Compositional Generative Inverse Design

TL;DR

CinDM addresses the challenge of inverse design by replacing surrogate forward models with a diffusion-based energy function, $E_\theta$, and enables compositional design through test-time combination of sub-energies. The method jointly optimizes the design trajectory and boundary via Langevin dynamics on $E_\theta$, with a diffusion-trained denoiser $\epsilon_\theta$ that approximates $\nabla_z E_\theta(z)$ and incorporates the design objective $\mathcal{J}$. It demonstrates compositional generalization across longer time horizons, more interacting bodies, and multi-airfoil boundaries, achieving superior MAE and competitive design objectives compared with strong baselines, and even discovering formation flying to reduce drag. The approach broadens the accessible design space for complex systems and has potential impact across materials, drug, and aerospace design, while requiring attention to computational cost and integration of physical priors for real-world deployment.

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.

Figures (18)

• 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.
• Figure 2: Example trajectories for N-body dataset with compositional inverse design in time (a) and bodies (b). The circles indicate CinDM-designed trajectory for the balls, drawn with every 2 steps and darker color indicating later states. The central star indicates the design target that the end state should be as close to as possible. "+" indicates ground-truth trajectory simulated by the solver.
• Figure 3: Discovered formation flying. In the 2-airfoil case, our model's designed boundary forms a "leader" and "follower" formation (a), reducing the drag by 53.6% and increases the lift-to-drag ratio by 66.1% compared to each airfoil flying separately (b)(c). Colors represent fluid vorticity.
• Figure 4: Diffusion model architecture of 2D inverse design.
• Figure 5: Example of Lily-Pad simulation.