In this talk, a computational method for the training of digital twins is presented which allows for the generation of virtual microstructures of all-solid-state-battery (ASSB) cathodes by stochastic simulation. To ensure that digital twins are realistic, they are calibrated by means of 3D microscopy image data, which stem from focused ion beam-scanning electron microscopy (FIB-SEM). The ASSB cathode consists of single crystal LiNi_0.83Co_0.11Mn_0.06O₂ active material and thiophosphate-based glassy Li₃PS₄-0.5LiI solid electrolyte, treated with various milling media which results in different solid electrolyte particle size distributions and different electrochemical performance. After calibration of the digital twins to FIB-SEM data, virtually generated microstructures resemble real ones [1-3].

Additionally, by means of systematic variation of a digital twin’s parameters, we can generate a large database of different structural scenarios (like various volume fractions of solid electrolyte, active material or pores). These virtual microstructures can then be used as realistic geometry input for numerical simulations of electrochemical properties [4,5]. In this way, combining the results of stochastic and numerical simulations, we are able to investigate the influence of morphological descriptors (like active material size and shape, particle porosity caused by cracks, electrode porosity, average shortest path lengths) of the microstructure onto functional properties like electrochemical performance. In other words, a digital twin enables the investigation of quantitative structure-property relationships [1] based on computer experiments, which in turn can reduce costs in both time and resources.

Recently, purely data-driven digital twins have emerged, namely, generative adversarial networks (GANs), which are flexible computational tools for the generation of rather complex microstructures [6]. However, after training (calibration) it is difficult to systematically vary the GAN’s parameters for the generation of microstructures with different morphologies, which is an important step for the creation of a database that is sufficiently large for deriving structure-property relationships. An alternative to GANs are interpretable models from stochastic geometry [7] like excursion sets of Gaussian random fields (GRFs) which can be parameterized easily, thus, enabling a systematic variation of parameters for the investigation of various structural scenarios. But, such “simple” GRF-based models from stochastic geometry do not suffice as digital twins of the image data considered in this talk, since ASSB cathodes exhibit a rather complex microstructure.

Therefore, we combine both approaches, namely GANs and more “advanced” models from stochastic geometry, i.e., excursion sets of more general random fields. These models are (i) flexible enough to suffice as digital twins of ASSB cathode microstructures and (ii) parametric for enabling systematic variation of parameters in order to investigate various structural scenarios. As the calibration of the “advanced” models’ parameters to image data can be quite challenging using conventional methods of spatial stochastic modeling, we leverage the generative adversarial framework of GANs for the purpose of model calibration (i.e., the model tries to generate virtual microstructures that “fool” the so-called discriminator network). Thus, the “advanced model” can be used to generate (i) virtual, but realistic ASSB cathode microstructures as well as (ii) a broad spectrum of virtual materials with different morphologies—an essential prerequisite for deriving structure-property relationships.