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Generative Inverse Design: From Single Point Optimization to a Diverse Design Portfolio via Conditional Variational Autoencoders

Muhammad Arif Hakimi Zamrai

TL;DR

The paper reframes inverse design fromSeeking a single optimal solution to generating a diverse portfolio of high-performing designs using a Conditional Variational Autoencoder (CVAE) conditioned on target performance. It demonstrates on the NASA airfoil self-noise task that the CVAE can produce 241 valid designs (94.1% validity) and that 77.2% of these designs outperform the SBO baseline in surrogate-predicted performance, with a top result of 74.83 dB. The approach learns a global design manifold, enabling rapid, parallel synthesis of diverse candidates and facilitating multi-criteria decision-making in engineering design. While validated with a surrogate, the method shows promise for accelerated innovation and richer design exploration, with future work focusing on high-fidelity validation and scalability via active learning.

Abstract

Inverse design, which seeks to find optimal parameters for a target output, is a central challenge in engineering. Surrogate-based optimization (SBO) has become a standard approach, yet it is fundamentally structured to converge to a single-point solution, thereby limiting design space exploration and ignoring potentially valuable alternative topologies. This paper presents a paradigm shift from single-point optimization to generative inverse design. We introduce a framework based on a Conditional Variational Autoencoder (CVAE) that learns a probabilistic mapping between a system's design parameters and its performance, enabling the generation of a diverse portfolio of high-performing candidates conditioned on a specific performance objective. We apply this methodology to the complex, non-linear problem of minimizing airfoil self-noise, using a high-performing SBO method from a prior benchmark study as a rigorous baseline. The CVAE framework successfully generated 256 novel designs with a 94.1\% validity rate. A subsequent surrogate-based evaluation revealed that 77.2\% of these valid designs achieved superior performance compared to the single optimal design found by the SBO baseline. This work demonstrates that the generative approach not only discovers higher-quality solutions but also provides a rich portfolio of diverse candidates, fundamentally enhancing the engineering design process by enabling multi-criteria decision-making.

Generative Inverse Design: From Single Point Optimization to a Diverse Design Portfolio via Conditional Variational Autoencoders

TL;DR

The paper reframes inverse design fromSeeking a single optimal solution to generating a diverse portfolio of high-performing designs using a Conditional Variational Autoencoder (CVAE) conditioned on target performance. It demonstrates on the NASA airfoil self-noise task that the CVAE can produce 241 valid designs (94.1% validity) and that 77.2% of these designs outperform the SBO baseline in surrogate-predicted performance, with a top result of 74.83 dB. The approach learns a global design manifold, enabling rapid, parallel synthesis of diverse candidates and facilitating multi-criteria decision-making in engineering design. While validated with a surrogate, the method shows promise for accelerated innovation and richer design exploration, with future work focusing on high-fidelity validation and scalability via active learning.

Abstract

Inverse design, which seeks to find optimal parameters for a target output, is a central challenge in engineering. Surrogate-based optimization (SBO) has become a standard approach, yet it is fundamentally structured to converge to a single-point solution, thereby limiting design space exploration and ignoring potentially valuable alternative topologies. This paper presents a paradigm shift from single-point optimization to generative inverse design. We introduce a framework based on a Conditional Variational Autoencoder (CVAE) that learns a probabilistic mapping between a system's design parameters and its performance, enabling the generation of a diverse portfolio of high-performing candidates conditioned on a specific performance objective. We apply this methodology to the complex, non-linear problem of minimizing airfoil self-noise, using a high-performing SBO method from a prior benchmark study as a rigorous baseline. The CVAE framework successfully generated 256 novel designs with a 94.1\% validity rate. A subsequent surrogate-based evaluation revealed that 77.2\% of these valid designs achieved superior performance compared to the single optimal design found by the SBO baseline. This work demonstrates that the generative approach not only discovers higher-quality solutions but also provides a rich portfolio of diverse candidates, fundamentally enhancing the engineering design process by enabling multi-criteria decision-making.

Paper Structure

This paper contains 20 sections, 6 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Problem Formulation
  4. Conditional Variational Autoencoders (CVAEs)
  5. Experimental Methodology
  6. Benchmark Task: Airfoil Self-Noise
  7. Performance Baseline: SBO
  8. CVAE Implementation and Generative Campaign
  9. Evaluation Metrics and Procedure
  10. Validity
  11. Diversity
  12. Performance
  13. Results and Analysis
  14. Portfolio Generation and Characteristics
  15. Quantitative Performance Analysis
  16. ...and 5 more sections

Figures (1)

  • Figure 1: Performance distribution of the 241 valid airfoil designs generated by the CVAE, as evaluated by a trained MLP surrogate model. The vertical dashed red line at 108.81 dB indicates the surrogate-predicted performance of the single best design found by the top-performing SBO method from our previous benchmark hakimi2025benchmark. A substantial majority of the generated designs (186 of 241, or 77.2%) fall to the left of this baseline, demonstrating superior (lower noise) performance. The generative approach not only finds better solutions but also provides a diverse portfolio of high-quality alternatives.