A physics-guided generative AI framework for property-targeted porous media design, combining a property-aware variational autoencoder, a conditional latent diffusion model, and an independently trained differentiable structure-to-property surrogate is proposed.
Abstract
Inverse design of three-dimensional porous media is central to applications in filtration, catalysis, energy storage, fuel cells, thermal management, and biomedical scaffolds, but remains challenging because many distinct pore geometries can share similar porosity or permeability while small structural changes can strongly affect transport behaviour. This paper proposes a physics-guided generative AI framework for property-targeted porous media design, combining a property-aware variational autoencoder, a conditional latent diffusion model, and an independently trained differentiable structure-to-property surrogate. The framework learns a compact, physically informative latent design space, generates porous structures conditioned on target porosity and directional permeability, and refines generated samples using property-level feedback during denoising and decoding. Experiments on procedurally generated structures and real micro-CT porous-media datasets show improved target-property matching, directional permeability control, and property correlation compared with representative property-aware variational-autoencoder and latent-diffusion baselines. The results demonstrate a scalable route towards controllable inverse design of complex porous geometries and establish a foundation for simulation-informed generative AI tools in engineering and advanced materials discovery.
Diffusion-based generative models with property guidance have emerged as a promising paradigm for inverse materials design by enabling the generation of crystalline materials with user-specified target properties. However, despite recent advances, the effectiveness of property guidance, its influence on crystallographic symmetry, and the physical viability of generated materials remain poorly understood. To address these questions, we develop a property-guided framework based on the lightweight diffusion model DiffCrysGen using parameter-efficient adapter fine-tuning and classifier-free guidance (CFG). The resulting framework enables efficient multi-property crystal generation while preserving the knowledge learned during unconditional pre-training. Using formation energy together with saturation magnetization and Vickers hardness as representative inverse-design tasks, we systematically investigate the influence of CFG across a broad range of guidance strengths. Increasing the guidance scale progressively steers the generated property distributions toward the prescribed targets while reducing the fraction of lowest-symmetry ($P1$) structures and increasing the proportion of higher-symmetry structures. To evaluate physical viability, generated structures are geometrically prescreened and subsequently validated using a machine-learning interatomic potential (MLIP)-based workflow comprising structural relaxation and thermodynamic, dynamical, and property-specific analyses. The framework identifies thermodynamically and dynamically stable magnetic and mechanically hard materials with overall success rates of 12.3\% and 3.9\%, respectively. These results establish property-guided DiffCrysGen as an efficient framework for inverse materials design while providing new insights into the role of classifier-free guidance in crystal generation.
The inverse design of resilient infrastructure materials is hindered by the combinatorial complexity inherent in optimizing stochastic, heterogeneous microstructures. Traditional Euclidean deep learning architectures, such as Convolutional Neural Networks (CNNs), fail to efficiently encode the sparse, non-local topology of disordered porous media, resulting in prohibitive computational redundancy. This work articulates a comprehensive graph-theoretic framework for the predictive modeling and optimization of self-healing cementitious composites. We propose a robust methodology for discretizing volumetric tomography into permutation-invariant heterogeneous graphs, where nodes encode discrete physical entities (aggregates, pores, and microcapsules) and edges represent mechanical and hydraulic connectivity. To capture global fracture dynamics and local transport phenomena, we employ specialized architectures, specifically Pore-GNNs and Long-Short-Edge MeshGraphNets, which function as high-speed surrogate models for multiphysics simulations. Computational validation against high-fidelity numerical solvers confirms the system’s efficacy: the proposed architecture achieves approximately 1.1×105-fold acceleration (inference plus preprocessing) in permeability prediction relative to Lattice Boltzmann Method simulations, while maintaining a prediction accuracy of R2 > 0.94 (mean±std over five random splits); the inference-only speedup, which excludes one-time graph-construction preprocessing, is approximately 1.8×106-fold. We note that the end-to-end figure (1.1×105) supersedes the inference-only figure quoted in the original submission metadata. Furthermore, the framework autonomously navigated the high-dimensional design space to isolate a non-intuitive geometric optimum within just 30 high-fidelity oracle evaluations: anisotropic microcapsules (ρc≈2.5) oriented at 45∘ relative to the shear plane. This configuration is predicted to resolve the conflicting physical constraints of the system, maximizing the probability of crack interception for effective healing. These results demonstrate that physics-informed graph learning can effectively decouple prediction accuracy from computational intensity, offering a scalable paradigm for the discovery of advanced functional materials.
Lei Qiu, Shuxin Zhang, Yongbin Yang et al.· PLoS ONE· 0 citations
Predicting relative permeability (kr) curves directly from three-dimensional (3D) digital rock images remains a significant challenge in digital rock physics (DRP). Existing methods either rely on computationally expensive pore network modeling (PNM) or direct numerical simulation (DNS) during inference, or use purely data-driven networks that lack physical consistency. This study introduces a permeability-field physics-informed neural network (PF-PINN), a coupled deep learning surrogate that maps a 3D binary rock image, through its local thickness transform, to drainage kr curves for both wetting and non-wetting phases. This approach embeds two-phase Darcy flow physics into the training loss, ensuring physically admissible predictions without requiring a simulation during inference. The model architecture integrates a 3D U-Net encoder to extract a spatially varying permeability field and a global morphological feature vector, a pressure multilayer perceptron (MLP) that satisfies Darcy boundary conditions, and a relative permeability MLP conditioned on pore geometry. Ground truth data were generated using a PNM workflow applied to 350 sub-volumes from seven rock types, with voxel resolutions ranging from 4.94 to 17.17 μm/voxel. Two evaluation protocols were employed, namely a stratified random split with a 20% holdout per rock and 70 test samples, and a rock-type holdout in which Bentheimer and Monte Gambier were fully withheld, resulting in 100 test samples. Under the stratified protocol, the PF-PINN achieved Rmean2 = 0.952 (Rw2 = 0.963, Rnw2 = 0.941). Under the rock-type holdout, the model achieved Rmean2 = 0.927 on unseen geological classes, demonstrating physics-informed cross-lithology generalization. The wetting-phase R2 difference between the two protocols was only 0.013, suggesting that embedding Darcy mass conservation enables an effective transfer of flow behavior across the geological families.
Pouya Abasmirzaie, S. Kamrava· The Physics of Fluids· 0 citations
Designing multilayered materials for controlled deformation is heavily bottlenecked by the immense computational costs and time of traditional, industrial-grade finite element methods (FEM). This excessive expense severely limits design space exploration and gradient-based optimization. To streamline the workflow, we propose a framework for parameterized physics-informed neural networks (P2INNs). The framework encompasses three core components: I. a FEM baseline with a Hex8 element and trilinear basis functions, II. a P2INN displacement field model across variable material stiffness and layer thicknesses, and III. FEM-referenced evaluation. The PINN enforces static linear elasticity via Navier-Cauchy residuals with training strategies that prioritize physics, including layerwise PDE decomposition, interface continuity penalty, and compliance aware scaling. For one-layer, pure physics-driven configurations, the PINN achieves a mean volume MAE of 1.56% and worst-case volume MAE of 2.87% against the FEM benchmark. For three-layer configurations with controlled supervised training, the PINN achieves a mean volume MAE of 2.53% and worst-case volume MAE of 4.66%, meeting the near-5% worst-case volume-MAE target for preliminary design-space exploration. The trained P2INN model remains a lightweight model with a simple forward pass for future calculations, creating an alternative to traditional FEM. By drastically reducing the need for expensive FEM evaluations, this approach could accelerate the inverse design and optimization of advanced layered architectures for protective structures in various load-heavy or potentially collision-heavy fields.
Accurate permeability tensor prediction from pore-scale microstructure is essential for subsurface flow modeling, yet direct numerical simulation requires hours per sample, fundamentally constraining large-scale uncertainty quantification. The proposed physics-informed deep learning framework resolves this computational bottleneck through three integrated contributions. First, a MaxViT hybrid CNN-Transformer leverages multi-axis attention to simultaneously resolve grain-scale geometry via block-local operations and representative elementary volume connectivity through grid-global operations, supplying the spatial hierarchy required for anisotropic prediction. Second, a differentiable physics-aware loss function penalizes violations of Onsager reciprocity and thermodynamic positive-definiteness, achieving a mean symmetry error of εsym=3.95×10-7 and 100 % constraint satisfaction without post-hoc correction. Third, a D4-equivariant augmentation strategy introduces a consistent second-order tensor label transformation that eliminates the label-image mismatch typical of naive augmentation. Evaluated on 20,000 synthetic 2D binary sandstone microstructures spanning three orders of magnitude in permeability, the framework achieves a variance-weighted R2=0.9960 ( [Formula: see text] , [Formula: see text] ) on a 4,000-sample test set, a significant reduction in unexplained variance over supervised baselines, with every reported metric improving monotonically across phases. Inference requires 120 ms per sample, a speedup of three orders of magnitude over lattice-Boltzmann references, while integrated Monte Carlo Dropout provides per-sample confidence estimates. Three-dimensional micro-CT extension and real-core validation are identified as the critical next steps toward operational deployment. Ultimately, these results establish transferable principles for scientific machine learning: visual pretraining generalizes across domain boundaries, physical constraints function best as differentiable architectural components, and progressive training guided by failure-mode analysis isolates precise structural performance drivers.
The inverse design of cellular metamaterials—finding unit-cell geometries that realize prescribed effective properties—is intrinsically one-to-many, yet conditional generators often collapse to narrow outputs and graded assembly can introduce interface discontinuities. We present Style-IH-GAN, a style-modulated generative adversarial network for triply periodic minimal surface (TPMS)-based cellular materials. A mapping network converts latent noise into style vectors that modulate a property-conditioned generator, while mode-seeking and property-consistency losses encourage geometric alternatives under fixed targets. For graded synthesis, the model emits a spatial field of TPMS descriptors in one batched forward pass, and trilinear interpolation supports continuous inter-cell reconstruction. The predictor is used only as a differentiable training signal and controlled baseline metric; unit-cell fidelity is evaluated by numerical homogenization over 750 generated samples across 15 targets. Compared with a vanilla conditional generative adversarial network, Style-IH-GAN achieves 2.2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document} higher shape-parameter diversity and 19% lower surrogate Young’s modulus error, while a 300-cell graded field is produced in sub-millisecond time. Accuracy remains strongest inside the supported training manifold and requires numerical-homogenization screening; boundary and extrapolated-density targets are reported as limitations. A graded cantilever provides a qualitative macroscopic continuity check.
Shaoliang Yang, Jun Wang· Engineering computations· 0 citations
