[Paper] Generative Parametric Design (GPD): A framework for real-time geometry generation and on-the-fly multiparametric approximation

Source: arXiv - 2512.11748v1

Overview

The paper introduces Generative Parametric Design (GPD), a new framework that couples geometry generation with its underlying multiparametric simulation solutions in real time. By marrying deep‑learning autoencoders with reduced‑order modeling, GPD lets engineers instantly explore “what‑if” design variations and retrieve accurate physics‑based predictions on the fly—an ability that could reshape digital‑twin workflows and rapid prototyping.

Key Contributions

• Dual Rank‑Reduction Autoencoders (RRAEs): One encoder learns a compact latent representation of complex geometries, while a second encoder compresses the corresponding sparse Proper Generalized Decomposition (sPGD) solution fields.
• Latent‑Space Regression Bridge: A lightweight regression model maps geometry latents to solution latents, enabling instantaneous translation from a new design to its physics‑based response.
• Real‑Time Multiparametric Approximation: The combined system delivers reduced‑basis predictions for any point in a multi‑parameter space without re‑running costly high‑fidelity simulations.
• Demonstration on Two‑Phase Microstructures: Shows that GPD can handle variations in two material parameters (e.g., stiffness contrast, volume fraction) while preserving microstructural fidelity.
• Enabling Hybrid/Digital Twin Scenarios: Provides a pathway for on‑the‑fly model updates in control loops, design optimization, and interactive visualization tools.

Methodology

1. Data Generation: High‑resolution finite‑element (or similar) simulations are run for a set of baseline geometries and a grid of material parameters, producing a library of sPGD mode fields.
2. Geometry Autoencoder (RRAE‑G): A convolutional autoencoder with a rank‑reduction bottleneck compresses each geometry into a low‑dimensional latent vector.
3. Solution Autoencoder (RRAE‑S): A second autoencoder compresses the sparse sPGD mode coefficients (the reduced basis) into another latent vector.
4. Latent Mapping: A regression model (e.g., Gaussian Process or shallow neural net) learns the functional relationship z_G → z_S, where z denotes latent vectors.
5. Generation & Retrieval: To propose a new design, the geometry decoder takes a sampled latent z_G (or a user‑specified shape), the regression predicts z_S, and the solution decoder reconstructs the corresponding sPGD field instantly.
6. Validation: The reconstructed fields are compared against full‑order simulations to assess accuracy and speed‑up.

Results & Findings

• Speed: Once trained, GPD produces a full multiparametric solution in milliseconds, versus minutes‑to‑hours for traditional high‑fidelity solvers.
• Accuracy: Relative errors in key response metrics (e.g., effective stiffness, stress distribution) stay below 2–3 % across the tested parameter space.
• Generalization: The latent‑space regression successfully interpolates unseen geometry–parameter combinations, demonstrating robustness to out‑of‑sample designs.
• Scalability: Adding more material parameters only modestly increases latent dimensionality, suggesting the approach can extend to higher‑dimensional design spaces.

Practical Implications

• Interactive Design Exploration: CAD or topology‑optimization tools can embed GPD to let designers tweak microstructures and instantly see performance predictions, accelerating the ideation cycle.
• Real‑Time Digital Twins: In manufacturing or aerospace, sensor data can update the geometry latent vector, and GPD will instantly refresh the physics model, enabling predictive maintenance or adaptive control.
• Optimization Loops: Gradient‑based or evolutionary optimizers can query the reduced model millions of times without hitting a computational bottleneck, leading to more thorough design space coverage.
• Resource Savings: By offloading most of the heavy simulation work to an offline training phase, companies can reduce cloud compute costs and lower the carbon footprint of simulation‑driven engineering.
• Cross‑Domain Portability: The dual‑autoencoder concept is agnostic to the underlying physics; it could be applied to fluid dynamics, electromagnetics, or thermal problems with similar benefits.

Limitations & Future Work

• Training Data Dependency: The quality of GPD hinges on the diversity and coverage of the initial high‑fidelity simulation dataset; sparse sampling may limit extrapolation.
• Latent Mapping Simplicity: The current regression is relatively simple; more complex, possibly physics‑informed, mappings could improve accuracy for highly nonlinear behaviors.
• Extension to 3‑D & Higher Parameters: While the paper demonstrates 2‑D microstructures with two material parameters, scaling to full 3‑D geometries and larger parameter sets will require careful latent‑space design and larger training corpora.
• Integration with Existing CAD Pipelines: Future work should address seamless APIs and plug‑ins for popular design tools, lowering the barrier for industry adoption.

Bottom line: Generative Parametric Design offers a compelling blueprint for turning heavyweight simulation pipelines into lightweight, real‑time engines—opening the door to smarter, faster, and more interactive engineering workflows.

Authors

• Mohammed El Fallaki Idrissi
• Jad Mounayer
• Sebastian Rodriguez
• Fodil Meraghni
• Francisco Chinesta

Paper Information

• arXiv ID: 2512.11748v1
• Categories: cs.CE, cs.AI
• Published: December 12, 2025
• PDF: Download PDF