Over the last decade, networks have largely increased in size and complexity due to the wide adoption of mobile devices and wireless access. In parallel, the prospection of new verticals in the context of 5G (Internet of Things, Vehicles, and Drones) has necessitated the support of multiple service level agreements with heterogeneous guarantees (latency, reliability, rate, terminal number). In an attempt to streamline the network management, both research community and industrial stakeholders have been progressively adopting network virtualization and softwarization technologies. However, this wave of virtualization has exponentially increased the degrees of freedom in the network management process. In addition, the combination of terrestrial and non-terrestrial links (e.g. satellite) in transport networks has introduced new dimensions of network heterogeneity and dynamicity. In this context, the project ASWELL (AutonomouS NetWork Slicing for IntEgrated SateLlite-TerrestriaL Transport Networks) aims at devising efficient and scalable machine-learning or deep-learning (ML/DL) solutions for autonomous network slicing in integrated satellite-terrestrial transport networks. We will apply ML/DL to provide a viable alternative to conventional human-engineered heuristic or optimization-based algorithms, which cannot rise to the occasion of heterogeneous dynamic large-scale software-defined networks. In this direction, the ML/DL-driven paradigm will be employed a) to accelerate the flow management algorithms for large-dimensional graphs, b) to autonomously manage the on-line network flows for graphs with temporal dynamics, c) to consider joint flow and node resource slicing for networks which include processing/storage functionalities. Addressing the aforementioned challenges will contributed towards self-managing, self-adapting, and self-optimizing slicing with the aim of supporting the operational monitoring and configuration of integrated transport networks.