Compositional Generative Inverse Design

Abstract: Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem that arises across fields such as mechanical engineering to aerospace engineering. Inverse design is typically formulated as an optimization problem, with recent works leveraging optimization across learned dynamics models. However, as models are optimized they tend to fall into adversarial modes, preventing effective sampling. We illustrate that by instead optimizing over the learned energy function captured by the diffusion model, we can avoid such adversarial examples and significantly improve design performance. We further illustrate how such a design system is compositional, enabling us to combine multiple different diffusion models representing subcomponents of our desired system to design systems with every specified component. In an N-body interaction task and a challenging 2D multi-airfoil design task, we demonstrate that by composing the learned diffusion model at test time, our method allows us to design initial states and boundary shapes that are more complex than those in the training data. Our method generalizes to more objects for N-body dataset and discovers formation flying to minimize drag in the multi-airfoil design task. Project website and code can be found at https://github.com/AI4Science-WestlakeU/cindm.

• The paper proposes a novel framework using diffusion models to reframe inverse design as an energy optimization problem.
• It composes multiple subcomponent models to effectively capture complex design parameters and avoid adversarial pitfalls.
• Experimental results in N-body and 2D airfoil tasks demonstrate superior design performance and enhanced aerodynamic efficiency.

Summary of "Compositional Generative Inverse Design" (2401.13171)

Introduction

The paper "Compositional Generative Inverse Design" addresses inverse design problems prevalent in various engineering domains, including mechanical, materials, and aerospace engineering. These problems involve designing input variables to optimize an objective function and are typically formulated as high-dimensional optimization tasks. Recent approaches utilize neural surrogate models for forward dynamics approximation and simulation trajectory optimization. However, such methods often result in adversarial modes leading to poor performance. The authors propose an alternative approach leveraging diffusion models to optimize learned energy functions, thereby avoiding adversarial examples and improving design performance. The compositional nature of the approach allows combining multiple diffusion models to effectively design complex systems at test time.

Methodology

The innovative method introduced in this paper reframes inverse design as an energy optimization problem, where constraints are implicitly captured through a diffusion model's generative energy function. The process optimizes design parameters to minimize this energy, ensuring that solutions remain in distribution without adverse deviations.

Compositional Diffusion

The core novelty is the compositional aspect, where multiple subcomponent models are used together. Each diffusion model captures a subset of the design parameters. By composing these learned models during inference, the method can design initial states and boundary shapes that are significantly more complex than those observed in training data. This compositional capability is demonstrated across scenarios such as N-body interaction tasks and multi-airfoil aerodynamic design.

Figure 1: CinDM schematic. By composing generative models specified over subsets of inputs, we present an approach which design materials significantly more complex than those seen at training.

Practical Implications

The use of diffusion models enables the model to generalize beyond the training dataset, discovering novel configurations such as formation flying in multi-airfoil tasks to minimize drag. This represents a powerful extension over traditional methods, providing both increased adaptability and exploration capabilities.

Experimental Results

The experimental setup includes benchmarks in two key areas: N-body interaction tasks and 2D airfoil design. These tests highlight the compositional generalization capabilities of the method.

N-body Interaction Tasks

In these experiments, the method designed configurations involving more objects and extended time steps compared to what was seen during training. The results show superior performance both in terms of the design objective and prediction accuracy, evaluated using ground-truth solvers to ensure fairness.

2D Multi-airfoil Design

The paper showcases the ability to generate complex airfoil configurations that achieve better lift-to-drag ratios compared to existing baselines. This includes the discovery of an optimized formation flying pattern for multiple airfoils, showcasing significant aerodynamic efficiency improvements.

Figure 2: Compositional design results of our method in 2D airfoil generation. Each row represents an example. We show the heatmap of velocity in horizontal and vertical direction and pressure in the initial time step, inside which we plot the generated airfoil boundaries.

Related Work

The authors review recent deep learning advancements in inverse design, contrasting their diffusion-based method against surrogate model approaches which can fall into adversarial modes. The paper also discusses compositional models, highlighting related work in 2D synthesis and multimodal perception, establishing the relevance and extension of their approach within this broader context.

Conclusion

"Compositional Generative Inverse Design" offers a novel energy-based framework for tackling complex inverse design problems through the use of diffusion models. By combining compositional capabilities and avoiding adversarial modes, the method shows promise in outperforming traditional surrogate approaches across various applications. Future work may explore extensions to other domains such as material and molecule design, broadening the scope of the method's applicability.

Figure 3: Design performance (lift-to-drag) of different B in 2D airfoil inverse design.

This methodology could change how complex engineering problems are approached, driving forward the field of generative design through deep learning frameworks.