Multi-fidelity Reinforcement Learning (RL) frameworks efficiently utilize computational resources by integrating analysis models of varying accuracy and costs. The prevailing methodologies, characterized by transfer learning, human-inspired strategies, control variate techniques, and adaptive sampling, predominantly depend on a structured hierarchy of models. However, this reliance on a model hierarchy can exacerbate variance in policy learning when the underlying models exhibit heterogeneous error distributions across the design space. To address this challenge, this work proposes a novel adaptive multi-fidelity RL framework, in which multiple heterogeneous, non-hierarchical low-fidelity models are dynamically leveraged alongside a high-fidelity model to efficiently learn a high-fidelity policy. Specifically, low-fidelity policies and their experience data are adaptively used for efficient targeted learning, guided by their alignment with the high-fidelity policy. The effectiveness of the approach is demonstrated in an octocopter design optimization problem, utilizing two low-fidelity models alongside a high-fidelity simulator. The results demonstrate that the proposed approach substantially reduces variance in policy learning, leading to improved convergence and consistent high-quality solutions relative to traditional hierarchical multi-fidelity RL methods. Moreover, the framework eliminates the need for manually tuning model usage schedules, which can otherwise introduce significant computational overhead. This positions the framework as an effective variance-reduction strategy for multi-fidelity RL, while also mitigating the computational and operational burden of manual fidelity scheduling.

Multi-fidelity Reinforcement Learning (RL) frameworks significantly enhance the efficiency of engineering design by leveraging analysis models with varying levels of accuracy and computational costs. The prevailing methodologies, characterized by transfer learning, human-inspired strategies, control variate techniques, and adaptive sampling, predominantly depend on a structured hierarchy of models. However, this reliance on a model hierarchy overlooks the heterogeneous error distributions of models across the design space, extending beyond mere fidelity levels. This work proposes ALPHA (Adaptively Learned Policy with Heterogeneous Analyses), a novel multi-fidelity RL framework to efficiently learn a high-fidelity policy by adaptively leveraging an arbitrary set of non-hierarchical, heterogeneous, low-fidelity models alongside a high-fidelity model. Specifically, low-fidelity policies and their experience data are dynamically used for efficient targeted learning, guided by their alignment with the high-fidelity policy. The effectiveness of ALPHA is demonstrated in analytical test optimization and octocopter design problems, utilizing two low-fidelity models alongside a high-fidelity one. The results highlight ALPHA's adaptive capability to dynamically utilize models across time and design space, eliminating the need for scheduling models as required in a hierarchical framework. Furthermore, the adaptive agents find more direct paths to high-performance solutions, showing superior convergence behavior compared to hierarchical agents.

Volatility, which indicates the dispersion of returns, is a crucial measure of risk and is hence used extensively for pricing and discriminating between different financial investments. As a result, accurate volatility prediction receives extensive attention. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model and its succeeding variants are well established models for stock volatility forecasting. More recently, deep learning models have gained popularity in volatility prediction as they demonstrated promising accuracy in certain time series prediction tasks. Inspired by Physics-Informed Neural Networks (PINN), we constructed a new, hybrid Deep Learning model that combines the strengths of GARCH with the flexibility of a Long Short-Term Memory (LSTM) Deep Neural Network (DNN), thus capturing and forecasting market volatility more accurately than either class of models are capable of on their own. We refer to this novel model as a GARCH-Informed Neural Network (GINN). When compared to other time series models, GINN showed superior out-of-sample prediction performance in terms of the Coefficient of Determination ($R^2$), Mean Squared Error (MSE), and Mean Absolute Error (MAE).

Material selection plays a pivotal role in many industries, from manufacturing to construction. Material selection is usually carried out after several cycles of conceptual design, during which designers iteratively refine the design solution and the intended manufacturing approach. In design research, material selection is typically treated as an optimization problem with a single correct answer. Moreover, it is also often restricted to specific types of objects or design functions, which can make the selection process computationally expensive and time-consuming. In this paper, we introduce MSEval, a novel dataset which is comprised of expert material evaluations across a variety of design briefs and criteria. This data is designed to serve as a benchmark to facilitate the evaluation and modification of machine learning models in the context of material selection for conceptual design.

Additive manufacturing has revolutionized structural optimization by enhancing component strength and reducing material requirements. One approach used to achieve these improvements is the application of multi-lattice structures, where the macro-scale performance relies on the detailed design of mesostructural lattice elements. Many current approaches to designing such structures use data-driven design to generate multi-lattice transition regions, making use of machine learning models that are informed solely by the geometry of the mesostructures. However, it remains unclear if the integration of mechanical properties into the dataset used to train such machine learning models would be beneficial beyond using geometric data alone. To address this issue, this work implements and evaluates a hybrid geometry/property Variational Autoencoder (VAE) for generating multi-lattice transition regions. In our study, we found that hybrid VAEs demonstrate enhanced performance in maintaining stiffness continuity through transition regions, indicating their suitability for design tasks requiring smooth mechanical properties.

Transport phenomena (e.g., fluid flows) are governed by time-dependent partial differential equations (PDEs) describing mass, momentum, and energy conservation, and are ubiquitous in many engineering applications. However, deep learning architectures are fundamentally incompatible with the simulation of these PDEs. This paper clearly articulates and then solves this incompatibility. The local-dependency of generic transport PDEs implies that it only involves local information to predict the physical properties at a location in the next time step. However, the deep learning architecture will inevitably increase the scope of information to make such predictions as the number of layers increases, which can cause sluggish convergence and compromise generalizability. This paper aims to solve this problem by proposing a distributed data scoping method with linear time complexity to strictly limit the scope of information to predict the local properties. The numerical experiments over multiple physics show that our data scoping method significantly accelerates training convergence and improves the generalizability of benchmark models on large-scale engineering simulations. Specifically, over the geometries not included in the training data for heat transferring simulation, it can increase the accuracy of Convolutional Neural Networks (CNNs) by 21.7 \% and that of Fourier Neural Operators (FNOs) by 38.5 \% on average.

Access to large amounts of diverse design solutions can support designers during the early stage of the design process. In this paper, we explore the efficacy of large language models (LLM) in producing diverse design solutions, investigating the level of impact that parameter tuning and various prompt engineering techniques can have on the diversity of LLM-generated design solutions. Specifically, LLMs are used to generate a total of 4,000 design solutions across five distinct design topics, eight combinations of parameters, and eight different types of prompt engineering techniques, comparing each combination of parameter and prompt engineering method across four different diversity metrics. LLM-generated solutions are compared against 100 human-crowdsourced solutions in each design topic using the same set of diversity metrics. Results indicate that human-generated solutions consistently have greater diversity scores across all design topics. Using a post hoc logistic regression analysis we investigate whether these differences primarily exist at the semantic level. Results show that there is a divide in some design topics between humans and LLM-generated solutions, while others have no clear divide. Taken together, these results contribute to the understanding of LLMs' capabilities in generating a large volume of diverse design solutions and offer insights for future research that leverages LLMs to generate diverse design solutions for a broad range of design tasks (e.g., inspirational stimuli).

Material selection is a crucial step in conceptual design due to its significant impact on the functionality, aesthetics, manufacturability, and sustainability impact of the final product. This study investigates the use of Large Language Models (LLMs) for material selection in the product design process and compares the performance of LLMs against expert choices for various design scenarios. By collecting a dataset of expert material preferences, the study provides a basis for evaluating how well LLMs can align with expert recommendations through prompt engineering and hyperparameter tuning. The divergence between LLM and expert recommendations is measured across different model configurations, prompt strategies, and temperature settings. This approach allows for a detailed analysis of factors influencing the LLMs' effectiveness in recommending materials. The results from this study highlight two failure modes, and identify parallel prompting as a useful prompt-engineering method when using LLMs for material selection. The findings further suggest that, while LLMs can provide valuable assistance, their recommendations often vary significantly from those of human experts. This discrepancy underscores the need for further research into how LLMs can be better tailored to replicate expert decision-making in material selection. This work contributes to the growing body of knowledge on how LLMs can be integrated into the design process, offering insights into their current limitations and potential for future improvements.

High-fidelity, data-driven models that can quickly simulate thermal behavior during additive manufacturing (AM) are crucial for improving the performance of AM technologies in multiple areas, such as part design, process planning, monitoring, and control. However, the complexities of part geometries make it challenging for current models to maintain high accuracy across a wide range of geometries. Additionally, many models report a low mean square error (MSE) across the entire domain (part). However, in each time step, most areas of the domain do not experience significant changes in temperature, except for the heat-affected zones near recent depositions. Therefore, the MSE-based fidelity measurement of the models may be overestimated. This paper presents a data-driven model that uses Fourier Neural Operator to capture the local temperature evolution during the additive manufacturing process. In addition, the authors propose to evaluate the model using the $R^2$ metric, which provides a relative measure of the model's performance compared to using mean temperature as a prediction. The model was tested on numerical simulations based on the Discontinuous Galerkin Finite Element Method for the Direct Energy Deposition process, and the results demonstrate that the model achieves high fidelity as measured by $R^2$ and maintains generalizability to geometries that were not included in the training process.

Additive manufacturing is advantageous for producing lightweight components while addressing complex design requirements. This capability has been bolstered by the introduction of unit lattice cells and the gradation of those cells. In cases where loading varies throughout a part, it may be beneficial to use multiple, distinct lattice cell types, resulting in multi-lattice structures. In such structures, abrupt transitions between unit cell topologies may cause stress concentrations, making the boundary between unit cell types a primary failure point. Thus, these regions require careful design in order to ensure the overall functionality of the part. Although computational design approaches have been proposed, smooth transition regions are still difficult to achieve, especially between lattices of drastically different topologies. This work demonstrates and assesses a method for using variational autoencoders to automate the creation of transitional lattice cells, examining the factors that contribute to smooth transitions. Through computational experimentation, it was found that the smoothness of transition regions was strongly predicted by how closely the endpoints were in the latent space, whereas the number of transition intervals was not a sole predictor.