RECIPE (REliable power and time-ConstraInts-aware Predictive management of heterogeneous Exascale systems) is a recently started project funded within the H2020 FETHPC programme, which is expressly targeted at exploring new High-Performance Computing (HPC) technologies. RECIPE aims at introducing a hierarchical runtime resource management infrastructure to optimize energy efficiency and minimize the occurrence of thermal hotspots, while enforcing the time constraints imposed by the applications and ensuring reliability for both time-critical and throughput-oriented computation that run on deeply heterogeneous accelerator-based systems. This paper presents a detailed overview of RECIPE, identifying the fundamental challenges as well as the key innovations addressed by the project. In particular, the need for predictive reliability approaches to maximizing hardware lifetime and guarantee application performance is identified as the key concern for RECIPE. We address it through hierarchical resource management of the heterogeneous architectural components of the system, driven by estimates of the application latency and hardware reliability obtained respectively through timing analysis and modeling thermal properties and mean-time-to-failure of subsystems. We show the impact of prediction accuracy on the overheads imposed by the checkpointing policy, as well as a possible application to a weather forecasting use case. (c) 2020 Elsevier B.V. All rights reserved.