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 outperforms state-of-the-art neural inverse design method by an average of 41.5% in prediction MAE and 14.3% in design objective for the 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.

翻译：逆向设计旨在通过优化输入变量以达成底层目标函数，是机械工程至航空航天工程等领域的关键问题。传统上，逆向设计被形式化为优化问题，近期工作利用经学习动力学模型进行优化。然而，模型在优化过程中易陷入对抗模式，阻碍有效采样。我们证明，通过优化扩散模型所捕获的已学习能量函数，可避免此类对抗样本并显著提升设计性能。进一步研究表明，此类设计系统具有组合性，能合并多个代表目标系统子组件的扩散模型，从而设计出包含指定组件的系统。在N体交互任务与具有挑战性的二维多翼型设计任务中，我们展示了通过在测试时组合已学扩散模型，该方法可设计出比训练数据更复杂的初始状态与边界形状。在N体数据集上，本方法相比最先进的神经逆向设计方法，预测MAE平均降低41.5%，设计目标提升14.3%；在多翼型设计任务中，本方法发现编队飞行以最小化阻力。项目网站与代码见https://github.com/AI4Science-WestlakeU/cindm。