Inverse problems and inverse design in multiphase media, i.e., recovering or engineering microstructures to achieve target macroscopic responses, require operating on discrete-valued material fields, rendering the problem non-differentiable and incompatible with gradient-based methods. Existing approaches either relax to continuous approximations, compromising physical fidelity, or employ separate heavyweight models for forward and inverse tasks. We propose GenPANIS, a unified generative framework that preserves exact discrete microstructures while enabling gradient-based inference through continuous latent embeddings. The model learns a joint distribution over microstructures and PDE solutions, supporting bidirectional inference (forward prediction and inverse recovery) within a single architecture. The generative formulation enables training with unlabeled data, physics residuals, and minimal labeled pairs. A physics-aware decoder incorporating a differentiable coarse-grained PDE solver preserves governing equation structure, enabling extrapolation to varying boundary conditions and microstructural statistics. A learnable normalizing flow prior captures complex posterior structure for inverse problems. Demonstrated on Darcy flow and Helmholtz equations, GenPANIS maintains accuracy on challenging extrapolative scenarios - including unseen boundary conditions, volume fractions, and microstructural morphologies, with sparse, noisy observations. It outperforms state-of-the-art methods while using 10 - 100 times fewer parameters and providing principled uncertainty quantification.

翻译：多相介质中的反问题与反设计（即恢复或设计微观结构以实现目标宏观响应）需要在离散值材料场上操作，这使得问题不可微分且与基于梯度的方法不兼容。现有方法要么松弛为连续近似而牺牲物理保真度，要么为正向和逆向任务分别采用独立的重型模型。我们提出GenPANIS，一个统一的生成框架，在通过连续潜嵌入实现基于梯度推理的同时，保持精确的离散微观结构。该模型学习微观结构与偏微分方程解的联合分布，支持在单一架构内进行双向推理（正向预测与逆向恢复）。生成式框架支持使用无标签数据、物理残差和极少量标记对进行训练。融入可微分粗粒度偏微分方程求解器的物理感知解码器保留了控制方程结构，使其能够外推至变化的边界条件和微观结构统计特性。可学习的标准化流先验捕获了反问题中复杂的后验结构。在达西流和亥姆霍兹方程上的实验表明，GenPANIS在具有挑战性的外推场景（包括未见过的边界条件、体积分数和微观结构形态，以及稀疏、含噪声的观测数据）中保持准确性。其性能优于现有最先进方法，同时使用参数减少10-100倍，并提供原则性的不确定性量化。