skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Toward Reusable Surrogate Models: Graph-Based Transfer Learning on Trusses
Abstract Surrogate models have several uses in engineering design, including speeding up design optimization, noise reduction, test measurement interpolation, gradient estimation, portability, and protection of intellectual property. Traditionally, surrogate models require that all training data conform to the same parametrization (e.g., design variables), limiting design freedom and prohibiting the reuse of historical data. In response, this article proposes graph-based surrogate models (GSMs) for trusses. The GSM can accurately predict displacement fields from static loads given the structure’s geometry as input, enabling training across multiple parametrizations. GSMs build upon recent advancements in geometric deep learning, which have led to the ability to learn on undirected graphs: a natural representation for trusses. To further promote flexible surrogate models, this article explores transfer learning within the context of engineering design and demonstrates positive knowledge transfer across data sets of different topologies, complexities, loads, and applications, resulting in more flexible and data-efficient surrogate models for trusses.  more » « less
Award ID(s):
1854833
PAR ID:
10378717
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal of Mechanical Design
Volume:
144
Issue:
2
ISSN:
1050-0472
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; (, Computer Graphics Forum)
    Abstract This paper introduces the Simulated Jet Engine Bracket Dataset (SimJEB) [WBM21]: a new, public collection of crowdsourced mechanical brackets and accompanying structural simulations. SimJEB is applicable to a wide range of geometry processing tasks; the complexity of the shapes in SimJEB offer a challenge to automated geometry cleaning and meshing, while categorical labels and structural simulations facilitate classification and regression (i.e. engineering surrogate modeling). In contrast to existing shape collections, SimJEB's models are all designed for the same engineering function and thus have consistent structural loads and support conditions. On the other hand, SimJEB models are more complex, diverse, and realistic than the synthetically generated datasets commonly used in parametric surrogate model evaluation. The designs in SimJEB were derived from submissions to the GrabCAD Jet Engine Bracket Challenge: an open engineering design competition with over 700 hand‐designed CAD entries from 320 designers representing 56 countries. Each model has been cleaned, categorized, meshed, and simulated with finite element analysis according to the original competition specifications. The result is a collection of 381 diverse, high‐quality and application‐focused designs for advancing geometric deep learning, engineering surrogate modeling, automated cleaning and related geometry processing tasks. 
    more » « less
  2. ; ; (, Computer Methods in Applied Mechanics and Engineering)
    Efficient real-time solvers for forward and inverse problems are essential in engineering and science applications. Machine learning surrogate models have emerged as promising alter- natives to traditional methods, offering substantially reduced computational time. Never- theless, these models typically demand extensive training datasets to achieve robust gen- eralization across diverse scenarios. While physics-based approaches can partially mitigate this data dependency and ensure physics-interpretable solutions, addressing scarce data regimes remains a challenge. Both purely data-driven and physics-based machine learning approaches demonstrate severe overfitting issues when trained with insufficient data. We propose a novel model-constrained Tikhonov autoencoder neural network framework, called TAEN, capable of learning both forward and inverse surrogate models using a single arbitrary observational sample. We develop comprehensive theoretical foundations including forward and inverse inference error bounds for the proposed approach for linear cases. For compara- tive analysis, we derive equivalent formulations for pure data-driven and model-constrained approach counterparts. At the heart of our approach is a data randomization strategy with theoretical justification, which functions as a generative mechanism for exploring the train- ing data space, enabling effective training of both forward and inverse surrogate models even with a single observation, while regularizing the learning process. We validate our approach through extensive numerical experiments on two challenging inverse problems: 2D heat conductivity inversion and initial condition reconstruction for time-dependent 2D Navier–Stokes equations. Results demonstrate that TAEN achieves accuracy comparable to traditional Tikhonov solvers and numerical forward solvers for both inverse and forward problems, respectively, while delivering orders of magnitude computational speedups. 
    more » « less
  3. ; ; (, Journal of Mechanical Design)
    Abstract In engineering design, global sensitivity analysis (GSA) is used for analyzing the effects of inputs on the system response and is commonly studied with analytical or surrogate models. However, such models fail to capture nonlinear behaviors in complex systems and involve several modeling assumptions. Besides model-focused methods, a data-driven GSA approach, rooted in interpretable machine learning, would also identify the relationships between system components. Moreover, a special need in engineering design extends beyond performing GSA for input variables individually, but instead evaluating the contributions of variable groups on the system response. In this article, we introduce a flexible, interpretable artificial neural network model to uncover individual as well as grouped global sensitivity indices for understanding complex physical interactions in engineering design problems. The proposed model allows the investigation of the main effects and second-order effects in GSA according to functional analysis of variance (FANOVA) decomposition. To draw a higher-level understanding, we further use the subset decomposition method to analyze the significance of the groups of input variables. Using the design of a programmable material system (PMS) as an example, we demonstrate the use of our approach for examining the impact of material, architecture, and stimulus variables as well as their interactions. This information lays the foundation for managing design space complexity, summarizing the relationships between system components, and deriving design guidelines for PMS development. 
    more » « less
  4. ; ; (, Design Science)
    Abstract Data-driven generative design (DDGD) methods utilize deep neural networks to create novel designs based on existing data. The structure-aware DDGD method can handle complex geometries and automate the assembly of separate components into systems, showing promise in facilitating creative designs. However, determining the appropriate vectorized design representation (VDR) to evaluate 3D shapes generated from the structure-aware DDGD model remains largely unexplored. To that end, we conducted a comparative analysis of surrogate models’ performance in predicting the engineering performance of 3D shapes using VDRs from two sources: the trained latent space of structure-aware DDGD models encoding structural and geometric information and an embedding method encoding only geometric information. We conducted two case studies: one involving 3D car models focusing on drag coefficients and the other involving 3D aircraft models considering both drag and lift coefficients. Our results demonstrate that using latent vectors as VDRs can significantly deteriorate surrogate models’ predictions. Moreover, increasing the dimensionality of the VDRs in the embedding method may not necessarily improve the prediction, especially when the VDRs contain more information irrelevant to the engineering performance. Therefore, when selecting VDRs for surrogate modeling, the latent vectors obtained from training structure-aware DDGD models must be used with caution, although they are more accessible once training is complete. The underlying physics associated with the engineering performance should be paid attention. This paper provides empirical evidence for the effectiveness of different types of VDRs of structure-aware DDGD for surrogate modeling, thus facilitating the construction of better surrogate models for AI-generated designs. 
    more » « less
  5. ; ; ; (, IEEE Transactions on Artificial Intelligence)
    Designing and/or controlling complex systems in science and engineering relies on appropriate mathematical modeling of systems dynamics. Classical differential equation based solutions in applied and computational mathematics are often computationally demanding. Recently, the connection between reduced-order models of high-dimensional differential equation systems and surrogate machine learning models has been explored. However, the focus of both existing reduced-order and machine learning models for complex systems has been how to best approximate the high fidelity model of choice. Due to high complexity and often limited training data to derive reduced-order or machine learning surrogate models, it is critical for derived reduced-order models to have reliable uncertainty quantification at the same time. In this paper, we propose such a novel framework of Bayesian reduced-order models naturally equipped with uncertainty quantification as it learns the distributions of the parameters of the reduced-order models instead of their point estimates. In particular, we develop learnable Bayesian proper orthogonal decomposition (BayPOD) that learns the distributions of both the POD projection bases and the mapping from the system input parameters to the projected scores/coefficients so that the learned BayPOD can help predict high-dimensional systems dynamics/fields as quantities of interest in different setups with reliable uncertainty estimates. The developed learnable BayPOD inherits the capability of embedding physics constraints when learning the POD-based surrogate reduced-order models, a desirable feature when studying complex systems in science and engineering applications where the available training data are limited. Furthermore, the proposed BayPOD method is an end-to-end solution, which unlike other surrogate-based methods, does not require separate POD and machine learning steps. The results from a real-world case study of the pressure field around an airfoil. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email