manufacturing system engineers

Abstract: Many complex systems are observed only through temporally unpaired distribution snapshots, making trajectory-based dynamical learning difficult without additional assumptions. We therefore formulate the problem directly in distribution space, treating the distribution itself as the dynamical state. The challenge is that distribution space is infinite-dimensional, making compact and approximately closed representations difficult to learn from finite snapshots. We introduce DisKO, which extends deep Koopman learning to distribution dynamics by jointly learning predictive distributional observables, a finite-dimensional Koopman representation, and a generative map back to the full distribution. Across seven diverse benchmarks, DisKO achieves state-of-the-art extrapolation performance, with substantially slower error accumulation on long-horizon prediction tasks. DisKO further recovers leading Koopman eigenvalues and eigenfunctions on systems with analytic spectra, revealing meaningful dynamical structure in the learned representation.

Abstract: The Asset Administration Shell (AAS) is increasingly recognized as a fundamental model for the realization of and data exchange between digital twins in manufacturing. An AAS defines a hierarchical data structure to represent any type of asset throughout its entire lifecycle. In the context of AAS-based systems, comparing different AAS instances constitutes a practical challenge, as neither a widely accepted methodological framework nor a maturity model are available to systematically support such analyses. To address this gap, we propose a novel concept of AAS maturity that characterizes the extent to which established digital twin criteria are met and thus enabling comparability of AAS instances. The concepts are derived from the literature and applied through exemplification. These emerging results enable practitioners and researchers to systematically compare AAS instances and support the identification and assessment of further development steps in the digital twin engineering process.