Title: Deep Generative Prior for First Order Inverse Optimization
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Inverse Design; Generative AI Applications;AI for Inverse Optimization

Abstract: Inverse design aims to recover system parameters from observed responses, a central challenge in domains such as semiconductor manufacturing, structural engineering, materials science, and fluid dynamics. The absence of explicit mathematical formulations in many systems complicates this task and prevents the use of standard first-order optimization methods.  
Existing approaches, such as generative models and Bayesian optimization, mitigate these challenges but face notable limitations: generative models often require high-fidelity paired data, while Bayesian optimization depends heavily on surrogate models, leading to scalability issues, sensitivity to priors, and vulnerability to noise.  

We introduce \textbf{Deep Generative Prior (DGP)}, a new framework that enables first-order, gradient-based inverse optimization with surrogate machine learning models. Formally, DGP constrains the optimization of design parameters through a pretrained prior $G(q)$, such that gradients are propagated via the surrogate forward model $F$, i.e.,
$\nabla_q \mathcal{L}(F(G(q)), u)$,
which enforces optimization along the data manifold induced by $G$. By leveraging pretrained Neural Operators as auxiliary priors, DGP enables stable and effective gradient flow through complex surrogate models.  

We validate DGP on diverse and challenging inverse design tasks, including {2D Darcy flow} (\textbf{standard}), {2D Navier--Stokes fluid dynamics} (\textbf{ill-posed}), and {semiconductor lithography inverse problems} (\textbf{ill-posed} and \textbf{out-of-distribution solutions}). 
Across these domains, DGP consistently achieves higher solution quality and efficiency compared to existing methods.

TL;DR: We propose a data-driven methodology for first-order inverse design optimization by learning a forward surrogate operator and a generative prior model to ensure optimization along true data manifold.