecture for why and when diversity may affect human-subject or design team experiments.