The 3D microstructure of porous media, such as electrodes in lithium-ion batteries or fiber-based materials, significantly impacts the resulting macroscopic properties, including effective diffusivity or permeability. Consequently, quantitative structure-property relationships, which link structural descriptors of 3D microstructures such as porosity or geodesic tortuosity to effective transport properties, are crucial for further optimizing the performance of porous media. To overcome the limitations of 3D imaging, parametric stochastic 3D microstructure modeling is a powerful tool to generate many virtual but realistic structures at the cost of computer simulations. The present paper uses 90,000 virtually generated 3D microstructures of porous media derived from literature by systematically varying parameters of stochastic 3D microstructure models. Previously, this data set has been used to establish quantitative microstructure-property relationships. The present paper extends these findings by applying a hybrid AI framework to this data set. More precisely, symbolic regression, powered by deep neural networks, genetic algorithms, and graph attention networks, is used to derive precise and robust analytical equations. These equations model the relationships between structural descriptors and effective transport properties without requiring manual specification of the underlying functional relationship. By integrating AI with traditional computational methods, the hybrid AI framework not only generates predictive equations but also enhances conventional modeling approaches by capturing relationships influenced by specific microstructural features traditionally underrepresented. Thus, this paper significantly advances the predictive modeling capabilities in materials science, offering vital insights for designing and optimizing new materials with tailored transport properties.

This paper presents a computational method for generating virtual 3D morphologies of functional materials using low-parametric stochastic geometry models, i.e., digital twins, calibrated with 2D microscopy images. These digital twins allow systematic parameter variations to simulate various morphologies, that can be deployed for virtual materials testing by means of spatially resolved numerical simulations of macroscopic properties. Generative adversarial networks (GANs) have gained popularity for calibrating models to generate realistic 3D morphologies. However, GANs often comprise of numerous uninterpretable parameters make systematic variation of morphologies for virtual materials testing challenging. In contrast, low-parametric stochastic geometry models (e.g., based on Gaussian random fields) enable targeted variation but may struggle to mimic complex morphologies. Combining GANs with advanced stochastic geometry models (e.g., excursion sets of more general random fields) addresses these limitations, allowing model calibration solely from 2D image data. This approach is demonstrated by generating a digital twin of all-solid-state battery (ASSB) cathodes. Since the digital twins are parametric, they support systematic exploration of structural scenarios and their macroscopic properties. The proposed method facilitates simulation studies for optimizing 3D morphologies, benefiting not only ASSB cathodes but also other materials with similar structures.

Understanding structure-property relationships of Li-ion battery cathodes is crucial for optimizing rate-performance and cycle-life resilience. However, correlating the morphology of cathode particles, such as in NMC811, and their inner grain architecture with electrode performance is challenging, particularly, due to the significant length-scale difference between grain and particle sizes. Experimentally, it is currently not feasible to image such a high number of particles with full granular detail to achieve representivity. A second challenge is that sufficiently high-resolution 3D imaging techniques remain expensive and are sparsely available at research institutions. To address these challenges, a stereological generative adversarial network (GAN)-based model fitting approach is presented that can generate representative 3D information from 2D data, enabling characterization of materials in 3D using cost-effective 2D data. Once calibrated, this multi-scale model is able to rapidly generate virtual cathode particles that are statistically similar to experimental data, and thus is suitable for virtual characterization and materials testing through numerical simulations. A large dataset of simulated particles with inner grain architecture has been made publicly available.

Influenced mixed moving average fields are a versatile modeling class for spatio-temporal data. However, their predictive distribution is not generally known. Under this modeling assumption, we define a novel spatio-temporal embedding and a theory-guided machine learning approach that employs a generalized Bayesian algorithm to make ensemble forecasts. We employ Lipschitz predictors and determine fixed-time and any-time PAC Bayesian bounds in the batch learning setting. Performing causal forecast is a highlight of our methodology as its potential application to data with spatial and temporal short and long-range dependence. We then test the performance of our learning methodology by using linear predictors and data sets simulated from a spatio-temporal Ornstein-Uhlenbeck process.

Wide-angle light scattering (WALS) offers the possibility of a highly temporally and spatially resolved measurement of droplets in spray-based methods for nanoparticle synthesis. The size of these droplets is a critical variable affecting the final properties of synthesized materials such as hetero-aggregates. However, conventional methods for determining droplet sizes from WALS image data are labor-intensive and may introduce biases, particularly when applied to complex systems like spray flame synthesis (SFS). To address these challenges, we introduce a fully automatic machine learning-based approach that employs convolutional neural networks (CNNs) in order to streamline the droplet sizing process. This CNN-based methodology offers further advantages: it requires few manual labels and can utilize transfer learning, making it a promising alternative to conventional methods, specifically with respect to efficiency. To evaluate the performance of our machine learning models, we consider WALS data from an ethanol spray flame process at various heights above the burner surface (HABs), where the models are trained and cross-validated on a large dataset comprising nearly 35000 WALS images.