Digital Twins (DTs) are high-fidelity virtual models that behave-like, look-like and connect-to a physical system. In this work, the physical systems are operations and processes from energy-intensive industrial plants and their local communities. The creation of DTs demands expertise not just in engineering, but also in computer science, data science, and artificial intelligence. Here, we introduce the Adaptive Digital Twins (ADT) concept, anchored in five attributes inspired by the self-adaptive systems field from software engineering. These attributes are self-learning, self-optimizing, self-evolving, self-monitoring, and self-protection. This new approach merges cutting-edge computing with pragmatic engineering needs. ADTs can enhance decision-making in both the design phase and real-time operation of industrial facilities and allow for versatile 'what-if' scenario simulations. Seven applications within the energy-intensive industries are described where ADTs could be transformative.