# Design Space Exploration and Explanation via Conditional Variational Autoencoders in Meta-model-based Conceptual Design of Pedestrian Bridges

arXiv: https://arxiv.org/abs/2211.16406 · HTML: https://mlsanity.com/paper/2211.16406/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 73 references that are in the map.
- First posted on arXiv 29 Nov 2022.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Flexibly Fair Representation Learning by Disentanglement](https://mlsanity.com/paper/1906.02589/) (2019)
- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [House-GAN: Relational Generative Adversarial Networks for Graph-constrained House Layout Generation](https://mlsanity.com/paper/2003.06988/) (2020)
- [Generative Design by Reinforcement Learning: Enhancing the Diversity of Topology Optimization Designs](https://mlsanity.com/paper/2008.07119/) (2020)
- [3D Shape Synthesis for Conceptual Design and Optimization Using Variational Autoencoders](https://mlsanity.com/paper/1904.07964/) (2019)
- [Inverse design optimization framework via a two-step deep learning approach: application to a wind turbine airfoil](https://mlsanity.com/paper/2108.08500/) (2021)
- [Inverse Aerodynamic Design of Gas Turbine Blades using Probabilistic Machine Learning](https://mlsanity.com/paper/2108.10163/) (2021)
- [Explainable Machine Learning using Real, Synthetic and Augmented Fire Tests to Predict Fire Resistance and Spalling of RC Columns](https://mlsanity.com/paper/2108.09862/) (2021)
- [Data-Driven Design: Exploring new Structural Forms using Machine Learning and Graphic Statics](https://mlsanity.com/paper/1809.08660/) (2018)
- [Struct-MRT: Immersive Learning and Teaching of Design and Verification in Structural Civil Engineering using Mixed Reality](https://mlsanity.com/paper/2109.09489/) (2021)

## Built on by (most cited first, 5 of 5)

- [Generative AI in the Construction Industry: Opportunities & Challenges](https://mlsanity.com/paper/2310.04427/) (2023)
- [An attempt to generate new bridge types from latent space of variational autoencoder](https://mlsanity.com/paper/2311.03380/) (2023)
- [Discovery of Fatigue Strength Models via Feature Engineering and automated eXplainable Machine Learning applied to the welded Transverse Stiffener](https://mlsanity.com/paper/2507.02005/) (2025)
- [Bayesian Surrogates for Risk-Aware Pre-Assessment of Aging Bridge Portfolios](https://mlsanity.com/paper/2509.25031/) (2025)
- [GLUE: Coordinating Pre-Trained Generative Models for System-Level Design](https://mlsanity.com/paper/2512.19469/) (2025)

## Abstract (arXiv)

For conceptual design, engineers rely on conventional iterative (often manual) techniques. Emerging parametric models facilitate design space exploration based on quantifiable performance metrics, yet remain time-consuming and computationally expensive. Pure optimisation methods, however, ignore qualitative aspects (e.g. aesthetics or construction methods). This paper provides a performance-driven design exploration framework to augment the human designer through a Conditional Variational Autoencoder (CVAE), which serves as forward performance predictor for given design features as well as an inverse design feature predictor conditioned on a set of performance requests. The CVAE is trained on 18'000 synthetically generated instances of a pedestrian bridge in Switzerland. Sensitivity analysis is employed for explainability and informing designers about (i) relations of the model between features and/or performances and (ii) structural improvements under user-defined objectives. A case study proved our framework's potential to serve as a future co-pilot for conceptual design studies of pedestrian bridges and beyond.