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LAMP: Data-Efficient Linear Affine Weight-Space Models for Parameter-Controlled 3D Shape Generation and Extrapolation

Ghadi Nehme, Yanxia Zhang, Dule Shu, Matt Klenk, Faez Ahmed

TL;DR

This paper introduces LAMP, a data-efficient framework for parameter-controlled 3D mesh generation that aligns exemplar SDF decoders into a shared weight space and performs parameter-constrained affine mixing to synthesize new geometries. A linearity-mismatch safety metric guards against invalid extrapolations, ensuring generated shapes remain geometrically consistent. Evaluated on DrivAerNet++ and BlendedNet, LAMP demonstrates accurate interpolation within the dataset, safe extrapolation up to large parameter differences, and performance-driven optimization, outperforming DNI and AE-LPA baselines in both data efficiency and robustness. The approach offers a scalable design engine for constrained yet creative geometry synthesis, with practical impact in design exploration, dataset augmentation, and physics-informed optimization.

Abstract

Generating high-fidelity 3D geometries that satisfy specific parameter constraints has broad applications in design and engineering. However, current methods typically rely on large training datasets and struggle with controllability and generalization beyond the training distributions. To overcome these limitations, we introduce LAMP (Linear Affine Mixing of Parametric shapes), a data-efficient framework for controllable and interpretable 3D generation. LAMP first aligns signed distance function (SDF) decoders by overfitting each exemplar from a shared initialization, then synthesizes new geometries by solving a parameter-constrained mixing problem in the aligned weight space. To ensure robustness, we further propose a safety metric that detects geometry validity via linearity mismatch. We evaluate LAMP on two 3D parametric benchmarks: DrivAerNet++ and BlendedNet. We found that LAMP enables (i) controlled interpolation within bounds with as few as 100 samples, (ii) safe extrapolation by up to 100% parameter difference beyond training ranges, (iii) physics performance-guided optimization under fixed parameters. LAMP significantly outperforms conditional autoencoder and Deep Network Interpolation (DNI) baselines in both extrapolation and data efficiency. Our results demonstrate that LAMP advances controllable, data-efficient, and safe 3D generation for design exploration, dataset generation, and performance-driven optimization.

LAMP: Data-Efficient Linear Affine Weight-Space Models for Parameter-Controlled 3D Shape Generation and Extrapolation

TL;DR

This paper introduces LAMP, a data-efficient framework for parameter-controlled 3D mesh generation that aligns exemplar SDF decoders into a shared weight space and performs parameter-constrained affine mixing to synthesize new geometries. A linearity-mismatch safety metric guards against invalid extrapolations, ensuring generated shapes remain geometrically consistent. Evaluated on DrivAerNet++ and BlendedNet, LAMP demonstrates accurate interpolation within the dataset, safe extrapolation up to large parameter differences, and performance-driven optimization, outperforming DNI and AE-LPA baselines in both data efficiency and robustness. The approach offers a scalable design engine for constrained yet creative geometry synthesis, with practical impact in design exploration, dataset augmentation, and physics-informed optimization.

Abstract

Generating high-fidelity 3D geometries that satisfy specific parameter constraints has broad applications in design and engineering. However, current methods typically rely on large training datasets and struggle with controllability and generalization beyond the training distributions. To overcome these limitations, we introduce LAMP (Linear Affine Mixing of Parametric shapes), a data-efficient framework for controllable and interpretable 3D generation. LAMP first aligns signed distance function (SDF) decoders by overfitting each exemplar from a shared initialization, then synthesizes new geometries by solving a parameter-constrained mixing problem in the aligned weight space. To ensure robustness, we further propose a safety metric that detects geometry validity via linearity mismatch. We evaluate LAMP on two 3D parametric benchmarks: DrivAerNet++ and BlendedNet. We found that LAMP enables (i) controlled interpolation within bounds with as few as 100 samples, (ii) safe extrapolation by up to 100% parameter difference beyond training ranges, (iii) physics performance-guided optimization under fixed parameters. LAMP significantly outperforms conditional autoencoder and Deep Network Interpolation (DNI) baselines in both extrapolation and data efficiency. Our results demonstrate that LAMP advances controllable, data-efficient, and safe 3D generation for design exploration, dataset generation, and performance-driven optimization.
Paper Structure (46 sections, 19 equations, 20 figures, 7 tables)

This paper contains 46 sections, 19 equations, 20 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Generative Models for 3D Shapes.
  4. Controllable and Conditional Generation.
  5. Weight-Space Interpolation and Model Merging
  6. Parametric Design and Engineering Constraints.
  7. Shape Interpolation and Extrapolation.
  8. Position of This Work.
  9. Method
  10. Problem Setup and SDF Weight Space
  11. Parameter-Constrained Mixing
  12. Theoretical Justification of Mixing
  13. Safety Metric: Linearity Mismatch
  14. Experiments, Results, and Discussion
  15. Evaluation Metrics
  16. ...and 31 more sections

Figures (20)

  • Figure 1: Overview of LAMP: (I) aligned SDF weight space construction, (II) parameter-constrained mixing, and (III) mesh extraction, enabling parametric control and large-range extrapolation.
  • Figure 2: Single-parameter extrapolation showing LAMP's smooth, plausible geometries.
  • Figure 3: Single-parameter extrapolation beyond the dataset range, with all other parameters allowed to vary. Left: surrogate-predicted vs. target parameters. Right: decoded cross-sections. LAMP extrapolates smoothly, while DNI collapses and AE-LPA fails to reach the expected parameter range.
  • Figure 4: Four-parameter extrapolation. Left: distribution of generated meshes in a 2D point cloud embedding. Right: decoded examples. LAMP remains within plausible regions, DNI collapses to invalid meshes, and AE-LPA remains stuck in the dataset convex hull, lacking diversity.
  • Figure 5: Linearity-mismatch safety metric for diffuser angle extrapolation. Failures (e.g., sample f) occur when the metric exceeds the threshold. See Appendix \ref{['app:safety-validation']} for more.
  • ...and 15 more figures