This study presents a machine learning framework for the inverse reconstruction of open-cell porous metamaterials, targeting specific hydraulic properties such as porosity and intrinsic permeability. Utilizing a combination of synthetic 3D porous microstructures and CT-scan-based representative volume elements of porous open-foam specimens, the framework leverages a property-variational Autoencoder (pVAE) to establish robust mappings between 3D microstructures and their corresponding hydraulic properties. The pVAE integrates a variational Autoencoder (VAE) with a regression network, providing a compact latent space that enables efficient interpolation and optimization. Moreover, a convolutional neural network (CNN) is trained to predict the hydraulic properties, thereby generating a computationally efficient dataset to train the pVAE, circumventing the high cost of direct numerical simulations. In particular, the VAE comprises a convolutional encoder, which compresses input structures into a low-dimensional latent space modeled as a Gaussian distribution, and a decoder, which reconstructs 3D geometries. The training process minimizes a composite loss function that includes a reconstruction loss, ensuring fidelity to the input data, and a Kullback-Leibler divergence term, which regularizes the latent space for smoothness and semantic continuity. A regression loss term also aligns the latent space with target hydraulic properties, optimizing the model's ability to predict and generate structures with specific attributes. By leveraging the continuous and interpretable latent space for optimization and sampling, the pVAE generates structures tailored to desired hydraulic properties. This approach enables scalable, data-driven design of metamaterials for multiscale engineering systems, advancing structure-property mapping methodologies. REFERENCES [1] Heider Y., Aldakheel F., Ehlers W. A multiscale CNN-based intrinsic permeability prediction in deformable porous media. Applied Sciences 15(5), 2589, 2025. [2] Zheng L., Karapiperis K., Kumar S., Kochmann DM. Unifying the design space and optimizing linear and nonlinear truss metamaterials by generative modeling. Nat Commun. 14, 7563, 2023.