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Learning Feasibility-Aware Latent Spaces for Preference-Based Exploration of Procedural Automotive Wheel Designs
Takashi Owaki, Yuki Koyama, Tomoyasu Nakano, Takahiro Yamaguchi, Masataka Goto, Hiroyuki Sakai
TL;DR
Preference-based design interfaces need search representations that are both meaningful and feasible, but procedural parameters can be entangled and produce many invalid outputs. The paper screens procedural wheel designs, learns a reduced latent space with optional functional alignment, and finds that a 5D feasibility-aware space improves shape similarity and feasibility over the original 9D parameterization. The authors conclude that the interaction space itself is central to intelligent engineering-design interfaces.
Problem
Procedural parameters can be entangled, poorly reflect visual similarity, and generate many invalid outputs, making preference-based exploration less useful.
Method
The pipeline screens procedural samples geometrically and structurally, learns a reduced latent space from the screened subset, and optionally aligns latent dimensions with engineering measures.
Results
A 5D feasibility-aware space improves target-retrieval efficiency and feasible-suggestion rates compared with the original 9D procedural parameterization in simulations and a 40-participant study.
Takeaways & Limitations
The representation exposed to users is a central part of interaction design for preference-based engineering optimization, alongside the optimizer itself.
Takeaways & Limitations
The simplified wheel model and FEA omit manufacturing constraints, dynamic loads, fatigue, thermal effects, regulatory validation, and other requirements for real automotive engineering.
Abstract
from arXiv · showhide
Intelligent design interfaces that rely on preference-based optimization are most useful when their suggestions are both meaningful to users and feasible within the target domain. Procedural models offer compact and editable design spaces, but their native parameters can be entangled and can generate many invalid outputs, causing human-in-the-loop optimizers to waste comparisons. We propose an interaction-oriented representation-learning pipeline for procedural models and study it in automotive wheel design. The method first screens procedurally generated samples using geometric rules and finite-element analysis, then learns a reduced latent space from the screened subset. We further introduce supervised functional alignment, which reserves selected latent dimensions for stiffness, strength-related stress response, or weight so that search can be biased toward functionally meaningful regions. Simulation experiments show that screened reduction improves target-shape retrieval and the feasibility rate of suggestions, whereas unscreened reduction degrades both. Additional simulations show that constraining search along learned functional dimensions accelerates exploration toward target functional properties. A controlled study with 40 participants further shows that a 5D feasibility-aware space yields higher shape similarity and more feasible suggestions than the original 9D procedural parameterization. These results suggest that, for intelligent user interfaces in engineering design, the representation exposed to the user is a central part of the interaction design, not merely a preprocessing step for the optimizer.
1 Introduction
The paper treats the representation searched by preference-based optimization as an interaction-design problem, proposing a screened, reduced latent space with optional functional alignment for procedural wheel design.
- Motivation: Native procedural parameters can be entangled, poorly reflect visual similarity, and generate many geometrically or structurally infeasible outputs.Invalid suggestions consume user attention and weaken the optimizer’s feedback signal.
- Approach: The pipeline screens procedural samples with geometric and structural tests before learning a reduced latent space from the screened subset.This reshapes the search space before interaction rather than treating feasibility only as an online constraint or acquisition penalty.
- Approach: Supervised functional alignment trains selected latent coordinates to track stiffness, stress response, or weight.The method aims to support meaningful functional restrictions without claiming that all latent coordinates become semantically disentangled.
- Evaluation: The study instantiates the approach in a simplified procedural automotive wheel-spoke model and evaluates it through target-retrieval simulations and a 40-participant user study.Target retrieval is used as an objective proxy for efficient guidance through the candidate space, not as a measure of open-ended creative agency or industrial design quality.
- Findings: The learned interaction space improves target-search performance and substantially increases feasible suggestions compared with the original procedural parameterization.The paper combines offline screening, image-based shape features, and VAE-based dimensionality reduction.
2 Related Work
Prior work supports learned interfaces for navigating complex procedural spaces and preference-based optimization, while this paper changes the search space itself to improve feasibility.
- Learned design spaces: Procedural modeling and design-gallery systems have exposed large structured parameter spaces for navigating complex designs.Later systems learned lower-dimensional or example-based interfaces for procedural spaces, fonts, layouts, and fabrication.
- Preference-based optimization: Preference-driven optimization replaces explicit scalar objectives with user judgments and uses preference learning to select informative queries.The related work traces this paradigm from interactive evolutionary computation through Gaussian-process preference learning and preference-based Bayesian optimization.
- Feasibility-aware search: The paper positions offline feasibility screening as a way to give the optimizer a higher prior probability of yielding feasible designs.This connects the representation to the quality of the optimizer’s starting domain.
- Feasibility-aware search: Unlike algorithmic responses such as random embeddings or trust-region models, the proposed strategy changes the search space through learned reduction.Autoencoders and VAEs provide low-dimensional codes supporting reconstruction, interpolation, and generation.
3 Feasibility-Aware Latent-Space Learning
The pipeline screens procedural wheel designs for geometric and structural feasibility, combines procedural and image-based shape features, and learns a reduced VAE interaction space with optional functional alignment.
- Overview: PBO operates in a normalized m-dimensional latent space, with m∈{3, 4, 5}, learned from screened procedural and spoke-shape features.Functional alignment can train one latent dimension to track a normalized engineering measure and support functionally biased search.
- Procedural Wheel Model: The wheel model enumerates nine procedural parameters, including Bézier control-point locations, planar transformations, and rectangular cross-section controls.A full wheel radially replicates a single spoke and combines it with a fixed hub and rim.
- Feasibility Screening: Only 30,502 of 2,450,000 parameter combinations survive geometric and FEA-based structural screening.The geometric checks reject invalid spoke geometry, while simplified FEA removes designs unstable under the specified loading scenario.
- Spoke-Shape Feature Extraction: A convolutional autoencoder extracts local single-spoke geometry features that are concatenated with the original procedural parameters.Single-spoke training makes the descriptor independent of the number of radial repetitions in the full wheel.
- Latent-Space Learning: The VAE encourages a smoother latent distribution for continuous slider exploration and is trained separately for 3D, 4D, and 5D spaces under four alignment conditions.The alignment conditions are no functional alignment, stiffness, strength, and weight.
- Functional Alignment: 5D models achieve the lowest total loss across all alignment conditions, while stiffness alignment makes one latent axis more interpretable through spoke-thickness changes affecting structural response.Strength- and weight-aligned spaces likewise show dominant changes along their aligned axes, though strength-related changes can appear less intuitive because stress depends on local structure.
4 Simulation Experiments
The simulations test whether screening improves preference-based exploration and whether supervised functional dimensions steer search toward target physical properties. Screened latent reduction improves retrieval and feasibility, while functional range restrictions improve both shape similarity and property matching.
- 4.1 Effect of Screening on Exploration Efficiency: The study compares the original 9D procedural space, a screened latent space, and an unscreened vanilla latent space.The latter two use the same CAE+VAE reduction pipeline, differing in whether screening is applied.
- 4.1 Effect of Screening on Exploration Efficiency: Screened reduction improves target-search efficiency and proposal feasibility relative to the original 9D space, whereas vanilla reduction degrades both.Across 100 targets, trials used 20 preference iterations, with mean IoU and feasible-shape ratio evaluated over time.
- 4.2 Effect of Functional Dimensions on Exploration Efficiency: Five-dimensional models are used for the main functional-dimension results because they achieve the lowest training loss and are also used in the user study.The 3D and 4D results are reported in the appendix.
- 4.2 Effect of Functional Dimensions on Exploration Efficiency: Learned functional coordinates show strong monotonic relations with stiffness, strength-related stress response, or weight.Negative coordinates mostly correspond to below-median properties, while positive coordinates mostly correspond to above-median properties.
- 4.2 Effect of Functional Dimensions on Exploration Efficiency: Restricting functional coordinates to [-2, 0] or [0, 2] consistently increases IoU and reduces distance to the target property.The interval is selected according to whether the target property is below or above the median.
5 User Study
The controlled user study compares preference-based target retrieval in the original 9D procedural space and a screened 5D latent space. The 5D condition performs better on shape similarity and feasibility, while the study remains limited to controlled retrieval rather than open-ended exploration.
- 5.1 Study Design: The study compares the original 9D procedural space with the screened 5D latent space because 5D combines the best reconstruction loss with a practical interaction dimensionality.Participants repeatedly selected the closest-looking wheel from four suggestions.
- 5.1 Study Design: Target retrieval measures whether the representation helps users steer preference-based optimization through a candidate space, not open-ended creativity, agency, or satisfaction.All participants share the same objective, enabling measurement with IoU and feasibility rate.
- 5.2 Participants and Procedure: Forty participants searched for 10 screened-dataset targets in each condition, completing 20 selection rounds per target.The within-subjects study counterbalanced condition order across odd- and even-numbered participants.
- 5.3 Results: The 5D condition searches a screened latent space, whereas the 9D condition can still propose wheels violating geometric validity checks.The comparison directly tests whether the representation changes the quality of the explored candidate space.
- 5.3 Results: The 5D condition outperforms the 9D condition on mean IoU and feasible-shape ratio for nearly the entire interaction.After 20 selections, paired tests were significant for mean IoU (p=7.4 × 10^-7) and feasible-shape ratio (p=3.8 × 10^-15).
- 5.3 Results: Fewer suggestions are wasted on implausible designs, making each comparison more informative in the feasibility-aware space.This is the authors’ interpretation of the human-study replication of the simulation findings.
- 5.3 Results: The 5D condition achieves higher IoU for 8 of 10 targets and slightly shorter response intervals: 5.47 ± 1.52 s versus 5.82 ± 1.46 s.The timing difference is statistically significant (p=0.0164) but is interpreted cautiously.
6 Discussion
The discussion frames feasibility-aware latent spaces as an interaction-design contribution, while limiting claims about creative practice, interpretability, engineering deployment, and scalability.
- Interaction Contribution and Evaluation Scope: Screening before dimensionality reduction organizes the latent space around valid designs, improving IoU and feasible-shape ratio compared with unscreened reduction.The authors attribute this to excluding invalid and semantically unhelpful regions before preference optimization begins.
- Interaction Contribution and Evaluation Scope: The controlled target-retrieval evaluation does not establish support for all creative design practice, where goals may evolve and remain subjective or underspecified.The authors call for open-ended studies measuring agency, satisfaction, trust, and serendipitous discovery.
- Functional Alignment, Supervision, and Interpretability: Functional alignment makes one selected latent coordinate track stiffness, stress response, or weight, enabling range-based biasing toward desired properties.This is a supervised design choice rather than an emergent property of the VAE.
- Functional Alignment, Supervision, and Interpretability: Unaligned latent axes may lack stable semantic meanings, so interfaces should label aligned functions, show distributions and examples, and avoid implying general disentanglement.The aligned coordinate mitigates interpretability concerns for one selected measure at a time.
- Scalability and Engineering Scope: The wheel model and FEA use simplified assumptions, including a 1 MPa screening proxy, so professional deployment requires richer geometry, realistic simulations, and expert validation.Omitted factors include manufacturing constraints, dynamic loads, fatigue, thermal effects, and regulatory validation.
- Scalability and Engineering Scope: Exhaustive screening is practical for the nine-parameter grid but may not scale to larger grammars, continuous ranges, or disconnected feasible manifolds.The discussion suggests adaptive or stratified sampling, surrogate models, parallel simulation, and potentially multiple local or hierarchical latent spaces.
7 Practical and Societal Impact
Feasibility-aware representations may reduce wasted effort in intelligent design tools, but screening can conceal assumptions and should not be mistaken for engineering validation.
- Practical Benefits: Feasibility-aware representations can reduce wasted user effort by showing fewer invalid or obviously unusable candidates during interaction.The authors suggest this may improve accessibility for users without expertise in optimization, procedural modeling, or structural simulation.
- Risks and Responsibilities: Incomplete or biased screening may prematurely exclude unconventional designs, so deployed systems should expose criteria and allow experts to audit excluded regions.Functional labels should also be communicated as approximations tied to a particular simulation setup.
- Risks and Responsibilities: Passing simplified screening does not validate an automotive design; professional use requires domain review, certified simulation and testing, and clear responsibility boundaries.The wheel case is presented as especially relevant to this safety concern.
8 Conclusion
The paper presents a feasibility-aware latent-space pipeline for procedural wheel exploration and reports improved target retrieval and feasible suggestions across simulations and a 40-participant study.
- Conclusion: The pipeline screens procedural samples with geometric checks and simplified FEA, learns a reduced latent space, and optionally adds supervised functional dimensions.The aligned dimensions target stiffness, strength-related stress response, and weight.
- Conclusion: Across simulations and a 40-participant controlled study, the reduced space improves target-retrieval efficiency and feasible-suggestion proportion versus the original 9D parameterization.The conclusion identifies the interaction space as central alongside the optimization algorithm.
A Distribution of Wheel Shapes in Encoded 3D Space with Functional Dimension Aligned with Other Than Stiffness
The 3D latent-space analysis examines wheel-shape distributions on planes with functional alignment to strength or weight, finding continuous variation and aligned-axis changes associated with the corresponding measure.
- Distribution of Wheel Shapes: Figures 8 and 9 show wheel-shape distributions on three planes in 3D latent spaces aligned with strength and weight, respectively.Shapes generally vary continuously across these planes.
- Distribution of Wheel Shapes: Changes along the aligned axis generally follow the corresponding functional measure, although strength-aligned arrangements can appear less intuitive because maximum von Mises stress depends on local structure.The passage contrasts this with the more intuitive patterns for other aligned measures.
B Evaluation of Functional Dimensions for Stiffness, Strength, and Weight (3D and 4D)
The 3D and 4D latent spaces evaluate learned dimensions aligned with stiffness, strength, and weight. Their correlations remain high, and the reported design-exploration efficiency observations persist despite being slightly below the 5D results.
- 3D latent space: 0.970, 0.977, and 0.979 are the 3D correlations for stiffness, strength, and weight, respectively.
- 4D latent space: 0.990, 0.987, and 0.990 are the corresponding 4D correlations for stiffness, strength, and weight.
- Comparison: Although 3D and 4D correlations are slightly below the 5D values, the same qualitative observations about design-exploration efficiency hold.
- 3D latent space: The 3D latent space includes a functional dimension aligned with strength for visualizing wheel-shape distributions across three latent planes.
- 3D latent space: The 3D latent space also includes a functional dimension aligned with weight for visualizing wheel-shape distributions across three latent planes.
- Evaluation procedure: Figures 10 and 11 organize each functional analysis as a histogram, scatter plot, cumulative distribution, and mean IoU visualization.