用预训练神经算子构建物理先验，实现高效逆向优化。
Deep Generative Prior for First Order Inverse Optimization
- 通过预训练神经算子建立物理先验，支持梯度驱动的逆向优化。
- 在无明确数学表达式时仍能稳定求解，避免传统方法的次优结果。
- 适用于半导体、材料等缺乏显式模型的领域，尤其适合数据稀疏场景。
逆向设计优化旨在从观测解中推断系统参数，在半导体制造、结构工程、材料科学和流体动力学等领域具有重要意义。然而，许多系统缺乏显式数学表达式，导致一阶优化不可行。主流方法如生成式AI计算成本高，而基于代理模型的贝叶斯优化存在可扩展性差、对先验敏感及噪声敏感等问题，常导致次优解。本文提出深度物理先验（DPP），一种利用预训练辅助神经算子的新型方法，使基于梯度的一阶逆向优化成为可能。DPP通过施加先验分布约束，确保解的鲁棒性和合理性，尤其在先验数据与观测分布未知时表现优异。
原文摘要 · Abstract (English)
Inverse design optimization aims to infer system parameters from observed solutions, posing critical challenges across domains such as semiconductor manufacturing, structural engineering, materials science, and fluid dynamics. The lack of explicit mathematical representations in many systems complicates this process and makes the first order optimization impossible. Mainstream approaches, including generative AI and Bayesian optimization, address these challenges but have limitations. Generative AI is computationally expensive, while Bayesian optimization, relying on surrogate models, suffers from scalability, sensitivity to priors, and noise issues, often leading to suboptimal solutions. This paper introduces Deep Physics Prior (DPP), a novel method enabling first-order gradient-based inverse optimization with surrogate machine learning models. By leveraging pretrained auxiliary Neural Operators, DPP enforces prior distribution constraints to ensure robust and meaningful solutions. This approach is particularly effective when prior data and observation distributions are unknown.
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